Pub Date : 2008-06-05DOI: 10.1080/00018730902831009
P. Jacquod, C. Petitjean
In this review we summarize and amplify recent investigations of coupled quantum dynamical systems with few degrees of freedom in the short-wavelength, semiclassical limit. Focusing on the correspondence between quantum and classical physics, we mathematically formulate and attempt to answer three fundamental questions. (i) How can one drive a small dynamical quantum system to behave classically? (ii) What determines the rate at which two single-particle quantum-mechanical subsystems become entangled when they interact? (iii) How does irreversibility occur in quantum systems with few degrees of freedom? These three questions are posed in the context of the quantum-classical correspondence for dynamical systems with few degrees of freedom, and we accordingly rely on two short-wavelength approximations to quantum mechanics to answer them: the trajectory-based semiclassical approach on the one hand, and random matrix theory on the other hand. We construct novel investigative procedures towards decoherence and the emergence of classicality out of quantumness in dynamical systems coupled to external degrees of freedom. In particular, we show how dynamical properties of chaotic classical systems, such as local exponential instability in phase space, also affects their quantum counterparts. For instance, it is often the case that the fidelity with which a quantum state is reconstructed after an imperfect time-reversal operation decays with the Lyapunov exponent of the corresponding classical dynamics. For related reasons, but perhaps more surprisingly, the rate at which two interacting quantum subsystems become entangled can also be governed by the subsystem's Lyapunov exponents. Our method allows us to differentiate quantum coherent effects (those related to phase interferences) from classical ones (those related to the necessarily extended envelope of quantal wavefunctions) at each stage in our investigations. This makes it clear that all occurrences of Lyapunov exponents we witness have a classical origin, although they require rather strong decoherence effects to be observed. We extensively rely on numerical experiments to illustrate our findings and briefly comment on possible extensions to more complex problems involving environments with many interacting dynamical systems, going beyond the uncoupled harmonic oscillators model of Caldeira and Leggett.
{"title":"Decoherence, entanglement and irreversibility in quantum dynamical systems with few degrees of freedom","authors":"P. Jacquod, C. Petitjean","doi":"10.1080/00018730902831009","DOIUrl":"https://doi.org/10.1080/00018730902831009","url":null,"abstract":"In this review we summarize and amplify recent investigations of coupled quantum dynamical systems with few degrees of freedom in the short-wavelength, semiclassical limit. Focusing on the correspondence between quantum and classical physics, we mathematically formulate and attempt to answer three fundamental questions. (i) How can one drive a small dynamical quantum system to behave classically? (ii) What determines the rate at which two single-particle quantum-mechanical subsystems become entangled when they interact? (iii) How does irreversibility occur in quantum systems with few degrees of freedom? These three questions are posed in the context of the quantum-classical correspondence for dynamical systems with few degrees of freedom, and we accordingly rely on two short-wavelength approximations to quantum mechanics to answer them: the trajectory-based semiclassical approach on the one hand, and random matrix theory on the other hand. We construct novel investigative procedures towards decoherence and the emergence of classicality out of quantumness in dynamical systems coupled to external degrees of freedom. In particular, we show how dynamical properties of chaotic classical systems, such as local exponential instability in phase space, also affects their quantum counterparts. For instance, it is often the case that the fidelity with which a quantum state is reconstructed after an imperfect time-reversal operation decays with the Lyapunov exponent of the corresponding classical dynamics. For related reasons, but perhaps more surprisingly, the rate at which two interacting quantum subsystems become entangled can also be governed by the subsystem's Lyapunov exponents. Our method allows us to differentiate quantum coherent effects (those related to phase interferences) from classical ones (those related to the necessarily extended envelope of quantal wavefunctions) at each stage in our investigations. This makes it clear that all occurrences of Lyapunov exponents we witness have a classical origin, although they require rather strong decoherence effects to be observed. We extensively rely on numerical experiments to illustrate our findings and briefly comment on possible extensions to more complex problems involving environments with many interacting dynamical systems, going beyond the uncoupled harmonic oscillators model of Caldeira and Leggett.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"58 1","pages":"196 - 67"},"PeriodicalIF":0.0,"publicationDate":"2008-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018730902831009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58772487","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 : 2008-05-01DOI: 10.1080/00018730802218067
L. Chirolli, G. Burkard
The interaction of solid-state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid-state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review, we discuss how decoherence affects two of the most successful realizations of solid-state qubits, namely, spin qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented by confining the electron spin in a semiconductor quantum dot. Superconducting devices show quantum behaviour at low temperatures, and the qubit is encoded in the two lowest energy levels of a superconducting circuit. The electron spin in a quantum dot has two main decoherence channels, a (Markovian) phonon-assisted relaxation channel, due to the presence of a spin–orbit interaction, and a (non-Markovian) spin bath constituted by the spins of the nuclei in the quantum dot that interact with the electron spin via the hyperfine interaction. In a superconducting qubit, decoherence takes place as a result of fluctuations in the control parameters, such as bias currents, applied flux and bias voltages, and via losses in the dissipative circuit elements.
