Pub Date : 2015-07-04DOI: 10.1080/00018732.2015.1109817
D. Leitner
We review a theory for coupled many-nonlinear oscillator systems that describes quantum ergodicity and energy flow in molecules. The theory exploits the isomorphism between quantum energy flow in Fock space, that is, vibrational state space, and single-particle quantum transport in disordered solid-state systems. The quantum ergodicity transition in molecules is thereby analogous to the Anderson transition in disordered solids. The theory reviewed here, local random matrix theory (LRMT), describes the nature of the quantum ergodicity transition, statistical properties of vibrational eigenstates, and quantum energy flow through the vibrational states of molecules. Predictions of LRMT have been observed in computational studies of coupled nonlinear oscillator systems, which are summarized here. We also review applications of LRMT to molecular spectroscopy and chemical reaction rate theory, including adoption of LRMT in theories that predict rates of conformational change of molecules taking place at energies corresponding to those below and above the quantum ergodicity transition. A number of specific examples are reviewed, including the application of LRMT to predict (1) dilution factors of IR spectra of organic molecules, (2) rates of conformational change in chemical and photochemical reactions, (3) conformational dynamics of biological molecules in molecular beams, (4) rates of hydrogen bond breaking and rearrangement in clusters of biological molecules and water, and (5) excited state proton transfer reactions in proteins.
{"title":"Quantum ergodicity and energy flow in molecules","authors":"D. Leitner","doi":"10.1080/00018732.2015.1109817","DOIUrl":"https://doi.org/10.1080/00018732.2015.1109817","url":null,"abstract":"We review a theory for coupled many-nonlinear oscillator systems that describes quantum ergodicity and energy flow in molecules. The theory exploits the isomorphism between quantum energy flow in Fock space, that is, vibrational state space, and single-particle quantum transport in disordered solid-state systems. The quantum ergodicity transition in molecules is thereby analogous to the Anderson transition in disordered solids. The theory reviewed here, local random matrix theory (LRMT), describes the nature of the quantum ergodicity transition, statistical properties of vibrational eigenstates, and quantum energy flow through the vibrational states of molecules. Predictions of LRMT have been observed in computational studies of coupled nonlinear oscillator systems, which are summarized here. We also review applications of LRMT to molecular spectroscopy and chemical reaction rate theory, including adoption of LRMT in theories that predict rates of conformational change of molecules taking place at energies corresponding to those below and above the quantum ergodicity transition. A number of specific examples are reviewed, including the application of LRMT to predict (1) dilution factors of IR spectra of organic molecules, (2) rates of conformational change in chemical and photochemical reactions, (3) conformational dynamics of biological molecules in molecular beams, (4) rates of hydrogen bond breaking and rearrangement in clusters of biological molecules and water, and (5) excited state proton transfer reactions in proteins.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"64 1","pages":"445 - 517"},"PeriodicalIF":0.0,"publicationDate":"2015-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018732.2015.1109817","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58773493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-05-04DOI: 10.1080/00018732.2015.1068524
H. Weng, Rui Yu, X. Hu, X. Dai, Z. Fang
Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically doped topological insulator (TI) completed a quantum Hall trio—quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). On the theoretical front, it was understood that the intrinsic AHE is related to Berry curvature and U(1) gauge field in momentum space. This understanding established connection between the QAHE and the topological properties of electronic structures characterized by the Chern number. With the time-reversal symmetry (TRS) broken by magnetization, a QAHE system carries dissipationless charge current at edges, similar to the QHE where an external magnetic field is necessary. The QAHE and corresponding Chern insulators are also closely related to other topological electronic states, such as TIs and topological semimetals, which have been extensively studied recently and have been known to exist in various compounds. First-principles electronic structure calculations play important roles not only for the understanding of fundamental physics in this field, but also towards the prediction and realization of realistic compounds. In this article, a theoretical review on the Berry phase mechanism and related topological electronic states in terms of various topological invariants will be given with focus on the QAHE and Chern insulators. We will introduce the Wilson loop method and the band inversion mechanism for the selection and design of topological materials, and discuss the predictive power of first-principles calculations. Finally, remaining issues, challenges and possible applications for future investigations in the field will be addressed.
