arXiv subjects

J. G. Brankov

Publications and source records attributed to J. G. Brankov.

17 recordsLinked to original sources

arXiv2019

One-dimensional discrete aggregation-fragmentation model

We study here one-dimensional model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time kinetics of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) on open chains. Isolated particles and the first particle of a cluster of particles hop one site forward with probability $p$; when the first particle of a cluster hops, the remaining particles of the same cluster may hop with a modified probability $p_m$, modelling a special kinematic interaction between neighboring particles, or remain in place with probability $1-p_m$. The model contains as special cases the TASEP with parallel update ($p_m =0$) and with sequential backward-ordered update ($p_m =p$). These cases have been exactly solved for the stationary states and their properties thoroughly studied. The limiting case of $p_m =1$, which corresponds to irreversible aggregation, has been recently studied too. Its phase diagram in the plane of injection ($α$) and ejection ($β$) probabilities was found to have a different topology. Here we focus on the stationary properties of the gTASEP in the generic case of attraction $p<p_m<1$ when aggregation-fragmentation of clusters occurs. We find that the topology of the phase diagram at $p_m =1$ changes sharply to the one corresponding to $p_m =p$ as soon as $p_m$ becomes less than $1$. Then a maximum current phase appears in the square domain $α_c(p,p_m)\leα\le 1$ and $β_c(p,p_m) \le β\le 1$, where $α_c(p,p_m)= β_c(p,p_m)\equiv σ_c(p,p_m)$ are parameter-dependent injection/ejection critical values. The properties of the phase transitions between the three stationary phases at $p< p_m <1$ are assessed by computer simulations and random walk theory.

cond-mat.stat-mech↗

arXiv2017

A model of irreversible jam formation in dense traffic

We study an one-dimensional stochastic model of vehicular traffic on open segments of a single-lane road of finite size $L$. The vehicles obey a stochastic discrete-time dynamics which is a limiting case of the generalized Totally Asymmetric Simple Exclusion Process. This dynamics has been previously used by Bunzarova and Pesheva [Phys. Rev. E 95, 052105 (2017)] for an one-dimensional model of irreversible aggregation. The model was shown to have three stationary phases: a many-particle one, MP, a phase with completely filled configuration, CF, and a boundary perturbed MP+CF phase, depending on the values of the particle injection ($α$), ejection ($β$) and hopping ($p$) probabilities. Here we extend the results for the stationary properties of the MP+CF phase, by deriving exact expressions for the local density at the first site of the chain and the probability P(1) of a completely jammed configuration. The unusual phase transition, characterized by jumps in both the bulk density and the current (in the thermodynamic limit), as $α$ crosses the boundary $α=p$ from the MP to the CF phase, is explained by the finite-size behavior of P(1). By using a random walk theory, we find that, when $α$ approaches from below the boundary $α=p$, three different regimes appear, as the size $L\rightarrow \infty$: (i) the lifetime of the gap between the rightmost clusters is of the order $O(L)$ in the MP phase; (ii) small jams, separated by gaps with lifetime $O(1)$, exist in the MP+CF phase close to the left chain boundary; and (iii) when $β=p$, the jams are divided by gaps with lifetime of the order $O(L^{1/2})$. These results are supported by extensive Monte Carlo calculations.

cond-mat.stat-mech↗

arXiv2015

On the appearance of traffic jams in a long chain with a shortcut in the bulk

The appearance of traffic jams on chains with a shunted section between two simple chain segments in the maximum current phase is studied in the framework of the Totally Asymmetric Simple Exclusion Process. The conditions for the occurrence of this phenomenon are investigated both within the effective rates approximation and numerically for arbitrary length of the shortcut. The problem is interesting on its own because the conditions for coexistence of low- and high density phases are essentially different from those for a simple chain between two reservoirs. Our main results are: (1) For any values of the external rates in the domain of the maximum current phase, there exists a position of the shortcut where the shunted segment is in a phase of coexistence with a completely delocalized domain wall; (2) The main features of the coexistence phase and the density profiles in the whole network are well described by the domain wall theory. Apart from the negligible inter-chain correlations, they depend only on the current through the shortcut; (3) The model displays an unexpected feature: the current through the longer shunted segment is larger than the current through the shortcut; (4) From the viewpoint of vehicular traffic, most comfortable conditions for the drivers are provided when the shortcut is shifted downstream from the position of coexistence, when both the shunted segment and the shortcut exhibit low-density lamellar flow. Most unfavorable is the opposite case of upstream shifted shortcut, when both the shunted segment and the shortcut are in a high-density phase describing congested traffic of slowly moving cars. The above results are relevant also to phenomena like crowding of molecular motors moving along twisted protofilaments.

