{"title":"Complete positivity and thermal relaxation in quadratic quantum master equations.","authors":"F Nicacio, T Koide","doi":"10.1103/PhysRevE.110.054116","DOIUrl":"https://doi.org/10.1103/PhysRevE.110.054116","url":null,"abstract":"<p><p>The ultimate goal of this paper is to develop a systematic method for deriving quantum master equations that satisfy the requirements of a completely positive and trace-preserving (CPTP) map, further describing thermal relaxation processes. In this paper, we assume that the quantum master equation is obtained through the canonical quantization of the generalized Brownian motion proposed in our recent paper [T. Koide and F. Nicacio, Phys. Lett. A 494, 129277 (2024)0375-960110.1016/j.physleta.2023.129277]. At least classically, this dynamics describes the thermal relaxation process regardless of the choice of the system Hamiltonian. The remaining task is to identify the parameters ensuring that the quantum master equation meets complete positivity. We limit our discussion to many-body quadratic Hamiltonians and establish a CPTP criterion for our quantum master equation. This criterion is useful for applying our quantum master equation to models with interaction such as a network model, which has been used to investigate how quantum effects modify heat conduction.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054116"},"PeriodicalIF":2.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142847345","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}
Oluwafemi P Adejumobi, Vladimir N Mantsevich, Vladimir V Palyulin
{"title":"Diffusion of fast and slow excitons with an exchange in quasi-two-dimensional systems.","authors":"Oluwafemi P Adejumobi, Vladimir N Mantsevich, Vladimir V Palyulin","doi":"10.1103/PhysRevE.110.054139","DOIUrl":"https://doi.org/10.1103/PhysRevE.110.054139","url":null,"abstract":"<p><p>By means of analytical calculations and numerical simulations, we study the diffusion properties in quasi-two-dimensional structures with two exciton subsystems with an exchange between them. The experimental realization is possible in systems where fast and slow exciton subsystems appear. For substantially different diffusion coefficients of the species, the negative diffusion can be observed if one measures the transport properties of only a single subsystem, just as was obtained in experimental studies for quasi-two-dimensional semiconductor systems. The initial transition from a fast subsystem to a slow one results in a delayed release of fast excitons in the area close to the original excitation spot. Hence, the signal from the fast excitons alone includes the delayed replenishment from the transition of slow quasiparticles. This is seen as the narrowing of the exciton density profile or decrease of mean-squared displacement which is then interpreted as a negative diffusion. We show that the analytical theory matches the available experimental data for negative diffusion quite well. The average diffusion coefficients for the combined population are analytically expressed through the diffusion coefficients of fast and slow excitons. Simple analytical expressions for effective diffusion coefficients obtained in limiting cases are of interest both for theoretical and experimental analysis of not only the exciton transport, but also for a variety of systems, where fast and slow moving subsystems are present.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054139"},"PeriodicalIF":2.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142847351","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}
Gianmarco Zanardi, Paolo Bettotti, Jules Morand, Lorenzo Pavesi, Luca Tubiana
{"title":"Metaplasticity and memory in multilevel recurrent feed-forward networks.","authors":"Gianmarco Zanardi, Paolo Bettotti, Jules Morand, Lorenzo Pavesi, Luca Tubiana","doi":"10.1103/PhysRevE.110.054304","DOIUrl":"https://doi.org/10.1103/PhysRevE.110.054304","url":null,"abstract":"<p><p>Network systems can exhibit memory effects in which the interactions between different pairs of nodes adapt in time, leading to the emergence of preferred connections, patterns, and subnetworks. To a first approximation, this memory can be modeled through a \"plastic\" Hebbian or homophily mechanism, in which edges get reinforced proportionally to the amount of information flowing through them. However, recent studies on glia-neuron networks have highlighted how memory can evolve due to more complex dynamics, including multilevel network structures and \"metaplastic\" effects that modulate reinforcement. Inspired by those systems, here we develop a simple and general model for the dynamics of an adaptive network with an additional metaplastic mechanism that varies the rate of Hebbian strengthening of its edge connections. The metaplastic term acts on a second network level in which edges are grouped together, simulating local, longer timescale effects. Specifically, we consider a biased random walk on a cyclic feed-forward network. The random walk chooses its steps according to the weights of the network edges. The weights evolve through a Hebbian mechanism modulated by a metaplastic reinforcement, biasing the walker to prefer edges that have been already explored. We study the dynamical emergence (memorization) of preferred paths and their retrieval and identify three regimes: one dominated by the Hebbian term, one in which the metareinforcement drives memory formation, and a balanced one. We show that, in the latter two regimes, metareinforcement allows the retrieval of a previously stored path even after the weights have been reset to zero to erase Hebbian memory.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054304"},"PeriodicalIF":2.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142847398","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}