{"title":"Quantum anomalous Hall effect and related topological electronic states","authors":"H. Weng, Rui Yu, X. Hu, X. Dai, Z. Fang","doi":"10.1080/00018732.2015.1068524","DOIUrl":"https://doi.org/10.1080/00018732.2015.1068524","url":null,"abstract":"Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically doped topological insulator (TI) completed a quantum Hall trio—quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). On the theoretical front, it was understood that the intrinsic AHE is related to Berry curvature and U(1) gauge field in momentum space. This understanding established connection between the QAHE and the topological properties of electronic structures characterized by the Chern number. With the time-reversal symmetry (TRS) broken by magnetization, a QAHE system carries dissipationless charge current at edges, similar to the QHE where an external magnetic field is necessary. The QAHE and corresponding Chern insulators are also closely related to other topological electronic states, such as TIs and topological semimetals, which have been extensively studied recently and have been known to exist in various compounds. First-principles electronic structure calculations play important roles not only for the understanding of fundamental physics in this field, but also towards the prediction and realization of realistic compounds. In this article, a theoretical review on the Berry phase mechanism and related topological electronic states in terms of various topological invariants will be given with focus on the QAHE and Chern insulators. We will introduce the Wilson loop method and the band inversion mechanism for the selection and design of topological materials, and discuss the predictive power of first-principles calculations. Finally, remaining issues, challenges and possible applications for future investigations in the field will be addressed.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"64 1","pages":"227 - 282"},"PeriodicalIF":0.0,"publicationDate":"2015-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018732.2015.1068524","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58773478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-05-04DOI: 10.1080/00018732.2015.1057979
V. Lubchenko
The random first-order transition theory of the structural glass transition is reviewed in a pedagogical fashion. The rigidity that emerges in crystals and glassy liquids is of the same fundamental origin. In both cases, it corresponds with a breaking of the translational symmetry; analogies with freezing transitions in spin systems can also be made. The common aspect of these seemingly distinct phenomena is a spontaneous emergence of the molecular field, a venerable and well-understood concept. In crucial distinction from periodic crystallisation, the free energy landscape of a glassy liquid is vastly degenerate, which gives rise to new length and time scales while rendering the emergence of rigidity gradual. We obviate the standard notion that to be mechanically stable a structure must be essentially unique; instead, we show that bulk degeneracy is perfectly allowed but should not exceed a certain value. The present microscopic description thus explains both crystallisation and the emergence of the landscape regime followed by vitrification in a unified, thermodynamics-rooted fashion. The article contains a self-contained exposition of the basics of the classical density functional theory and liquid theory, which are subsequently used to quantitatively estimate, without using adjustable parameters, the key attributes of glassy liquids, viz., the relaxation barriers, glass transition temperature, and cooperativity size. These results are then used to quantitatively discuss many diverse glassy phenomena, including the intrinsic connection between the excess liquid entropy and relaxation rates, the non-Arrhenius temperature dependence of α-relaxation, the dynamic heterogeneity, violations of the fluctuation-dissipation theorem, glass ageing and rejuvenation, rheological and mechanical anomalies, super-stable glasses, enhanced crystallisation near the glass transition, the excess heat capacity and phonon scattering at cryogenic temperatures, the Boson peak and plateau in thermal conductivity, and the puzzling midgap electronic states in amorphous chalcogenides.
