Pub Date : 2024-07-30DOI: 10.1103/physreve.110.014610
Cristian Villalobos, María Luisa Cordero, Eric Clément, Rodrigo Soto
The properties of an active fluid, for example, a bacterial bath or a collection of microtubules and molecular motors, can be accessed through the dynamics of passive particle probes. Here, in the perspective of analyzing experimental situations of confinement in droplets, we consider the kinematics of a negatively buoyant probe particle in an active fluid, both confined within a spherical domain. The active bath generates a fluctuating flow that pushes the particle with a velocity that is modeled as a colored stochastic noise, characterized by two parameters, the intensity and memory time of the active flow. When the particle departs a little from the bottom of the spherical domain, the configuration is well approximated by a particle in a two-dimensional harmonic trap subjected to the colored noise, in which case an analytical solution exists, which is the base for quantitative analysis. We numerically simulate the dynamics of the particle and use the planar, two-dimensional mean square displacement to recover the activity parameters of the bath. This approach yields satisfactory results as long as the particle remains relatively confined; that is, as long as the intensity of the colored noise remains low.
{"title":"Recovering the activity parameters of an active fluid confined in a sphere","authors":"Cristian Villalobos, María Luisa Cordero, Eric Clément, Rodrigo Soto","doi":"10.1103/physreve.110.014610","DOIUrl":"https://doi.org/10.1103/physreve.110.014610","url":null,"abstract":"The properties of an active fluid, for example, a bacterial bath or a collection of microtubules and molecular motors, can be accessed through the dynamics of passive particle probes. Here, in the perspective of analyzing experimental situations of confinement in droplets, we consider the kinematics of a negatively buoyant probe particle in an active fluid, both confined within a spherical domain. The active bath generates a fluctuating flow that pushes the particle with a velocity that is modeled as a colored stochastic noise, characterized by two parameters, the intensity and memory time of the active flow. When the particle departs a little from the bottom of the spherical domain, the configuration is well approximated by a particle in a two-dimensional harmonic trap subjected to the colored noise, in which case an analytical solution exists, which is the base for quantitative analysis. We numerically simulate the dynamics of the particle and use the planar, two-dimensional mean square displacement to recover the activity parameters of the bath. This approach yields satisfactory results as long as the particle remains relatively confined; that is, as long as the intensity of the colored noise remains low.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-07-30DOI: 10.1103/physreve.110.015002
Théophile Rémond, Vincent Dolique, Renaud G. Rinaldi, Jean-Christophe Géminard
We report on an experimental study of the normal impact on a solid surface of a table tennis ball that rotates around its linear velocity vector. We observe that the ratio of the reflected velocity to the incident velocity does not depend on the initial spin. In contrast, the reflected spin depends not only on the incident spin but also on the incident velocity. The experimental results, which reveal the tricky role played by the friction in the region of contact, are accounted for by simple theoretical arguments.
{"title":"Normal impact of a ball rotating around its linear velocity","authors":"Théophile Rémond, Vincent Dolique, Renaud G. Rinaldi, Jean-Christophe Géminard","doi":"10.1103/physreve.110.015002","DOIUrl":"https://doi.org/10.1103/physreve.110.015002","url":null,"abstract":"We report on an experimental study of the normal impact on a solid surface of a table tennis ball that rotates around its linear velocity vector. We observe that the ratio of the reflected velocity to the incident velocity does not depend on the initial spin. In contrast, the reflected spin depends not only on the incident spin but also on the incident velocity. The experimental results, which reveal the tricky role played by the friction in the region of contact, are accounted for by simple theoretical arguments.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-07-29DOI: 10.1103/physreve.110.014145
Ryan Buechele, Jesse Berezovsky
The organization of disordered sounds into the ordered structures of music can be understood through an analogy to the emergent ordering of physical systems undergoing phase transitions. This work builds off a prior mean-field model for pitch in music [J. Berezovsky, Sci. Adv.5, eaav8490 (2019)] by using renormalization-group techniques to study the effects of dimensionality and local correlations. We corroborate the results of the mean-field model by showing convergence of the phase diagram as lattice dimension is increased, while also uncovering new phases which the mean-field model does not reveal. We also compute the nearest-neighbor correlations and provide comparisons to the mean-field model, as well as historical tuning systems used by different groups of musicians. The new phases and resulting correlations revealed in this work suggest a number of possible avenues for further exploration, including generating new music using the pitch distributions suggested by the model.
