Pub Date : 2023-10-09DOI: 10.1088/1751-8121/acfddd
Alessandro Bravetti, Connor Jackman, David Sloan
Abstract We state conditions under which a symplectic Hamiltonian system admitting a certain type of symmetry (a scaling symmetry ) may be reduced to a type of contact Hamiltonian system, on a space of one less dimension. We observe that such contact reductions underly the well-known McGehee blow-up process from classical mechanics. As a consequence of this broader perspective, we associate a type of variational Herglotz principle associated to these classical blow-ups. Moreover, we consider some more flexible situations for certain Hamiltonian systems depending on parameters, to which the contact reduction may be applied to yield contact Hamiltonian systems along with their Herglotz variational counterparts as the underlying systems of the associated scale-invariant dynamics. From a philosophical perspective, one obtains an equivalent description for the same physical phenomenon, but with fewer inputs needed, thus realizing Poincaré’s dream of a scale-invariant description of the Universe.
{"title":"Scaling symmetries, contact reduction and Poincaré’s dream","authors":"Alessandro Bravetti, Connor Jackman, David Sloan","doi":"10.1088/1751-8121/acfddd","DOIUrl":"https://doi.org/10.1088/1751-8121/acfddd","url":null,"abstract":"Abstract We state conditions under which a symplectic Hamiltonian system admitting a certain type of symmetry (a scaling symmetry ) may be reduced to a type of contact Hamiltonian system, on a space of one less dimension. We observe that such contact reductions underly the well-known McGehee blow-up process from classical mechanics. As a consequence of this broader perspective, we associate a type of variational Herglotz principle associated to these classical blow-ups. Moreover, we consider some more flexible situations for certain Hamiltonian systems depending on parameters, to which the contact reduction may be applied to yield contact Hamiltonian systems along with their Herglotz variational counterparts as the underlying systems of the associated scale-invariant dynamics. From a philosophical perspective, one obtains an equivalent description for the same physical phenomenon, but with fewer inputs needed, thus realizing Poincaré’s dream of a scale-invariant description of the Universe.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135044186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-09DOI: 10.1088/1751-8121/acf9d0
Simon Ekhammar, Joseph A Minahan, Charles Thull
Abstract Using the supergravity dual and the plane-wave limit as a guide, we conjecture the asymptotic large coupling form of the Hagedorn temperature for planar super Yang-Mills to order 1/λ . This is two orders beyond the presently known behavior. Using the quantum spectral curve procedure of Harmark and Wilhelm, we show that our conjectured form is in excellent agreement with the numerical results.
{"title":"The asymptotic form of the Hagedorn temperature in planar N=4 super Yang-Mills","authors":"Simon Ekhammar, Joseph A Minahan, Charles Thull","doi":"10.1088/1751-8121/acf9d0","DOIUrl":"https://doi.org/10.1088/1751-8121/acf9d0","url":null,"abstract":"Abstract Using the supergravity dual and the plane-wave limit as a guide, we conjecture the asymptotic large coupling form of the Hagedorn temperature for planar <?CDATA $mathcal{N} = 4$?> super Yang-Mills to order <?CDATA $1/sqrt{lambda}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msqrt> <mml:mi>λ</mml:mi> </mml:msqrt> </mml:math> . This is two orders beyond the presently known behavior. Using the quantum spectral curve procedure of Harmark and Wilhelm, we show that our conjectured form is in excellent agreement with the numerical results.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-09DOI: 10.1088/1751-8121/acfd6d
Frank Aurzada, Volker Betz, Mikahil Lifshits
Abstract We show that a properly scaled stretched long Brownian chain converges to a two-parametric stochastic process, given by the sum of an explicit deterministic continuous function and the solution of the stochastic heat equation with zero boundary conditions.