{"title":"Theory of the structural glass transition: a pedagogical review","authors":"V. Lubchenko","doi":"10.1080/00018732.2015.1057979","DOIUrl":"https://doi.org/10.1080/00018732.2015.1057979","url":null,"abstract":"The random first-order transition theory of the structural glass transition is reviewed in a pedagogical fashion. The rigidity that emerges in crystals and glassy liquids is of the same fundamental origin. In both cases, it corresponds with a breaking of the translational symmetry; analogies with freezing transitions in spin systems can also be made. The common aspect of these seemingly distinct phenomena is a spontaneous emergence of the molecular field, a venerable and well-understood concept. In crucial distinction from periodic crystallisation, the free energy landscape of a glassy liquid is vastly degenerate, which gives rise to new length and time scales while rendering the emergence of rigidity gradual. We obviate the standard notion that to be mechanically stable a structure must be essentially unique; instead, we show that bulk degeneracy is perfectly allowed but should not exceed a certain value. The present microscopic description thus explains both crystallisation and the emergence of the landscape regime followed by vitrification in a unified, thermodynamics-rooted fashion. The article contains a self-contained exposition of the basics of the classical density functional theory and liquid theory, which are subsequently used to quantitatively estimate, without using adjustable parameters, the key attributes of glassy liquids, viz., the relaxation barriers, glass transition temperature, and cooperativity size. These results are then used to quantitatively discuss many diverse glassy phenomena, including the intrinsic connection between the excess liquid entropy and relaxation rates, the non-Arrhenius temperature dependence of α-relaxation, the dynamic heterogeneity, violations of the fluctuation-dissipation theorem, glass ageing and rejuvenation, rheological and mechanical anomalies, super-stable glasses, enhanced crystallisation near the glass transition, the excess heat capacity and phonon scattering at cryogenic temperatures, the Boson peak and plateau in thermal conductivity, and the puzzling midgap electronic states in amorphous chalcogenides.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"64 1","pages":"283 - 443"},"PeriodicalIF":0.0,"publicationDate":"2015-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018732.2015.1057979","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58773436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-02DOI: 10.1080/00018732.2015.1037068
Jin Wang
We present a review of the recently developed landscape and flux theory for non-equilibrium dynamical systems. We point out that the global natures of the associated dynamics for non-equilibrium system are determined by two key factors: the underlying landscape and, importantly, a curl probability flux. The landscape (U) reflects the probability of states (P) () and provides a global characterization and a stability measure of the system. The curl flux term measures how much detailed balance is broken and is one of the two main driving forces for the non-equilibrium dynamics in addition to the landscape gradient. Equilibrium dynamics resembles electron motion in an electric field, while non-equilibrium dynamics resembles electron motion in both electric and magnetic fields. The landscape and flux theory has many interesting consequences including (1) the fact that irreversible kinetic paths do not necessarily pass through the landscape saddles; (2) non-equilibrium transition state theory at the new saddle on the optimal paths for small but finite fluctuations; (3) a generalized fluctuation–dissipation relationship for non-equilibrium dynamical systems where the response function is not just equal to the fluctuations at the steady state alone as in the equilibrium case but there is an additional contribution from the curl flux in maintaining the steady state; (4) non-equilibrium thermodynamics where the free energy change is not just equal to the entropy production alone, as in the equilibrium case, but also there is an additional house-keeping contribution from the non-zero curl flux in maintaining the steady state; (5) gauge theory and a geometrical connection where the flux is found to be the origin of the gauge field curvature and the topological phase in analogy to the Berry phase in quantum mechanics; (6) coupled landscapes where non-adiabaticity of multiple landscapes in non-equilibrium dynamics can be analyzed using the landscape and flux theory and an eddy current emerges from the non-zero curl flux; (7) stochastic spatial dynamics where landscape and flux theory can be generalized for non-equilibrium field theory. We provide concrete examples of biological systems to demonstrate the new insights from the landscape and flux theory. These include models of (1) the cell cycle where the landscape attracts the system down to an oscillation attractor while the flux drives the coherent motion on the oscillation ring, the different phases of the cell cycle are identified as local basins on the cycle path and biological checkpoints are identified as local barriers or transition states between the local basins on the cell-cycle path; (2) stem cell differentiation where the Waddington landscape for development as well as the differentiation and reprogramming paths can be quantified; (3) cancer biology where cancer can be described as a disease of having multiple cellular states and the cancer state as well as the normal state can be quantified as b