{"title":"Decoherence in solid-state qubits","authors":"L. Chirolli, G. Burkard","doi":"10.1080/00018730802218067","DOIUrl":"https://doi.org/10.1080/00018730802218067","url":null,"abstract":"The interaction of solid-state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid-state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review, we discuss how decoherence affects two of the most successful realizations of solid-state qubits, namely, spin qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented by confining the electron spin in a semiconductor quantum dot. Superconducting devices show quantum behaviour at low temperatures, and the qubit is encoded in the two lowest energy levels of a superconducting circuit. The electron spin in a quantum dot has two main decoherence channels, a (Markovian) phonon-assisted relaxation channel, due to the presence of a spin–orbit interaction, and a (non-Markovian) spin bath constituted by the spins of the nuclei in the quantum dot that interact with the electron spin via the hyperfine interaction. In a superconducting qubit, decoherence takes place as a result of fluctuations in the control parameters, such as bias currents, applied flux and bias voltages, and via losses in the dissipative circuit elements.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"49 1","pages":"225 - 285"},"PeriodicalIF":0.0,"publicationDate":"2008-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018730802218067","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58772326","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 : 2008-03-01DOI: 10.1080/14789940801912366
F. Verstraete, V. Murg, J. Cirac
This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.
本文综述了利用矩阵积态和投影纠缠对态的变分重整化群方法的理论认识和数值实现方面的最新进展。
{"title":"Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems","authors":"F. Verstraete, V. Murg, J. Cirac","doi":"10.1080/14789940801912366","DOIUrl":"https://doi.org/10.1080/14789940801912366","url":null,"abstract":"This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"57 1","pages":"143 - 224"},"PeriodicalIF":0.0,"publicationDate":"2008-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14789940801912366","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59874959","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 : 2008-01-01DOI: 10.1080/00018730701822522
H. Emmerich
Phase-field modelling is still a young discipline in condensed-matter physics, which established itself for the class of systems that can be characterised by domains of different phases separated by a distinct interface. Driven out of equilibrium, their dynamics result in the evolution of those interfaces which might develop into well defined-structures with characteristic length scales at the nano-, micro- or meso-scale. Since the material properties of such systems are to a large extent determined by those small-scale structures, acquiring a precise understanding of the mechanisms that drive the interfacial dynamics is a great challenge for scientists in this field. Phase-field modelling is an approach that allows this challenge to be tackled in a simulation-based manner. This review provides a critical overview of the conceptual background of the phase-field method, the most relevant fields of condensed-matter physics that have been approached using phase-field modelling, as well as the respective model formulations and the insight gained so far via their simulation and analysis. Moreover, we discuss directions of further development and the quality of the scientific contributions to be expected from those.
{"title":"Advances of and by phase-field modelling in condensed-matter physics","authors":"H. Emmerich","doi":"10.1080/00018730701822522","DOIUrl":"https://doi.org/10.1080/00018730701822522","url":null,"abstract":"Phase-field modelling is still a young discipline in condensed-matter physics, which established itself for the class of systems that can be characterised by domains of different phases separated by a distinct interface. Driven out of equilibrium, their dynamics result in the evolution of those interfaces which might develop into well defined-structures with characteristic length scales at the nano-, micro- or meso-scale. Since the material properties of such systems are to a large extent determined by those small-scale structures, acquiring a precise understanding of the mechanisms that drive the interfacial dynamics is a great challenge for scientists in this field. Phase-field modelling is an approach that allows this challenge to be tackled in a simulation-based manner. This review provides a critical overview of the conceptual background of the phase-field method, the most relevant fields of condensed-matter physics that have been approached using phase-field modelling, as well as the respective model formulations and the insight gained so far via their simulation and analysis. Moreover, we discuss directions of further development and the quality of the scientific contributions to be expected from those.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"57 1","pages":"1 - 87"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018730701822522","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58772283","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 : 2008-01-01DOI: 10.1080/00018730802567505
V. Barzykin, D. Pines
We present a detailed review of scaling behaviour in the magnetically underdoped cuprate superconductors (hole dopings less than 0.20) and show that it reflects the presence of two coupled components throughout this doping regime: a non-Landau Fermi liquid and a spin liquid whose behaviour maps onto the theoretical Monte Carlo calculations of the two-dimensional Heisenberg model of localized Cu spins for most of its temperature domain. We use this mapping to extract the doping dependence of the strength, f(x) of the spin liquid component and the effective interaction, J eff(x) between the remnant localized spins that compose it; we find that both decrease linearly with x as the doping level increases. We discuss the physical origin of pseudogap behaviour and conclude that it is consistent with scenarios in which the both the large energy gaps found in the normal state and their subsequent superconductivity are brought about by the coupling between the Fermi liquid quasiparticles and the spin liquid excitations, and that differences in this coupling between the 1–2–3 and 2–1–4 materials can explain the measured differences in their superconducting transition temperatures and other properties.