{"title":"Scaling limit of stretched Brownian chains","authors":"Frank Aurzada, Volker Betz, Mikahil Lifshits","doi":"10.1088/1751-8121/acfd6d","DOIUrl":"https://doi.org/10.1088/1751-8121/acfd6d","url":null,"abstract":"Abstract We show that a properly scaled stretched long Brownian chain converges to a two-parametric stochastic process, given by the sum of an explicit deterministic continuous function and the solution of the stochastic heat equation with zero boundary conditions.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135044323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-09DOI: 10.1088/1751-8121/acfc04
Agung Budiyono, Bobby Eka Gunara, Bagus Endar Bachtiar Nurhandoko, Hermawan Kresno Dipojono
Abstract We propose a characterization and a quantification of the general quantum correlation which is exhibited even by a separable (unentangled) mixed bipartite state in terms of the nonclassical values of the associated Kirkwood–Dirac (KD) quasiprobability. Such a general quantum correlation, wherein entanglement is a subset, is not only intriguing from a fundamental point of view, but it has also been recognized as a resource in a variety of schemes of quantum information processing and quantum technology. Given a bipartite state, we construct a quantity based on the imaginary part the associated KD quasiprobability defined over a pair of orthonormal product bases and an optimization procedure over all pairs of such bases. We show that it satisfies certain requirements expected for a quantifier of general quantum correlations. It gives a lower bound to the total sum of the quantum standard deviation of all the elements of the product (local) basis, minimized over all such bases. It suggests an interpretation as the minimum genuine quantum share of uncertainty in all local von-Neumann projective measurements. Moreover, it is a faithful witness for entanglement and measurement-induced nonlocality of pure bipartite states. We then discuss a variational scheme for its estimation, and based on this, we offer information theoretical meanings of the general quantum correlation. Our results suggest a deep connection between the nonclassical concept of general quantum correlation and the nonclassical values of the KD quasiprobability and the associated strange weak values.
{"title":"General quantum correlation from nonreal values of Kirkwood-Dirac quasiprobability over orthonormal product bases","authors":"Agung Budiyono, Bobby Eka Gunara, Bagus Endar Bachtiar Nurhandoko, Hermawan Kresno Dipojono","doi":"10.1088/1751-8121/acfc04","DOIUrl":"https://doi.org/10.1088/1751-8121/acfc04","url":null,"abstract":"Abstract We propose a characterization and a quantification of the general quantum correlation which is exhibited even by a separable (unentangled) mixed bipartite state in terms of the nonclassical values of the associated Kirkwood–Dirac (KD) quasiprobability. Such a general quantum correlation, wherein entanglement is a subset, is not only intriguing from a fundamental point of view, but it has also been recognized as a resource in a variety of schemes of quantum information processing and quantum technology. Given a bipartite state, we construct a quantity based on the imaginary part the associated KD quasiprobability defined over a pair of orthonormal product bases and an optimization procedure over all pairs of such bases. We show that it satisfies certain requirements expected for a quantifier of general quantum correlations. It gives a lower bound to the total sum of the quantum standard deviation of all the elements of the product (local) basis, minimized over all such bases. It suggests an interpretation as the minimum genuine quantum share of uncertainty in all local von-Neumann projective measurements. Moreover, it is a faithful witness for entanglement and measurement-induced nonlocality of pure bipartite states. We then discuss a variational scheme for its estimation, and based on this, we offer information theoretical meanings of the general quantum correlation. Our results suggest a deep connection between the nonclassical concept of general quantum correlation and the nonclassical values of the KD quasiprobability and the associated strange weak values.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"269 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-09DOI: 10.1088/1751-8121/ad018c
Francisco Navarro Lerida, Eugen Radu, D H Tchrakian
We consider axially symmetric solutions of the U(1) gauged Skyrme model supplemented with a Callan–Witten (CW) anomaly density term. The main properties of the solutions are studied, several specific features introduced by the presence of the CW term being identified. We find that the solitons possess a nonzero angular momentum proportional to the electric charge, which in addition to the usual Coulomb part, acquires an extra (topological) contribution from the CW term. Specifically, it is shown that the slope of mass/energy M vs. electric charge Qe and angular momentum J can be both positive and negative. Furthermore, it is shown that the gauged Skyrmion persists even when the quartic (Skyrme) kinetic term disappears.