{"title":"Recurrence solution of monomer-polymer models on two-dimensional rectangular lattices.","authors":"Yong Kong","doi":"10.1103/PhysRevE.110.054135","DOIUrl":"https://doi.org/10.1103/PhysRevE.110.054135","url":null,"abstract":"<p><p>The problem of counting polymer coverings on rectangular lattices is investigated. In this model, a linear rigid polymer covers k adjacent lattice sites such that no two polymers occupy a common site. Those unoccupied lattice sites are considered as monomers. We prove that for a given number of polymers (k-mers), the number of arrangements for the polymers on two-dimensional rectangular lattices satisfies simple recurrence relations. These recurrence relations are quite general and apply for arbitrary polymer length (k) and the width of the lattices (n). The well-studied monomer-dimer problem is a special case of the monomer-polymer model when k=2. It is known the enumeration of monomer-dimer configurations in planar lattices is #P complete. The recurrence relations shown here have the potential for hints for the solution of long-standing problems in this class of computational complexity.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054135"},"PeriodicalIF":2.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142847546","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}
{"title":"Scaling behavior of cross-entropy loss in the identification of percolation phase transitions.","authors":"Huiyao Li, Yu Zhao, Bo Yang","doi":"10.1103/PhysRevE.110.054133","DOIUrl":"https://doi.org/10.1103/PhysRevE.110.054133","url":null,"abstract":"<p><p>The cross-entropy loss function is widely used in machine learning to measure the performance of a classification model. Interestingly, our study find that this function has scaling behavior when deep neural networks are used to investigate percolation models. Specifically, we use convolutional neural networks with different pooling methods to study the site percolation on square lattices under two labeling methods (labeling based on spanning cluster and the exact solution of the critical point). Subsequently, graph convolutional neural networks (GCNs) with different pooling methods are utilized to do the same kind of experiment. Finally, the GCN with different pooling methods is used to study the percolation phase transitions on the Erdős-Rényi (ER) networks under labeling based on the critical point. The reliability of the classifiers is detected by the values of the critical point p_{c} and critical exponent ν which are obtained by the scaling behaviors of the percolation probability. The results demonstrate that the scaling exponent of cross-entropy ψ/ν depends on the labeling and pooling methods. Labeling based on critical points, which is equivalent to labeling based on spanning clusters in infinite systems, can be used to investigate the critical behaviors in finite systems. SAGPooling-Mean is an effective pooling method to study the scaling behavior of cross-entropy loss on two-dimensional square lattices and ER networks.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054133"},"PeriodicalIF":2.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142847563","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}
{"title":"Effect of external potential on the energy transport in harmonically driven segmented Frenkel-Kontorova lattices.","authors":"M Romero-Bastida","doi":"10.1103/PhysRevE.110.054115","DOIUrl":"https://doi.org/10.1103/PhysRevE.110.054115","url":null,"abstract":"<p><p>Thermal resonance, that is, the heat flux obtained by means of a periodic external driving, offers the possibility of controlling heat flux in nanoscale devices suitable for power generation, cooling, and thermoelectrics, among others. In this work we study the effect of the onsite potential period on the thermal resonance phenomenon present in a one-dimensional system composed of two dissimilar Frenkel-Kontorova lattices connected by a time-modulated coupling and in contact with two heat reservoirs operating at different temperature by means of molecular dynamics simulations. When the periods of the onsite potential on both sides of the system are equal, the maximum resonance is obtained for the lowest considered value of the period. For highly structurally asymmetric lattices, the heat flux toward the cold reservoir is maximized, and asymmetric periods of the onsite potential afford an extra way to control the magnitude of the heat fluxes in each side of the system. Our results highlight the importance of the substrate structure on thermal resonance and could inspire further developments in designing thermal devices.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054115"},"PeriodicalIF":2.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142847212","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}