{"title":"Universal behaviour and the two-component character of magnetically underdoped cuprate superconductors","authors":"V. Barzykin, D. Pines","doi":"10.1080/00018730802567505","DOIUrl":"https://doi.org/10.1080/00018730802567505","url":null,"abstract":"We present a detailed review of scaling behaviour in the magnetically underdoped cuprate superconductors (hole dopings less than 0.20) and show that it reflects the presence of two coupled components throughout this doping regime: a non-Landau Fermi liquid and a spin liquid whose behaviour maps onto the theoretical Monte Carlo calculations of the two-dimensional Heisenberg model of localized Cu spins for most of its temperature domain. We use this mapping to extract the doping dependence of the strength, f(x) of the spin liquid component and the effective interaction, J eff(x) between the remnant localized spins that compose it; we find that both decrease linearly with x as the doping level increases. We discuss the physical origin of pseudogap behaviour and conclude that it is consistent with scenarios in which the both the large energy gaps found in the normal state and their subsequent superconductivity are brought about by the coupling between the Fermi liquid quasiparticles and the spin liquid excitations, and that differences in this coupling between the 1–2–3 and 2–1–4 materials can explain the measured differences in their superconducting transition temperatures and other properties.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"58 1","pages":"1 - 65"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018730802567505","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58772448","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 : 2007-11-20DOI: 10.1080/00018732.2011.572452
L. D. Costa, O. N. Oliveira, G. Travieso, F. Rodrigues, P. R. Villas Boas, L. Antiqueira, M. Viana, Luis Enrique Correa Rocha
The success of new scientific areas can be assessed by their potential in contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis being developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling. A diversity of phenomena are surveyed, which may be classified into no less than 11 areas, providing a clear indication of the impact of the field of complex networks.
{"title":"Analyzing and modeling real-world phenomena with complex networks: a survey of applications","authors":"L. D. Costa, O. N. Oliveira, G. Travieso, F. Rodrigues, P. R. Villas Boas, L. Antiqueira, M. Viana, Luis Enrique Correa Rocha","doi":"10.1080/00018732.2011.572452","DOIUrl":"https://doi.org/10.1080/00018732.2011.572452","url":null,"abstract":"The success of new scientific areas can be assessed by their potential in contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis being developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling. A diversity of phenomena are surveyed, which may be classified into no less than 11 areas, providing a clear indication of the impact of the field of complex networks.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"60 1","pages":"329 - 412"},"PeriodicalIF":0.0,"publicationDate":"2007-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018732.2011.572452","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58772825","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 : 2007-09-01DOI: 10.1080/00018730701611677
S. W. Meier, Richard M. Lueptow, J. Ottino
The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.
{"title":"A dynamical systems approach to mixing and segregation of granular materials in tumblers","authors":"S. W. Meier, Richard M. Lueptow, J. Ottino","doi":"10.1080/00018730701611677","DOIUrl":"https://doi.org/10.1080/00018730701611677","url":null,"abstract":"The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"56 1","pages":"757 - 827"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018730701611677","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58771849","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 : 2007-09-01DOI: 10.1080/00018730701577548
R. Häggkvist, A. Rosengren, P. Lundow, K. Markström, Daniel Andrén, P. Kundrotas
The Ising model was introduced in 1920 to describe a uniaxial system of magnetic moments, localized on a lattice, interacting via nearest-neighbour exchange interaction. It is the generic model for a continuous phase transition and arguably the most studied model in theoretical physics. Since it was solved for a two-dimensional lattice by Onsager in 1944, thereby representing one of the very few exactly solvable models in dimensions higher than one, it has served as a testing ground for new developments in analytic treatment and numerical algorithms. Only series expansions and numerical approaches, such as Monte Carlo simulations, are available in three dimensions. This review focuses on Monte Carlo simulation. We build upon a data set of unprecedented size. A great number of quantities of the model are estimated near the critical coupling. We present both a conventional analysis and an analysis in terms of a Puiseux series for the critical exponents. The former gives distinct values of the high- and low-temperature exponents; by means of the latter we can get these exponents to be equal at the cost of having true asymptotic behaviour being found only extremely close to the critical point. The consequences of this for simulations of lattice systems are discussed at length.