{"title":"Renormalization-group approach to ordered phases in music","authors":"Ryan Buechele, Jesse Berezovsky","doi":"10.1103/physreve.110.014145","DOIUrl":"https://doi.org/10.1103/physreve.110.014145","url":null,"abstract":"The organization of disordered sounds into the ordered structures of music can be understood through an analogy to the emergent ordering of physical systems undergoing phase transitions. This work builds off a prior mean-field model for pitch in music [J. Berezovsky, <span>Sci. Adv.</span> <b>5</b>, eaav8490 (2019)] by using renormalization-group techniques to study the effects of dimensionality and local correlations. We corroborate the results of the mean-field model by showing convergence of the phase diagram as lattice dimension is increased, while also uncovering new phases which the mean-field model does not reveal. We also compute the nearest-neighbor correlations and provide comparisons to the mean-field model, as well as historical tuning systems used by different groups of musicians. The new phases and resulting correlations revealed in this work suggest a number of possible avenues for further exploration, including generating new music using the pitch distributions suggested by the model.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-07-29DOI: 10.1103/physreve.110.014213
J. Montes, F. J. Arranz, F. Borondo
The Maslov index of a periodic orbit is an important piece in the semiclassical quantization of nonintegrable systems, while almost all existing techniques that lead to a rigorous calculation of this index are elaborate and mathematically demanding. In this paper, we describe a straightforward technique, for systems with two degrees of freedom, based on the Lagrangian descriptors. Our method is illustrated by applying it to the two-dimensional coupled quartic oscillator.
{"title":"Using Lagrangian descriptors to calculate the Maslov index of periodic orbits","authors":"J. Montes, F. J. Arranz, F. Borondo","doi":"10.1103/physreve.110.014213","DOIUrl":"https://doi.org/10.1103/physreve.110.014213","url":null,"abstract":"The Maslov index of a periodic orbit is an important piece in the semiclassical quantization of nonintegrable systems, while almost all existing techniques that lead to a rigorous calculation of this index are elaborate and mathematically demanding. In this paper, we describe a straightforward technique, for systems with two degrees of freedom, based on the Lagrangian descriptors. Our method is illustrated by applying it to the two-dimensional coupled quartic oscillator.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-07-29DOI: 10.1103/physreve.110.014144
Marcin Łobejko, Marek Winczewski, Gerardo Suárez, Robert Alicki, Michał Horodecki
If a quantum system interacts with the environment, then the Hamiltonian acquires a correction known as the Lamb-shift term. There are two other corrections to the Hamiltonian, related to the stationary state. Namely, the stationary state is to first approximation a Gibbs state with respect to original Hamiltonian. However, if we have finite coupling, then the true stationary state will be different, and regarding it as a Gibbs state to some effective Hamiltonian, one can extract a correction, which is called “steady-state” correction. Alternatively, one can take a static point of view, and consider the reduced state of total equilibrium state, i.e., system plus bath Gibbs state. The extracted Hamiltonian correction is called the “mean-force” correction. This paper presents several analytical results on second-order corrections (in coupling strength) of the three types mentioned above. Instead of the steady state, we focus on a state annihilated by the Liouvillian of the master equation, labeling it as the “quasi-steady state.” Specifically, we derive a general formula for the mean-force correction as well as the quasi-steady state and Lamb-shift correction for a general class of master equations. Furthermore, specific formulas for corrections are obtained for the Davies, Bloch-Redfield, and cumulant equation (refined weak coupling). In particular, the cumulant equation serves as a case study of the Liouvillian, featuring a nontrivial fourth-order generator. This generator forms the basis for calculating the diagonal quasi-steady-state correction. We consider spin-boson model as an example, and in addition to using our formulas for corrections, we consider mean-force correction from reaction-coordinate approach.
{"title":"Corrections to the Hamiltonian induced by finite-strength coupling to the environment","authors":"Marcin Łobejko, Marek Winczewski, Gerardo Suárez, Robert Alicki, Michał Horodecki","doi":"10.1103/physreve.110.014144","DOIUrl":"https://doi.org/10.1103/physreve.110.014144","url":null,"abstract":"If a quantum system interacts with the environment, then the Hamiltonian acquires a correction known as the Lamb-shift term. There are two other corrections to the Hamiltonian, related to the stationary state. Namely, the stationary state is to first approximation a Gibbs state with respect to original Hamiltonian. However, if we have finite coupling, then the true stationary state will be different, and regarding it as a Gibbs state to some effective Hamiltonian, one can extract a correction, which is called “steady-state” correction. Alternatively, one can take a static point of view, and consider the reduced state of total equilibrium state, i.e., system plus bath Gibbs state. The extracted Hamiltonian correction is called the “mean-force” correction. This paper presents several analytical results on second-order corrections (in coupling strength) of the three types mentioned above. Instead of the steady state, we focus on a state annihilated by the Liouvillian of the master equation, labeling it as the “quasi-steady state.” Specifically, we derive a general formula for the mean-force correction as well as the quasi-steady state and Lamb-shift correction for a general class of master equations. Furthermore, specific formulas for corrections are obtained for the Davies, Bloch-Redfield, and cumulant equation (refined weak coupling). In particular, the cumulant equation serves as a case study of the Liouvillian, featuring a nontrivial fourth-order generator. This generator forms the basis for calculating the diagonal quasi-steady-state correction. We consider spin-boson model as an example, and in addition to using our formulas for corrections, we consider mean-force correction from reaction-coordinate approach.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-07-29DOI: 10.1103/physreve.110.014306
Onkar Sadekar, Andrea Civilini, Jesús Gómez-Gardeñes, Vito Latora, Federico Battiston
The emergence of collective cooperation in competitive environments is a well-known phenomenon in biology, economics, and social systems. While most evolutionary game models focus on the evolution of strategies for a fixed game, how strategic decisions coevolve with the environment has so far mostly been overlooked. Here, we consider a game selection model where not only the strategies but also the game can change over time following evolutionary principles. Our results show that coevolutionary dynamics of games and strategies can induce novel collective phenomena, fostering the emergence of cooperative environments. When the model is taken on structured populations the architecture of the interaction network can significantly amplify pro-social behavior, with a critical role played by network heterogeneity and the presence of clustered groups of similar players, distinctive features observed in real-world populations. By unveiling the link between the evolution of strategies and games for different structured populations, our model sheds new light on the origin of social dilemmas ubiquitously observed in real-world social systems.