{"title":"Landscape and flux theory of non-equilibrium dynamical systems with application to biology","authors":"Jin Wang","doi":"10.1080/00018732.2015.1037068","DOIUrl":"https://doi.org/10.1080/00018732.2015.1037068","url":null,"abstract":"We present a review of the recently developed landscape and flux theory for non-equilibrium dynamical systems. We point out that the global natures of the associated dynamics for non-equilibrium system are determined by two key factors: the underlying landscape and, importantly, a curl probability flux. The landscape (U) reflects the probability of states (P) () and provides a global characterization and a stability measure of the system. The curl flux term measures how much detailed balance is broken and is one of the two main driving forces for the non-equilibrium dynamics in addition to the landscape gradient. Equilibrium dynamics resembles electron motion in an electric field, while non-equilibrium dynamics resembles electron motion in both electric and magnetic fields. The landscape and flux theory has many interesting consequences including (1) the fact that irreversible kinetic paths do not necessarily pass through the landscape saddles; (2) non-equilibrium transition state theory at the new saddle on the optimal paths for small but finite fluctuations; (3) a generalized fluctuation–dissipation relationship for non-equilibrium dynamical systems where the response function is not just equal to the fluctuations at the steady state alone as in the equilibrium case but there is an additional contribution from the curl flux in maintaining the steady state; (4) non-equilibrium thermodynamics where the free energy change is not just equal to the entropy production alone, as in the equilibrium case, but also there is an additional house-keeping contribution from the non-zero curl flux in maintaining the steady state; (5) gauge theory and a geometrical connection where the flux is found to be the origin of the gauge field curvature and the topological phase in analogy to the Berry phase in quantum mechanics; (6) coupled landscapes where non-adiabaticity of multiple landscapes in non-equilibrium dynamics can be analyzed using the landscape and flux theory and an eddy current emerges from the non-zero curl flux; (7) stochastic spatial dynamics where landscape and flux theory can be generalized for non-equilibrium field theory. We provide concrete examples of biological systems to demonstrate the new insights from the landscape and flux theory. These include models of (1) the cell cycle where the landscape attracts the system down to an oscillation attractor while the flux drives the coherent motion on the oscillation ring, the different phases of the cell cycle are identified as local basins on the cycle path and biological checkpoints are identified as local barriers or transition states between the local basins on the cell-cycle path; (2) stem cell differentiation where the Waddington landscape for development as well as the differentiation and reprogramming paths can be quantified; (3) cancer biology where cancer can be described as a disease of having multiple cellular states and the cancer state as well as the normal state can be quantified as b","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"64 1","pages":"1 - 137"},"PeriodicalIF":0.0,"publicationDate":"2015-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018732.2015.1037068","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58773381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-12-14DOI: 10.1080/00018732.2016.1164490
K. Gustavsson, B. Mehlig
The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations have demonstrated that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: non-interacting particles may cluster together and form spatial patterns even though the fluid is incompressible, and the relative speeds of nearby particles can fluctuate strongly. Both phenomena depend sensitively on the parameters of the system. This parameter dependence is difficult to model from first principles since turbulence plays an essential role. Laboratory experiments are also very difficult, precisely since they must refer to a turbulent environment. But in recent years it has become clear that important aspects of the dynamics of heavy particles in turbulence can be understood in terms of statistical models where the turbulent fluctuations are approximated by Gaussian random functions with appropriate correlation functions. In this review, we summarise how such statistical-model calculations have led to a detailed understanding of the factors that determine heavy-particle dynamics in turbulence. We concentrate on spatial clustering of heavy particles in turbulence. This is an important question because spatial clustering affects the collision rate between the particles and thus the long-term fate of the system.