{"title":"The role of the Callan-Witten anomaly density as a Chern-Simons term in Skyrme model","authors":"Francisco Navarro Lerida, Eugen Radu, D H Tchrakian","doi":"10.1088/1751-8121/ad018c","DOIUrl":"https://doi.org/10.1088/1751-8121/ad018c","url":null,"abstract":"We consider axially symmetric solutions of the U(1) gauged Skyrme model supplemented with a Callan–Witten (CW) anomaly density term. The main properties of the solutions are studied, several specific features introduced by the presence of the CW term being identified. We find that the solitons possess a nonzero angular momentum proportional to the electric charge, which in addition to the usual Coulomb part, acquires an extra (topological) contribution from the CW term. Specifically, it is shown that the slope of mass/energy M vs. electric charge Qe and angular momentum J can be both positive and negative. Furthermore, it is shown that the gauged Skyrmion persists even when the quartic (Skyrme) kinetic term disappears.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135044601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-09DOI: 10.1088/1751-8121/acfd6c
David MacTaggart, Alberto Valli
Abstract Magnetic helicity is a conserved quantity of ideal magnetohydrodynamics (MHD) that is related to the topology of the magnetic field, and is widely studied in both laboratory and astrophysical plasmas. When the magnetic field has a non-trivial normal component on the boundary of the domain, the classical definition of helicity must be replaced by relative magnetic helicity . The purpose of this work is to review the various definitions of relative helicity and to show that they have a common origin—a general definition of relative helicity in multiply connected domains. We show that this general definition is both gauge-invariant and is conserved in time under ideal MHD, subject only to closed and line-tied boundary conditions. Other, more specific, formulae for relative helicity, that are used frequently in the literature, are shown to follow from the general expression by imposing extra conditions on the magnetic field or its vector potential.
{"title":"Relative magnetic helicity in multiply connected domains","authors":"David MacTaggart, Alberto Valli","doi":"10.1088/1751-8121/acfd6c","DOIUrl":"https://doi.org/10.1088/1751-8121/acfd6c","url":null,"abstract":"Abstract Magnetic helicity is a conserved quantity of ideal magnetohydrodynamics (MHD) that is related to the topology of the magnetic field, and is widely studied in both laboratory and astrophysical plasmas. When the magnetic field has a non-trivial normal component on the boundary of the domain, the classical definition of helicity must be replaced by relative magnetic helicity . The purpose of this work is to review the various definitions of relative helicity and to show that they have a common origin—a general definition of relative helicity in multiply connected domains. We show that this general definition is both gauge-invariant and is conserved in time under ideal MHD, subject only to closed and line-tied boundary conditions. Other, more specific, formulae for relative helicity, that are used frequently in the literature, are shown to follow from the general expression by imposing extra conditions on the magnetic field or its vector potential.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"270 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135044320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1088/1751-8121/acfcf3
Paul C Bressloff
Abstract In this paper, we develop an encounter-based model of partial surface adsorption for fractional diffusion in a bounded domain. We take the probability of adsorption to depend on the amount of particle-surface contact time, as specified by a Brownian functional known as the boundary local time ℓ(t) . If the rate of adsorption is state dependent, then the adsorption process is non-Markovian, reflecting the fact that surface activation/deactivation proceeds progressively by repeated particle encounters. The generalized adsorption event is identified as the first time that the local time crosses a randomly generated threshold. Different models of adsorption (Markovian and non-Markovian) then correspond to different choices for the random threshold probability density ψ(ℓ) . The marginal probability density for particle position X(t) prior to absorption depends on ψ and the joint probability density for the pair (X(t),ℓ(t)) , also known as the local time propagator. In the case of normal diffusion one can use a Feynman–Kac formula to derive an evolution equation for the propagator. Here we derive the local time propagator equation for fractional diffusion by taking a continuum limit of a heavy-tailed continuous-time random walk (CTRW). We begin by considering a CTRW on a one-dimensional lattice with a reflecting boundary at n = 0. We derive an evolution equation for the joint probability density of the particle location N(t)∈{n∈
