Condensed Matter

In a Markov chain population model subject to catastrophes, random immigration events (birth), promoting growth, are in balance with the effect of binomial catastrophes that cause recurrent mass removal (death). Using a generating function approach, we study two versions of such population models when the binomial catastrophic events are of a slightly different random nature. In both cases, we describe the subtle balance between the two birth and death conflicting effects.

We characterize equilibrium properties and relaxation dynamics of a two-dimensional lattice containing, at each site, two particles connected by a double-well potential (dumbbell). Dumbbells are oriented in the orthogonal direction with respect to the lattice plane and interact with each other through a Lennard-Jones potential truncated at the nearest neighbor distance. We show that the system's equilibrium properties are accurately described by a two-dimensional Ising model with an appropriate coupling constant. Moreover, we characterize the coarsening kinetics by calculating the cluster size as a function of time and compare the results with Monte Carlo simulations based on Glauber or reactive dynamics rate constants.

We revisit Fradkin and Raby's real-space renormalization-group method to study the quantum Z_2 gauge theory defined on links forming a two-dimensional square lattice. Following an old suggestion of theirs, a systematic perturbation expansion developed by Hirsch and Mazenko is used to improve the algorithm to second order in an intercell coupling, thereby incorporating the effects of discarded higher energy states. A careful derivation of gauge-invariant effective operators is presented in the Hamiltonian formalism. Renormalization group equations are analyzed near the nontrivial fixed point, reaffirming old work by Hirsch on the dual transverse field Ising model. In addition to recovering Hirsch's previous findings, critical exponents for the scaling of the spatial correlation length and energy gap in the electric free (deconfined) phase are compared. Unfortunately, their agreement is poor. The leading singular behavior of the ground state energy density is examined near the critical point: we compute both a critical exponent and estimate a critical amplitude ratio.

Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions, due to the divergence of all the moments (cumulants). We have solved this problem by introducing a `pseudo-cumulants' expansion. This allows us to develop a reduction methodology for heterogeneous spiking neural networks subject to extrinsinc and endogenous noise sources, thus generalizing the mean-field formulation introduced in [E. Montbrió et al., Phys. Rev. X 5, 021028 (2015)].

Using the Feynman-Kac formula, a work fluctuation theorem for a Brownian particle in a nonconfining potential, e.g., a potential well with finite depth, is derived. The theorem yields aninequality that puts a lower bound on the average work needed to change the potential in this http URL comparison to the Jarzynski equality, which holds for confining potentials, an additional termdescribing a form of energy related to the never ending diffusive expansion appears.

By working in the small persistence time limit, we determine the steady-state distribution of an Active Ornstein Uhlenbeck Particle (AOUP) experiencing, in addition to self-propulsion, a Gaussian white noise modelling a bath at temperature T. This allows us to derive analytical formulas for three quantities: the spatial density of a confined particle, the current induced by an asymmetric periodic potential and the entropy production rate. These formulas disentangle the respective roles of the passive and active noises on the steady state of AOUPs, showing that signatures of non-equilibrium can display surprising behaviors as the temperature is varied. Indeed, depending on the potential in which the particle evolves, both the current and the entropy production rate can be non-monotonic functions of T. The latter can even diverge at high temperature for steep enough confining potentials. Thus, depending on context, switching on translational diffusion may drive the particle closer to or further away from equilibrium. We then probe the range of validity of our quantitative derivations by numerical simulations. Finally, we explain how the method presented here to tackle perturbatively an Ornstein Uhlenbeck (OU) noise could be further generalized beyond the Brownian case.

We show that a wide class of spin chains with topological frustration cannot develop any local order. In particular, we consider translational-invariant one-dimensional chains with frustrated boundary conditions, i.e. periodic boundary conditions and an odd number of sites, which possess a global SU(2) symmetry. This condition implies, even at a finite sizes, an exact degeneracy of the ground state and is quite general in absence of external fields. We directly evaluate the expectation value of operators with support over a finite range of lattice sites and show that, except for some precise conditions, they all decay algebraically, or faster, with the chain length and vanish in the thermodynamic limit. The exceptions that admit a finite order are cases with a higher ground state degeneracy in which the translational symmetry is broken by the ground state choice.

We report accelerating diffusive solutions to the one--dimensional diffusion equation with a constant diffusion coefficient. The maximum values of the density evolve in an accelerating fashion. We also construct a Gaussian--modulated form of the solution that retains this feature.

We accurately simulate the phase diagram and critical behavior of the q -state clock model on the square lattice by using the state-of-the-art loop optimization for tensor network renormalzation(loop-TNR) algorithm. The two phase transition points for q≥5 are determined with very high accuracy. Furthermore, by computing the conformal scaling dimensions, we are able to accurately determine the compactification radius R of the compactified boson theories at both phase transition points. In particular, the compactification radius R at high-temperature critical point is precisely the same as the predicted R for Berezinskii-Kosterlitz-Thouless (BKT) transition. Moreover, we find that the fixed point tensors at high-temperature critical point also converge(up to numerical errors) to the same one for large enough q and the corresponding operator product expansion(OPE) coefficient of the compactified boson theory can also be read out directly from the fixed point tensor.

We study the position distribution of an active Brownian particle (ABP) in the presence of stochastic resetting in two spatial dimensions. We consider three different resetting protocols : (I) where both position and orientation of the particle are reset, (II) where only the position is reset, and (III) where only the orientation is reset with a certain rate r. We show that in the first two cases the ABP reaches a stationary state. Using a renewal approach, we calculate exactly the stationary marginal position distributions in the limiting cases when the resetting rate r is much larger or much smaller than the rotational diffusion constant D R of the ABP. We find that, in some cases, for a large resetting rate, the position distribution diverges near the resetting point; the nature of the divergence depends on the specific protocol. For the orientation resetting, there is no stationary state, but the motion changes from a ballistic one at short-times to a diffusive one at late times. We characterize the short-time non-Gaussian marginal position distributions using a perturbative approach.