{"title":"Evolutionary game selection creates cooperative environments","authors":"Onkar Sadekar, Andrea Civilini, Jesús Gómez-Gardeñes, Vito Latora, Federico Battiston","doi":"10.1103/physreve.110.014306","DOIUrl":"https://doi.org/10.1103/physreve.110.014306","url":null,"abstract":"The emergence of collective cooperation in competitive environments is a well-known phenomenon in biology, economics, and social systems. While most evolutionary game models focus on the evolution of strategies for a fixed game, how strategic decisions coevolve with the environment has so far mostly been overlooked. Here, we consider a game selection model where not only the strategies but also the game can change over time following evolutionary principles. Our results show that coevolutionary dynamics of games and strategies can induce novel collective phenomena, fostering the emergence of cooperative environments. When the model is taken on structured populations the architecture of the interaction network can significantly amplify pro-social behavior, with a critical role played by network heterogeneity and the presence of clustered groups of similar players, distinctive features observed in real-world populations. By unveiling the link between the evolution of strategies and games for different structured populations, our model sheds new light on the origin of social dilemmas ubiquitously observed in real-world social systems.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-07-29DOI: 10.1103/physreve.110.014142
Stephen Whitelam
The Jarzynski equality allows the calculation of free-energy differences using values of work measured from nonequilibrium trajectories. The number of trajectories required to accurately estimate free-energy differences in this way grows sharply with the size of work fluctuations, motivating the search for protocols that perform desired transformations with minimum work. However, protocols of this nature can involve varying temperature, to which the Jarzynski equality does not apply. We derive a variant of the Jarzynski equality that applies to varying-temperature protocols, and show that it can have better convergence properties than the standard version of the equality. We derive this modified equality and the associated fluctuation relation within the framework of Markovian stochastic dynamics, complementing related derivations done within the framework of Hamiltonian dynamics.
{"title":"Free-energy estimates from nonequilibrium trajectories under varying-temperature protocols","authors":"Stephen Whitelam","doi":"10.1103/physreve.110.014142","DOIUrl":"https://doi.org/10.1103/physreve.110.014142","url":null,"abstract":"The Jarzynski equality allows the calculation of free-energy differences using values of work measured from nonequilibrium trajectories. The number of trajectories required to accurately estimate free-energy differences in this way grows sharply with the size of work fluctuations, motivating the search for protocols that perform desired transformations with minimum work. However, protocols of this nature can involve varying temperature, to which the Jarzynski equality does not apply. We derive a variant of the Jarzynski equality that applies to varying-temperature protocols, and show that it can have better convergence properties than the standard version of the equality. We derive this modified equality and the associated fluctuation relation within the framework of Markovian stochastic dynamics, complementing related derivations done within the framework of Hamiltonian dynamics.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-07-29DOI: 10.1103/physreve.110.014143
Jong-Min Park, Hyunggyu Park, Jae Sung Lee
The conventional Langevin equation offers a mathematically convenient framework for investigating open stochastic systems interacting with their environment or a bath. However, it is not suitable for a wide variety of systems whose dynamics rely on the nature of the environmental interaction, as the equation does not incorporate any specific information regarding that interaction. Here, we present a stochastic differential equation (SDE) for an open system coupled to a thermostatic bath via an arbitrary interaction Hamiltonian. This SDE encodes the interaction information to a fictitious potential (mean force) and a position-dependent damping coefficient. Surprisingly, we find that the conventional Langevin equation can be recovered in the presence of arbitrary strong interactions given two conditions: translational invariance of the potential and mutual independence of baths. Our results provide a comprehensive framework for studying open stochastic systems with an arbitrary interaction Hamiltonian and yield deeper insight into why various experiments fit the conventional Langevin description regardless of the strength or type of interaction.