{"title":"Encounter-based reaction-subdiffusion model I: surface adsorption and the local time propagator","authors":"Paul C Bressloff","doi":"10.1088/1751-8121/acfcf3","DOIUrl":"https://doi.org/10.1088/1751-8121/acfcf3","url":null,"abstract":"Abstract In this paper, we develop an encounter-based model of partial surface adsorption for fractional diffusion in a bounded domain. We take the probability of adsorption to depend on the amount of particle-surface contact time, as specified by a Brownian functional known as the boundary local time <?CDATA $ell(t)$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>ℓ</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> . If the rate of adsorption is state dependent, then the adsorption process is non-Markovian, reflecting the fact that surface activation/deactivation proceeds progressively by repeated particle encounters. The generalized adsorption event is identified as the first time that the local time crosses a randomly generated threshold. Different models of adsorption (Markovian and non-Markovian) then correspond to different choices for the random threshold probability density <?CDATA $psi(ell)$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>ψ</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>ℓ</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> . The marginal probability density for particle position <?CDATA $mathbf{X}(t)$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mi mathvariant=\"bold\">X</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> prior to absorption depends on ψ and the joint probability density for the pair <?CDATA $(mathbf{X}(t),ell(t))$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mrow> <mml:mi mathvariant=\"bold\">X</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>,</mml:mo> <mml:mi>ℓ</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> , also known as the local time propagator. In the case of normal diffusion one can use a Feynman–Kac formula to derive an evolution equation for the propagator. Here we derive the local time propagator equation for fractional diffusion by taking a continuum limit of a heavy-tailed continuous-time random walk (CTRW). We begin by considering a CTRW on a one-dimensional lattice with a reflecting boundary at n = 0. We derive an evolution equation for the joint probability density of the particle location <?CDATA $N(t)in {nin {mathbb{Z}},nunicode{x2A7E} 0}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>N</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>∈</mml:mo> <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo> <mml:mi>n</mml:mi> <mml:mo>∈</mml:mo> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"double-struc","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"2018 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135302603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1088/1751-8121/acfcf4
Paul C Bressloff
Abstract In this paper we develop an encounter-based model of reaction-subdiffusion in a domain Ω with a partially absorbing interior trap . We assume that the particle can freely enter and exit , but is only absorbed within . We take the probability of absorption to depend on the amount of time a particle spends within the trap, which is specified by a Brownian functional known as the occupation time A ( t ). The first passage time (FPT) for absorption is identified with the point at which the occupation time crosses a random threshold Aˆ with probability density ψ(a) . Non-Markovian models of absorption can then be incorporated by taking ψ(a) to be non-exponential. The marginal probability density for particle position X(t) prior to absorption depends on ψ and the joint probability density for the pair (X(t),A(t)) , also known as the occupation time propagator. In the case of normal diffusion one can use a Feynman–Kac formula to derive an evolution equation for the propagator. However, care must be taken when combining fractional diffusion with chemical reactions in the same medium. Therefore, we derive the occupation time propagator equation from first principles by taking the continuum limit of a heavy-tailed continuous-time random walk. We then use the solution of the propagator equation to investigate conditions under which the mean FPT for absorption within a trap is finite. We show that this depends on the choice of threshold density ψ