cond-mat.stat-mech↗

arXiv2015

Non-contractible loops in the dense O(n) loop model on the cylinder

A lattice model of critical dense polymers $O(0)$ is considered for the finite cylinder geometry. Due to the presence of non-contractible loops with a fixed fugacity $ξ$, the model is a generalization of the critical dense polymers solved by Pearce, Rasmussen and Villani. We found the free energy for any height $N$ and circumference $L$ of the cylinder. The density $ρ$ of non-contractible loops is found for $N \rightarrow \infty$ and large $L$. The results are compared with those obtained for the anisotropic quantum chain with twisted boundary conditions. Using the latter method we obtained $ρ$ for any $O(n)$ model and an arbitrary fugacity.

cond-mat.stat-mech↗

arXiv2014

Transfer matrix for spanning trees, webs and colored forests

We use the transfer matrix formalism for dimers proposed by Lieb, and generalize it to address the corresponding problem for arrow configurations (or trees) associated to dimer configurations through Temperley's correspondence. On a cylinder, the arrow configurations can be partitioned into sectors according to the number of non-contractible loops they contain. We show how Lieb's transfer matrix can be adapted in order to disentangle the various sectors and to compute the corresponding partition functions. In order to address the issue of Jordan cells, we introduce a new, extended transfer matrix, which not only keeps track of the positions of the dimers, but also propagates colors along the branches of the associated trees. We argue that this new matrix contains Jordan cells.

cond-mat.stat-mech↗

arXiv2013

New Inequalities in Equilibrium Statistical Mechanics

Recently, new thermodynamic inequalities have been obtained, which set bounds on the quadratic fluctuations of intensive observables of statistical mechanical systems in terms of the Bogoliubov - Duhamel inner product and some thermal average values. It was shown that several well-known inequalities in equilibrium statistical mechanics emerge as special cases of these results. On the basis of the spectral representation, lower and upper bounds on the one-sided fidelity susceptibility were derived in analogous terms. Here, these results are reviewed and presented in a unified manner. In addition, the spectral representation of the symmetric two-sided fidelity susceptibility is derived, and it is shown to coincide with the one-sided case. Therefore, both definitions imply the same lower and upper bounds on the fidelity susceptibility.

quant-ph↗

arXiv2012

Some inequalities in the fidelity approach to phase transitions

We present some aspects of the fidelity approach to phase transitions based on lower and upper bounds on the fidelity susceptibility that are expressed in terms of thermodynamic quantities. Both commutative and non commutative cases are considered. In the commutative case, in addition, a relation between the fidelity and the nonequilibrium work done on the system in a process from an equilibrium initial state to an equilibrium final state has been obtained by using the Jarzynski equality.

cond-mat.stat-mech↗

arXiv2012

Lower and upper bounds on the fidelity susceptibility

We derive upper and lower bounds on the fidelity susceptibility in terms of macroscopic thermodynamical quantities, like susceptibilities and thermal average values. The quality of the bounds is checked by the exact expressions for a single spin in an external magnetic field. Their usefulness is illustrated by two examples of many-particle models which are exactly solved in the thermodynamic limit: the Dicke superradiance model and the single impurity Kondo model. It is shown that as far as divergent behavior is considered, the fidelity susceptibility and the thermodynamic susceptibility are equivalent for a large class of models exhibiting critical behavior.

quant-ph↗

arXiv2011

Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method

Infinite sets of inequalities which generalize all the known inequalities that can be used in the majorization step of the Approximating Hamiltonian method are derived. They provide upper bounds on the difference between the quadratic fluctuations of intensive observables of a $N$-particle system and the corresponding Bogoliubov-Duhamel inner product. The novel feature is that, under sufficiently mild conditions, the upper bounds have the same form and order of magnitude with respect to $N$ for all the quantities derived by a finite number of commutations of an original intensive observable with the Hamiltonian. The results are illustrated on two types of exactly solvable model systems: one with bounded separable attraction and the other containing interaction of a boson field with matter.

math-ph↗

arXiv2008

Two-dimensional spanning webs as (1,2) logarithmic minimal model

A lattice model of critical spanning webs is considered for the finite cylinder geometry. Due to the presence of cycles, the model is a generalization of the known spanning tree model which belongs to the class of logarithmic theories with central charge $c=-2$. We show that in the scaling limit the universal part of the partition function for closed boundary conditions at both edges of the cylinder coincides with the character of symplectic fermions with periodic boundary conditions and for open boundary at one edge and closed at the other coincides with the character of symplectic fermions with antiperiodic boundary conditions.

cond-mat.stat-mech↗

arXiv2008

One-Dimensional Traffic Flow Models: Theory and Computer Simulations

Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion process (TASEP) with open boundary conditions: particles are injected at the left end with rate alpha and removed at the right end with rate beta. Depending on the values of these parameters, the model exhibits three stationary phases, separated by lines of first- and second-order non-equilibrium phase transitions. New simulation results on the power spectrum of the fluctuating total number of particles in the different phases of the system are presented. Our theoretical contribution concerns the approximate evaluation of the power spectrum in the domain-wall picture of the coexisting low- and high-density phases. Finally, we review some of our recent results on the TASEP defined on an open network containing a double-chain section in the middle. With the aid of a simple theory, which neglects correlations at the junctions of the chain segments, the possible phase structures of the model are found. Density profiles and nearest-neighbor correlations in the steady states of the model at representative points of the phase diagram are obtained by means of computer simulations. On the coexistence line cross-correlations are found to exist between equivalent sites in the branches of the middle section.