{"title":"Statistical models for spatial patterns of heavy particles in turbulence","authors":"K. Gustavsson, B. Mehlig","doi":"10.1080/00018732.2016.1164490","DOIUrl":"https://doi.org/10.1080/00018732.2016.1164490","url":null,"abstract":"The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations have demonstrated that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: non-interacting particles may cluster together and form spatial patterns even though the fluid is incompressible, and the relative speeds of nearby particles can fluctuate strongly. Both phenomena depend sensitively on the parameters of the system. This parameter dependence is difficult to model from first principles since turbulence plays an essential role. Laboratory experiments are also very difficult, precisely since they must refer to a turbulent environment. But in recent years it has become clear that important aspects of the dynamics of heavy particles in turbulence can be understood in terms of statistical models where the turbulent fluctuations are approximated by Gaussian random functions with appropriate correlation functions. In this review, we summarise how such statistical-model calculations have led to a detailed understanding of the factors that determine heavy-particle dynamics in turbulence. We concentrate on spatial clustering of heavy particles in turbulence. This is an important question because spatial clustering affects the collision rate between the particles and thus the long-term fate of the system.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"65 1","pages":"1 - 57"},"PeriodicalIF":0.0,"publicationDate":"2014-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018732.2016.1164490","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58773552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-09-01DOI: 10.1080/00018732.2014.1029302
F. Bencivenga, F. Capotondi, E. Principi, Maya Kiskinova, C. Masciovecchio
The most recent light sources, extreme ultraviolet (EUV) and X-ray free electron lasers (FELs), have extended tabletop laser experiments to shorter wavelengths, adding element and chemical state specificity by exciting and probing electronic transitions from core levels. Through their unique properties, combining femtosecond X-ray pulses with coherence and enormous peak brightness, the FELs have enabled studies of a broad class of dynamic phenomena in matter that crosses many scientific disciplines and have led to major breakthroughs in the last few years. In this article, we review how the advances in the performance of the FELs, with respect to coherence, polarization and multi-color pulse production, have pushed the development of original experimental strategies to study non-equilibrium behavior of matter at the femtosecond–nanometer time–length scales. In this review, the emphasis is placed on the contribution of the EUV and soft X-ray FELs on three important subjects: (i) the new regime of X-ray matter interactions with ultrashort very intense X-ray pulses, (ii) the new potential of coherent imaging and scattering for answering questions about nano dynamics in complex materials and (iii) the unique possibility to stimulate and probe nonlinear phenomena that are at the heart of conversion of light into other forms of energy, relevant to photovoltaics, femtosecond magnetism and phase transitions in correlated materials.
{"title":"Coherent and transient states studied with extreme ultraviolet and X-ray free electron lasers: present and future prospects","authors":"F. Bencivenga, F. Capotondi, E. Principi, Maya Kiskinova, C. Masciovecchio","doi":"10.1080/00018732.2014.1029302","DOIUrl":"https://doi.org/10.1080/00018732.2014.1029302","url":null,"abstract":"The most recent light sources, extreme ultraviolet (EUV) and X-ray free electron lasers (FELs), have extended tabletop laser experiments to shorter wavelengths, adding element and chemical state specificity by exciting and probing electronic transitions from core levels. Through their unique properties, combining femtosecond X-ray pulses with coherence and enormous peak brightness, the FELs have enabled studies of a broad class of dynamic phenomena in matter that crosses many scientific disciplines and have led to major breakthroughs in the last few years. In this article, we review how the advances in the performance of the FELs, with respect to coherence, polarization and multi-color pulse production, have pushed the development of original experimental strategies to study non-equilibrium behavior of matter at the femtosecond–nanometer time–length scales. In this review, the emphasis is placed on the contribution of the EUV and soft X-ray FELs on three important subjects: (i) the new regime of X-ray matter interactions with ultrashort very intense X-ray pulses, (ii) the new potential of coherent imaging and scattering for answering questions about nano dynamics in complex materials and (iii) the unique possibility to stimulate and probe nonlinear phenomena that are at the heart of conversion of light into other forms of energy, relevant to photovoltaics, femtosecond magnetism and phase transitions in correlated materials.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"63 1","pages":"327 - 404"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018732.2014.1029302","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58772911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-07-17DOI: 10.1080/00018732.2015.1055918
M. Bukov, L. D'Alessio, A. Polkovnikov
We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper–Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case, one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer–Wolff transformation extending the latter to driven systems.