摘要在本文中，我们建立了一个基于相遇的反应-亚扩散模型，该模型在具有部分吸收的内部陷阱的Ω域中。我们假设粒子可以自由进出，但只在内部被吸收。我们认为吸收的概率取决于粒子在阱内停留的时间，这是由称为占用时间a (t)的布朗泛函指定的。吸收的第一次通过时间(FPT)被识别为占据时间超过随机阈值a的点，其概率密度为ψ (a)。非马尔可夫吸收模型可以通过取ψ (a)为非指数来合并。吸收前粒子位置X (t)的边际概率密度取决于ψ和粒子对(X (t)， A (t))的联合概率密度，也称为占用时间传播子。在正常扩散的情况下，可以用费曼-卡茨公式推导出传播子的演化方程。然而，当在同一介质中结合分式扩散和化学反应时，必须小心。因此，我们从第一性原理出发，通过取重尾连续时间随机漫步的连续极限，导出了占用时间传播方程。然后，我们使用传播方程的解来研究陷阱内吸收的平均FPT是有限的条件。我们证明这取决于阈值密度ψ (a)和次扩散率的选择。因此，正如先前在消失的反应-亚扩散模型中发现的那样，亚扩散过程和吸收过程是混合的。
{"title":"Encounter-based reaction-subdiffusion model II: partially absorbing traps and the occupation time propagator","authors":"Paul C Bressloff","doi":"10.1088/1751-8121/acfcf4","DOIUrl":"https://doi.org/10.1088/1751-8121/acfcf4","url":null,"abstract":"Abstract In this paper we develop an encounter-based model of reaction-subdiffusion in a domain Ω with a partially absorbing interior trap <?CDATA ${mathcal U}subset Omega$?> . We assume that the particle can freely enter and exit <?CDATA ${mathcal U}$?> , but is only absorbed within <?CDATA ${mathcal U}$?> . We take the probability of absorption to depend on the amount of time a particle spends within the trap, which is specified by a Brownian functional known as the occupation time A ( t ). The first passage time (FPT) for absorption is identified with the point at which the occupation time crosses a random threshold <?CDATA $widehat{A}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mover> <mml:mi>A</mml:mi> <mml:mo>ˆ</mml:mo> </mml:mover> </mml:math> with probability density <?CDATA $psi(a)$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>ψ</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> . Non-Markovian models of absorption can then be incorporated by taking <?CDATA $psi(a)$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>ψ</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> to be non-exponential. The marginal probability density for particle position <?CDATA $mathbf{X}(t)$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mi mathvariant=\"bold\">X</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> prior to absorption depends on ψ and the joint probability density for the pair <?CDATA $(mathbf{X}(t),A(t))$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mrow> <mml:mi mathvariant=\"bold\">X</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>,</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> , also known as the occupation time propagator. In the case of normal diffusion one can use a Feynman–Kac formula to derive an evolution equation for the propagator. However, care must be taken when combining fractional diffusion with chemical reactions in the same medium. Therefore, we derive the occupation time propagator equation from first principles by taking the continuum limit of a heavy-tailed continuous-time random walk. We then use the solution of the propagator equation to investigate conditions under which the mean FPT for absorption within a trap is finite. We show that this depends on the choice of threshold density <?CDATA $psi(a)$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>ψ</mml:mi> <mml:mo stretchy=\"fa","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135302601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1088/1751-8121/ad00ee
Nicolas Martzel
Abstract We first introduce the Zwanzig-Kawasaki version of the Generalized
Langevin Equation (GLE) and show as a preamble and under some hy-
pothesis about the relaxation of the fluctuations in the orthogonal sub-
space, that the commonly used term for the Markovian approximation
of the dissipation is rigorously vanishing, necessitating the use of the
next-order term, in an integral series we introduce. Independently, we
provide thereafter a comprehensive description of complex coarse-grained
molecules which, in addition to the classical positions and momenta of
their centers of mass, encompasses their shapes, angular momenta and
internal energies. The dynamics of these quantities is then derived as
the coarse-grained forces, torques, microscopic stresses, energy transfers,
from the coarse-grained potential built with their Berne-like anisotropic
interactions. By incorporating exhaustively the quadratic combinations of
the atomic degrees of freedom, this novel approach enriches considerably
the dynamics at the coarse-grained level and could serve as a foundation
for developing numerical models more holistic and accurate than Dissi-
pative Particle Dynamics (DPD) for the simulation of complex molecular
systems. This advancement opens up new possibilities for understand-
ing and predicting the behavior of such systems in various scientific and
engineering applications.