cond-mat.stat-mech↗

arXiv2005

The totally asymmetric exclusion process on a ring: Exact relaxation dynamics and associated model of clustering transition

The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary conditions. We prove that the so defined update leads to a stationary state in which all possible particle configurations have equal probabilities. Using the exact analytical expression for the propagator, we find the generating function for the conditional probabilities, average velocity and diffusion constant at all stages of evolution. An exact and explicit expression for the stationary velocity of TASEP on rings of arbitrary size and particle filling is derived. The evolution of small systems towards a steady state is clearly demonstrated. Considering the generating function as a partition function of a thermodynamic system, we study its zeros in planes of complex fugacities. At long enough times, the patterns of zeroes for rings with increasing size provide evidence for a transition of the associated two-dimensional lattice paths model into a clustered phase at low fugacities.

cond-mat.soft↗

arXiv2005

Once more on the equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems

In answer to the replies of Reslen {\it et al} [arXiv: quant-ph/0507164 (2005)], and Liberti and Zaffino [arXiv:cond-mat/0507019, (2005)], we comment once more on the temperature-dependent effective Hamiltonians for the Dicke model derived by them in [Europhys. Lett., {\bf 69} (2005) 8] and [Eur. Phys. J., {\bf 44} (2005) 535], respectively. These approximate Hamiltonians cannot be correct for any finite nonzero temperature because they both violate a rigorous result. The fact that the Dicke model belongs to the universality class of, and its thermodynamics is described by the infinitely coordinated transverse-field XY model is known for more than 30 years.

quant-ph↗

arXiv2005

Comment on equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems

In this Comment we show that the temperature-dependent effective Hamiltonian derived by Reslen {\it et al} [Europhys. Lett., {\bf 69} (2005) 8] or that one by Liberti and Zaffino [arXiv:cond-mat/0503742] for the Dicke model cannot be correct for any temperature. They both violate a rigorous result. The former is correct only in the quantum (zero-temperature) limit while the last one only in the classical (infinite temperature) limit. The fact that the Dicke model belongs to the universality class of the infinitely coordinated transverse-field XY model is known for more then 30 years.

quant-ph↗

arXiv1997

Surface critical exponents for a three-dimensional modified spherical model

A modified three-dimensional mean spherical model with a L-layer film geometry under Neumann-Neumann boundary conditions is considered. Two spherical fields are present in the model: a surface one fixes the mean square value of the spins at the boundaries at some $ρ> 0$, and a bulk one imposes the standard spherical constraint (the mean square value of the spins in the bulk equals one). The surface susceptibility $χ_{1,1}$ has been evaluated exactly. For $ρ=1$ we find that $χ_{1,1}$ is finite at the bulk critical temperature $T_c$, in contrast with the recently derived value $γ_{1,1}=1$ in the case of just one global spherical constraint. The result $γ_{1,1}=1$ is recovered only if $ρ=ρ_c= 2-(12 K_c)^{-1}$, where $K_c$ is the dimensionless critical coupling. When $ρ> ρ_c$, $χ_{1,1}$ diverges exponentially as $T\to T_c^{+}$. An effective hamiltonian which leads to an exactly solvable model with $γ_{1,1}=2$, the value for the $n\to \infty $ limit of the corresponding O(n) model, is proposed too.

cond-mat.stat-mech↗

arXiv1995

The Kasteleyn model and a cellular automaton approach to traffic flow

We propose a bridge between the theory of exactly solvable models and the investigation of traffic flow. By choosing the activities in an apropriate way the dimer configurations of the Kasteleyn model on a hexagonal lattice can be interpreted as space-time trajectories of cars. This then allows for a calculation of the flow-density relationship (fundamental diagram). We further introduce a closely-related cellular automaton model. This model can be viewed as a variant of the Nagel-Schreckenberg model in which the cars do not have a velocity memory. It is also exactly solvable and the fundamental diagram is calculated.

cond-mat↗

arXiv1995

Layer Features of the Lattice Gas Model for Self-Organized Criticality

A layer-by-layer description of the asymmetric lattice gas model for 1/f-noise suggested by Jensen [Phys. Rev. Lett. 64, 3103 (1990)] is presented. The power spectra of the lattice layers in the direction perpendicular to the particle flux is studied in order to understand how the white noise at the input boundary evolves, on the average, into 1/f-noise for the system. The effects of high boundary drive and uniform driving force on the power spectrum of the total number of diffusing particles are considered. In the case of nearest-neighbor particle interactions, high statistics simulation results show that the power spectra of single lattice layers are characterized by different $β_x$ exponents such that $β_x \to 1.9$ as one approaches the outer boundary.

cond-mat↗