{"title":"Current-vortex-sheet model of the magnetic Rayleigh-Taylor instability.","authors":"Seunghyeon Baek, Sung-Ik Sohn","doi":"10.1103/PhysRevE.110.055102","DOIUrl":"https://doi.org/10.1103/PhysRevE.110.055102","url":null,"abstract":"<p><p>This study investigates the Rayleigh-Taylor instability in the magnetic field applied parallel to the interface. The motion of the interface is described using a current-vortex-sheet model. The growth rate of the interface is obtained from a linear stability analysis of the model. The interface of a single mode k=1 is linearly stable for R_{A}≤1, where R_{A} denotes the Alfvén number. Further, we conduct numerical computations for the evolution of the interface from the model for both regimes of R_{A}≤1 and R_{A}>1. For R_{A}≤1, the interface oscillates vertically but does not intrude into the opposite phase. The amplitude of the interface and the oscillation period decrease with decrease in R_{A}. For 1<R_{A}≲1.5, the interface undergoes some growth at early times and then decreases. This oscillation is repeated, and no roll-ups are observed at the interface. Therefore, the nonlinear growth of the Rayleigh-Taylor instability is stabilized by a sufficiently strong magnetic field. For R_{A}≳3 the interface is unstable and the pattern of the interface evolution differs from the density ratio. In addition, the magnetic field is greatly amplified as R_{A} increases.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-2","pages":"055102"},"PeriodicalIF":2.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142847302","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}
{"title":"Narrow escape with imperfect reactions.","authors":"Anıl Cengiz, Sean D Lawley","doi":"10.1103/PhysRevE.110.054127","DOIUrl":"https://doi.org/10.1103/PhysRevE.110.054127","url":null,"abstract":"<p><p>The imperfect narrow escape problem considers the mean first passage time (MFPT) of a Brownian particle through one of several small, partially reactive traps on an otherwise reflecting boundary within a confining domain. Mathematically, this problem is equivalent to Poisson's equation with mixed Neumann-Robin boundary conditions. Here, we obtain this MFPT in general three-dimensional domains by using strong localized perturbation theory in the small trap limit. These leading-order results involve factors, which are analogous to electrostatic capacitances, and we use Brownian local time theory and kinetic Monte Carlo (KMC) algorithms to rapidly compute these factors. Furthermore, we use a heuristic approximation of such a capacitance to obtain a simple, approximate MFPT, which is valid for any trap reactivity. In addition, we develop KMC algorithms to efficiently simulate the full problem and find excellent agreement with our asymptotic approximations.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054127"},"PeriodicalIF":2.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142847409","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}
{"title":"Evidence that the de Almeida-Thouless transition disappears below six dimensions.","authors":"Bharadwaj Vedula, M A Moore, Auditya Sharma","doi":"10.1103/PhysRevE.110.054131","DOIUrl":"https://doi.org/10.1103/PhysRevE.110.054131","url":null,"abstract":"<p><p>One of the key predictions of Parisi's broken replica symmetry theory of spin glasses is the existence of a phase transition in an applied field to a state with broken replica symmetry. This transition takes place at the de Almeida-Thouless (AT) line in the h-T plane. We have studied this line in the power-law diluted Heisenberg spin glass in which the probability that two spins separated by a distance r interact with each other falls as 1/r^{2σ}. In the presence of a random vector field of variance h_{r}^{2} the phase transition is in the universality class of the Ising spin glass in a field. Tuning σ is equivalent to changing the dimension d of the short-range system, with the relation being d=2/(2σ-1) for σ<2/3. We have found by numerical simulations that h_{AT}^{2}∼(2/3-σ) implying that the AT line does not exist below six dimensions and that the Parisi scheme is not appropriate for spin glasses in three dimensions.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054131"},"PeriodicalIF":2.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142847229","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}
{"title":"Emergence of self-organized criticality and phase transition in the Olami-Feder-Christensen model with a single defect.","authors":"Tetsuto Otani, Nobuki Kame","doi":"10.1103/PhysRevE.110.054129","DOIUrl":"https://doi.org/10.1103/PhysRevE.110.054129","url":null,"abstract":"<p><p>We examine the conditions for the emergence of self-organized criticality in the Olami-Feder-Christensen model by introducing a single defect under periodic boundary conditions. Our findings reveal that strong localized energy dissipation is crucial for self-organized criticality emergence, while weak localized or global energy dissipation leads to its disappearance in this model. Furthermore, slight dissipation perturbations to a system in a self-organized criticality reveal a novel state characterized by a limit cycle of distinct configurations. This newly discovered state offers significant insights into the fundamental mechanisms governing the emergence of self-organized criticality.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054129"},"PeriodicalIF":2.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142847251","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}