{"title":"Nonlinear Mori-Zwanzig theory and quadratic coarse-grained coordinates for complex molecular systems","authors":"Nicolas Martzel","doi":"10.1088/1751-8121/ad00ee","DOIUrl":"https://doi.org/10.1088/1751-8121/ad00ee","url":null,"abstract":"Abstract We first introduce the Zwanzig-Kawasaki version of the Generalized&#xD;Langevin Equation (GLE) and show as a preamble and under some hy-&#xD;pothesis about the relaxation of the fluctuations in the orthogonal sub-&#xD;space, that the commonly used term for the Markovian approximation&#xD;of the dissipation is rigorously vanishing, necessitating the use of the&#xD;next-order term, in an integral series we introduce. Independently, we&#xD;provide thereafter a comprehensive description of complex coarse-grained&#xD;molecules which, in addition to the classical positions and momenta of&#xD;their centers of mass, encompasses their shapes, angular momenta and&#xD;internal energies. The dynamics of these quantities is then derived as&#xD;the coarse-grained forces, torques, microscopic stresses, energy transfers,&#xD;from the coarse-grained potential built with their Berne-like anisotropic&#xD;interactions. By incorporating exhaustively the quadratic combinations of&#xD;the atomic degrees of freedom, this novel approach enriches considerably&#xD;the dynamics at the coarse-grained level and could serve as a foundation&#xD;for developing numerical models more holistic and accurate than Dissi-&#xD;pative Particle Dynamics (DPD) for the simulation of complex molecular&#xD;systems. This advancement opens up new possibilities for understand-&#xD;ing and predicting the behavior of such systems in various scientific and&#xD;engineering applications.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135304416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1088/1751-8121/acfc09
Giovanni Battista Carollo, Massimiliano Semeraro, Giuseppe Gonnella, Marco Zamparo
Abstract We study the large fluctuations of the work injected by the random force into a Brownian particle under the action of a confining harmonic potential. In particular, we compute analytically the rate function for generic uncorrelated initial conditions, showing that, depending on the initial spread, it can exhibit no, one, or two singularities associated to the onset of linear tails. A dependence on the potential strength is observed for large initial spreads (entailing two singularities), which is lost for stationary initial conditions (giving one singularity) and concentrated initial values (no singularity). We discuss the mechanism responsible for the singularities of the rate function, identifying it as a big jump in the initial values. Analytical results are corroborated by numerical simulations.
{"title":"Work fluctuations for a confined Brownian particle: the role of initial conditions","authors":"Giovanni Battista Carollo, Massimiliano Semeraro, Giuseppe Gonnella, Marco Zamparo","doi":"10.1088/1751-8121/acfc09","DOIUrl":"https://doi.org/10.1088/1751-8121/acfc09","url":null,"abstract":"Abstract We study the large fluctuations of the work injected by the random force into a Brownian particle under the action of a confining harmonic potential. In particular, we compute analytically the rate function for generic uncorrelated initial conditions, showing that, depending on the initial spread, it can exhibit no, one, or two singularities associated to the onset of linear tails. A dependence on the potential strength is observed for large initial spreads (entailing two singularities), which is lost for stationary initial conditions (giving one singularity) and concentrated initial values (no singularity). We discuss the mechanism responsible for the singularities of the rate function, identifying it as a big jump in the initial values. Analytical results are corroborated by numerical simulations.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135302750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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