{"title":"On the Ising model for the simple cubic lattice","authors":"R. Häggkvist, A. Rosengren, P. Lundow, K. Markström, Daniel Andrén, P. Kundrotas","doi":"10.1080/00018730701577548","DOIUrl":"https://doi.org/10.1080/00018730701577548","url":null,"abstract":"The Ising model was introduced in 1920 to describe a uniaxial system of magnetic moments, localized on a lattice, interacting via nearest-neighbour exchange interaction. It is the generic model for a continuous phase transition and arguably the most studied model in theoretical physics. Since it was solved for a two-dimensional lattice by Onsager in 1944, thereby representing one of the very few exactly solvable models in dimensions higher than one, it has served as a testing ground for new developments in analytic treatment and numerical algorithms. Only series expansions and numerical approaches, such as Monte Carlo simulations, are available in three dimensions. This review focuses on Monte Carlo simulation. We build upon a data set of unprecedented size. A great number of quantities of the model are estimated near the critical coupling. We present both a conventional analysis and an analysis in terms of a Puiseux series for the critical exponents. The former gives distinct values of the high- and low-temperature exponents; by means of the latter we can get these exponents to be equal at the cost of having true asymptotic behaviour being found only extremely close to the critical point. The consequences of this for simulations of lattice systems are discussed at length.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"56 1","pages":"653 - 755"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018730701577548","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58771843","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 : 2007-08-15DOI: 10.1080/00018730801893043
Z. Eisler, I. Bartos, J. Kertész
Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form ‘fluctuations ≈ constant × averageα’, where the exponent α is predominantly in the range [1/2, 1]. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names Taylor's law or fluctuation scaling. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling. 1Dedicated to the memory of L. R. Taylor (1924–2007).
{"title":"Fluctuation scaling in complex systems: Taylor's law and beyond","authors":"Z. Eisler, I. Bartos, J. Kertész","doi":"10.1080/00018730801893043","DOIUrl":"https://doi.org/10.1080/00018730801893043","url":null,"abstract":"Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form ‘fluctuations ≈ constant × averageα’, where the exponent α is predominantly in the range [1/2, 1]. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names Taylor's law or fluctuation scaling. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling. 1Dedicated to the memory of L. R. Taylor (1924–2007).","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"57 1","pages":"142 - 89"},"PeriodicalIF":0.0,"publicationDate":"2007-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018730801893043","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58772296","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 : 2007-07-06DOI: 10.1080/00018730701627707
B. Edegger, V. N. Muthukumar, C. Gros
We review the resonating valence bond (RVB) theory of high-temperature superconductivity using Gutzwiller projected wave functions that incorporate strong correlations. After a general overview of the phenomenon of high-temperature superconductivity, we discuss Anderson's RVB picture and its implementation by renormalized mean-field theory (RMFT) and variational Monte Carlo (VMC) techniques. We review RMFT and VMC results with an emphasis on recent developments in extending VMC and RMFT techniques to excited states. We compare results obtained from these methods with angle-resolved photoemission spectroscopy (ARPES) and scanning tunnelling microscopy (STM). We conclude by summarizing recent successes of this approach and discuss open problems that need to be solved for a consistent and complete description of high-temperature superconductivity using Gutzwiller projected wave functions.
{"title":"Gutzwiller–RVB theory of high-temperature superconductivity: Results from renormalized mean-field theory and variational Monte Carlo calculations","authors":"B. Edegger, V. N. Muthukumar, C. Gros","doi":"10.1080/00018730701627707","DOIUrl":"https://doi.org/10.1080/00018730701627707","url":null,"abstract":"We review the resonating valence bond (RVB) theory of high-temperature superconductivity using Gutzwiller projected wave functions that incorporate strong correlations. After a general overview of the phenomenon of high-temperature superconductivity, we discuss Anderson's RVB picture and its implementation by renormalized mean-field theory (RMFT) and variational Monte Carlo (VMC) techniques. We review RMFT and VMC results with an emphasis on recent developments in extending VMC and RMFT techniques to excited states. We compare results obtained from these methods with angle-resolved photoemission spectroscopy (ARPES) and scanning tunnelling microscopy (STM). We conclude by summarizing recent successes of this approach and discuss open problems that need to be solved for a consistent and complete description of high-temperature superconductivity using Gutzwiller projected wave functions.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":"56 1","pages":"1033 - 927"},"PeriodicalIF":0.0,"publicationDate":"2007-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018730701627707","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58772276","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}
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