{"title":"Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering","authors":"M. Bukov, L. D'Alessio, A. Polkovnikov","doi":"10.1080/00018732.2015.1055918","DOIUrl":"https://doi.org/10.1080/00018732.2015.1055918","url":null,"abstract":"We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper–Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case, one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer–Wolff transformation extending the latter to driven systems.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"64 1","pages":"139 - 226"},"PeriodicalIF":0.0,"publicationDate":"2014-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018732.2015.1055918","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58773422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-07-04DOI: 10.1080/00018732.2014.974304
D. Viehland, E. Salje
Domain boundaries typically constitute only a minute fraction of the total volume of a crystal. However, a special (but not unusual) situation can occur in which the domain boundary energy becomes very small. Specifically, the domain size is miniaturized to near-atomic scales and the domain boundary density becomes extremely high. In such cases, the properties of the crystal become dominated by a combination of both the domains and the domain boundaries. This phenomenon differs from most ferromagnetic or ferroelectric materials wherein the motion of the domain boundaries dominates the response. As reported herein, novel emergent phenomena that differ from the properties of either the domains or the domain boundaries may be expected. In this article, we focus on one specific state found in ferroic materials – namely, the adaptive ferroic state. This state can be found, for example, in tweed-like structures in morphotropic phase boundary piezoelectric crystals, ferromagnetic shape memory alloys, and pre-martensitic states. In these materials, the properties of the twin boundaries represent the principal contributors to the functionality of a given system. In fact, further investigations of domain boundary-dominated phenomena could result in novel potential for tailoring functional properties for a desired outcome. It should also be noted that new properties can be designed into twin boundaries that are not the properties of the domains. In this paper, adaptive structures and functional twin boundaries are reviewed, and examples of various observed functionalities (e.g. superconductivity, polarity, and ferroelectricity) and corresponding twin boundary structures are provided. In addition, this review confirms that various theoretically predicted, structurally bridging low-symmetry phases do, in fact, exist. Moreover, the values of the lattice constants of the adaptive state are adjustable parameters that are determined by combinations of cubic, rhombohedral/tetragonal phases, and geometrical invariant conditions. Finally, we show that, in such cases, macroscopic properties are controlled by the unique functionality of the twin walls. Looking forward, domain boundary-dominated phenomena offer an important approach for enhancing the properties of the bulk, and to unique local properties where the “twin is the device”. We encourage the community to rethink their approaches to materials by design that have treated the structure as homogeneous and to consider the alternative paradigm where the local structure is different from the apparent average symmetry.