{"title":"Stochastic differential equation for a system coupled to a thermostatic bath via an arbitrary interaction Hamiltonian","authors":"Jong-Min Park, Hyunggyu Park, Jae Sung Lee","doi":"10.1103/physreve.110.014143","DOIUrl":"https://doi.org/10.1103/physreve.110.014143","url":null,"abstract":"The conventional Langevin equation offers a mathematically convenient framework for investigating open stochastic systems interacting with their environment or a bath. However, it is not suitable for a wide variety of systems whose dynamics rely on the nature of the environmental interaction, as the equation does not incorporate any specific information regarding that interaction. Here, we present a stochastic differential equation (SDE) for an open system coupled to a thermostatic bath via an arbitrary interaction Hamiltonian. This SDE encodes the interaction information to a fictitious potential (mean force) and a position-dependent damping coefficient. Surprisingly, we find that the conventional Langevin equation can be recovered in the presence of arbitrary strong interactions given two conditions: translational invariance of the potential and mutual independence of baths. Our results provide a comprehensive framework for studying open stochastic systems with an arbitrary interaction Hamiltonian and yield deeper insight into why various experiments fit the conventional Langevin description regardless of the strength or type of interaction.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-07-26DOI: 10.1103/physreve.110.l012204
Vijay Ganesh Sadhasivam, Andrew C. Hunt, Lars Meuser, Yair Litman, Stuart C. Althorpe
Quantum scrambling often gives rise to short-time exponential growth in out-of-time-ordered correlators. The scrambling rate over an isolated saddle point at finite temperature is shown here to be reduced by a hierarchy of quenching processes. Two of these appear in the classical limit, where escape from the neighborhood of the saddle reduces the rate by a factor of two, and thermal fluctuations around the saddle reduce it further; a third process can be explained semiclassically as arising from quantum thermal fluctuations around the saddle, which are also responsible for imposing the Maldacena-Shenker-Stanford bound.
{"title":"Thermal quenching of classical and semiclassical scrambling","authors":"Vijay Ganesh Sadhasivam, Andrew C. Hunt, Lars Meuser, Yair Litman, Stuart C. Althorpe","doi":"10.1103/physreve.110.l012204","DOIUrl":"https://doi.org/10.1103/physreve.110.l012204","url":null,"abstract":"Quantum scrambling often gives rise to short-time exponential growth in out-of-time-ordered correlators. The scrambling rate over an isolated saddle point at finite temperature is shown here to be reduced by a hierarchy of quenching processes. Two of these appear in the classical limit, where escape from the neighborhood of the saddle reduces the rate by a factor of two, and thermal fluctuations around the saddle reduce it further; a third process can be explained semiclassically as arising from quantum thermal fluctuations around the saddle, which are also responsible for imposing the Maldacena-Shenker-Stanford bound.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-07-26DOI: 10.1103/physreve.110.014140
Stéphane Ouvry, Alexios P. Polychronakos
We present the microscopic formulation of inclusion statistics, a counterpoint to exclusion statistics in which particles tend to coalesce more than ordinary bosons. We derive the microscopic occupation multiplicities of one-body quantum states and show that they factorize into a product of clusters of neighboring occupied states with enhanced statistical weights. Applying this statistics to a one-dimensional gas of particles in a harmonic well leads to a Calogero-like -body inclusion spectrum with interesting physical properties.
我们提出了包容统计的微观表述，它是排斥统计的对立面，在排斥统计中，粒子比普通玻色子更倾向于凝聚在一起。我们推导出单体量子态的微观占据乘数，并证明它们因数化为具有增强统计权重的相邻占据态群的乘积。将这一统计量应用于谐波井中的一维粒子气体，就会产生具有有趣物理特性的类似卡洛吉罗的 n 体包含谱。
{"title":"Microscopic inclusion statistics in a discrete one-body spectrum","authors":"Stéphane Ouvry, Alexios P. Polychronakos","doi":"10.1103/physreve.110.014140","DOIUrl":"https://doi.org/10.1103/physreve.110.014140","url":null,"abstract":"We present the microscopic formulation of inclusion statistics, a counterpoint to exclusion statistics in which particles tend to coalesce more than ordinary bosons. We derive the microscopic occupation multiplicities of one-body quantum states and show that they factorize into a product of clusters of neighboring occupied states with enhanced statistical weights. Applying this statistics to a one-dimensional gas of particles in a harmonic well leads to a Calogero-like <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>n</mi></math>-body inclusion spectrum with interesting physical properties.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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