{"title":"Domain boundary-dominated systems: adaptive structures and functional twin boundaries","authors":"D. Viehland, E. Salje","doi":"10.1080/00018732.2014.974304","DOIUrl":"https://doi.org/10.1080/00018732.2014.974304","url":null,"abstract":"Domain boundaries typically constitute only a minute fraction of the total volume of a crystal. However, a special (but not unusual) situation can occur in which the domain boundary energy becomes very small. Specifically, the domain size is miniaturized to near-atomic scales and the domain boundary density becomes extremely high. In such cases, the properties of the crystal become dominated by a combination of both the domains and the domain boundaries. This phenomenon differs from most ferromagnetic or ferroelectric materials wherein the motion of the domain boundaries dominates the response. As reported herein, novel emergent phenomena that differ from the properties of either the domains or the domain boundaries may be expected. In this article, we focus on one specific state found in ferroic materials – namely, the adaptive ferroic state. This state can be found, for example, in tweed-like structures in morphotropic phase boundary piezoelectric crystals, ferromagnetic shape memory alloys, and pre-martensitic states. In these materials, the properties of the twin boundaries represent the principal contributors to the functionality of a given system. In fact, further investigations of domain boundary-dominated phenomena could result in novel potential for tailoring functional properties for a desired outcome. It should also be noted that new properties can be designed into twin boundaries that are not the properties of the domains. In this paper, adaptive structures and functional twin boundaries are reviewed, and examples of various observed functionalities (e.g. superconductivity, polarity, and ferroelectricity) and corresponding twin boundary structures are provided. In addition, this review confirms that various theoretically predicted, structurally bridging low-symmetry phases do, in fact, exist. Moreover, the values of the lattice constants of the adaptive state are adjustable parameters that are determined by combinations of cubic, rhombohedral/tetragonal phases, and geometrical invariant conditions. Finally, we show that, in such cases, macroscopic properties are controlled by the unique functionality of the twin walls. Looking forward, domain boundary-dominated phenomena offer an important approach for enhancing the properties of the bulk, and to unique local properties where the “twin is the device”. We encourage the community to rethink their approaches to materials by design that have treated the structure as homogeneous and to consider the alternative paradigm where the local structure is different from the apparent average symmetry.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"63 1","pages":"267 - 326"},"PeriodicalIF":0.0,"publicationDate":"2014-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018732.2014.974304","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58773368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-05-04DOI: 10.1080/00018732.2014.940227
T. Das, R. Markiewicz, A. Bansil
We review the intermediate coupling model for treating electronic correlations in the cuprates. Spectral signatures of the intermediate coupling scenario are identified and used to adduce that the cuprates fall in the intermediate rather than the weak or the strong coupling limits. A robust, ‘beyond local-density approximation’ framework for obtaining wide-ranging properties of the cuprates via a GW-approximation based self-consistent self-energy correction for incorporating correlation effects is delineated. In this way, doping- and temperature-dependent spectra, from the undoped insulator to the overdoped metal, in the normal as well as the superconducting state, with features of both weak and strong coupling can be modeled in a material-specific manner with very few parameters. Efficacy of the model is shown by considering available spectroscopic data on electron- and hole-doped cuprates from angle-resolved photoemission, scanning tunneling microscopy/spectroscopy, neutron scattering, inelastic light scattering, optical and other experiments. Generalizations to treat systems with multiple correlated bands such as the heavy-fermions, the ruthenates and the actinides are discussed.
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Pub Date : 2014-03-04DOI: 10.1080/00018732.2014.933502
A. Daley
The study of open quantum systems – microscopic systems exhibiting quantum coherence that are coupled to their environment – has become increasingly important in the past years, as the ability to control quantum coherence on a single particle level has been developed in a wide variety of physical systems. In quantum optics, the study of open systems goes well beyond understanding the breakdown of quantum coherence. There, the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or to project the system onto known states via feedback in quantum measurements. Many mathematical frameworks have been developed to describe such systems, which for atomic, molecular, and optical (AMO) systems generally provide a very accurate description of the open quantum system on a microscopic level. In recent years, AMO systems including cold atomic and molecular gases and trapped ions have been applied heavily to the study of many-body physics, and it has become important to extend previous understanding of open system dynamics in single- and few-body systems to this many-body context. A key formalism that has already proven very useful in this context is the quantum trajectories technique. This method was developed in quantum optics as a numerical tool for studying dynamics in open quantum systems, and falls within a broader framework of continuous measurement theory as a way to understand the dynamics of large classes of open quantum systems. In this article, we review the progress that has been made in studying open many-body systems in the AMO context, focussing on the application of ideas from quantum optics, and on the implementation and applications of quantum trajectories methods in these systems. Control over dissipative processes promises many further tools to prepare interesting and important states in strongly interacting systems, including the realisation of parameter regimes in quantum simulators that are inaccessible via current techniques.
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