The underlying connection between the degrees of freedom of a system and its nonextensive thermodynamic behavior is addressed. The problem is handled by starting from a thermodynamical system with fractal structure and its analytical reduction to a f
inite ideal gas. In the limit where the thermofractal has no internal structure, it is found that it reproduces the basic properties of a nonextensive ideal gas with a finite number of particles as recently discussed (Lima & Deppman, Phys. Rev. E 101, 040102(R) 2020). In particular, the entropic $q$-index is calculated in terms of the number of particles both for the nonrelativistic and relativistic cases. In light of such results, the possible nonadditivity or additivity of the entropic structures are also critically analysed and new expressions to the entropy (per particle) for a composed system of thermofractals and its limiting case are derived.
A system of hard rigid rods of length $k$ on hypercubic lattices is known to undergo two phases transitions when chemical potential is increased: from a low density isotropic phase to an intermediate density nematic phase, and on further increase to
a high-density phase with no orientational order. In this paper, we argue that, for large $k$, the second phase transition is a first order transition with a discontinuity in density in all dimensions greater than $1$. We show the chemical potential at the transition is $approx k ln [k /ln k]$ for large $k$, and that the density of uncovered sites drops from a value $ approx (ln k)/k^2$ to a value of order $exp(-ak)$, where $a$ is some constant, across the transition. We conjecture that these results are asymptotically exact, in all dimensions $dgeq 2$. We also present evidence of coexistence of nematic and disordered phases from Monte Carlo simulations for rods of length $9$ on the square lattice.
The current interest in compositionally complex alloys including so called high entropy alloys has caused renewed interest in the general problem of solute hardening. It has been suggested that this problem can be addressed by treating the alloy as a
n effective medium containing a random distribution of dilatation and compression centers representing the volumetric misfit of atoms of different species. The mean square stresses arising from such a random distribution can be calculated analytically, their spatial correlations are strongly anisotropic and exhibit long-range tails with third-order power law decay. Here we discuss implications of the anisotropic and long-range nature of the correlation functions for the pinning of dislocations of arbitrary orientation. While edge dislocations are found to follow the standard pinning paradigm, for dislocations of near screw orientation we demonstrate the co-existence of two types of pinning energy minima.
High-temperature thermopower is interpreted as entropy that a carrier carries. Owing to spin and orbital degrees of freedom, a transition metal perovskite exhibits large thermopower at high temperatures. In this paper, we revisit the high-temperature
thermopower in the perovskites to shed light on the degrees of freedom. Thus, we theoretically derive an expression of thermopower in one-dimensional octahedral-MX6-clusters chain using linear-response theory and electronic structure calculation of the chain based on the tight-binding approximation. The derived expression of the thermopower is consistent with the extended Heikes formula and well reproduced experimental data of several perovskite oxides at high temperatures. In this expression, a degeneracy of many electron states in octahedral ligand field (which is characterized by multiplet term) appears instead of the spin and orbital degeneracies. Complementarity in between our expression and the extended Heikes formula is discussed.
To illustrate Boltzmanns construction of an entropy function that is defined for a single microstate of a system, we present here the simple example of the free expansion of a one dimensional gas of hard point particles. The construction requires one
to define macrostates, corresponding to macroscopic observables. We discuss two different choices, both of which yield the thermodynamic entropy when the gas is in equilibrium. We show that during the free expansion process, both the entropies converge to the equilibrium value at long times. The rate of growth of entropy, for the two choice of macrostates, depends on the coarse graining used to define them, with different limiting behaviour as the coarse graining gets finer. We also find that for only one of the two choices is the entropy a monotonically increasing function of time. Our system is non-ergodic, non-chaotic and essentially non-interacting; our results thus illustrate that these concepts are not very relevant for the question of irreversibility and entropy increase. Rather, the notions of typicality, large numbers and coarse-graining are the important factors. We demonstrate these ideas through extensive simulations as well as analytic results.
Based on tensor network simulations, we discuss the emergence of dynamical quantum phase transitions (DQPTs) in a half-filled one-dimensional lattice described by the extended Fermi-Hubbard model. Considering different initial states, namely noninter
acting, metallic, insulating spin and charge density waves, we identify several types of sudden interaction quenches which lead to dynamical criticality. In different scenarios, clear connections between DQPTs and particular properties of the mean double occupation or charge imbalance can be established. Dynamical transitions resulting solely from high-frequency time-periodic modulation are also found, which are well described by a Floquet effective Hamiltonian. State-of-the-art cold-atom quantum simulators constitute ideal platforms to implement several reported DQPTs experimentally.
It is well known that in Anderson localized systems, starting from a random product state the entanglement entropy remains bounded at all times. However, we show that adding a single boundary term to an otherwise Anderson localized Hamiltonian leads
to unbounded growth of entanglement. Our results imply that Anderson localization is not a local property. One cannot conclude that a subsystem has Anderson localized behavior without looking at the whole system, as a term that is arbitrarily far from the subsystem can affect the dynamics of the subsystem in such a way that the features of Anderson localization are lost.
The net charge of solvated entities, ranging from polyelectrolytes and biomolecules to charged nanoparticles and membranes, depends on the local dissociation equilibrium of individual ionizable groups. Incorporation of this phenomenon, emph{charge re
gulation}, in theoretical and computational models requires dynamic, configuration-dependent recalculation of surface charges and is therefore typically approximated by assuming constant net charge on particles. Various computational methods exist that address this. We present an alternative, particularly efficient charge regulation Monte Carlo method (CR-MC), which explicitly models the redistribution of individual charges and accurately samples the correct grand-canonical charge distribution. In addition, we provide an open-source implementation in the LAMMPS molecular dynamics (MD) simulation package, resulting in a hybrid MD/CR-MC simulation method. This implementation is designed to handle a wide range of implicit-solvent systems that model discreet ionizable groups or surface sites. The computational cost of the method scales linearly with the number of ionizable groups, thereby allowing accurate simulations of systems containing thousands of individual ionizable sites. By matter of illustration, we use the CR-MC method to quantify the effects of charge regulation on the nature of the polyelectrolyte coil--globule transition and on the effective interaction between oppositely charged nanoparticles.
We present exact results on a novel kind of emergent random matrix universality that quantum many-body systems at infinite temperature can exhibit. Specifically, we consider an ensemble of pure states supported on a small subsystem, generated from pr
ojective measurements of the remainder of the system in a local basis. We rigorously show that the ensemble, derived for a class of quantum chaotic systems undergoing quench dynamics, approaches a universal form completely independent of system details: it becomes uniformly distributed in Hilbert space. This goes beyond the standard paradigm of quantum thermalization, which dictates that the subsystem relaxes to an ensemble of quantum states that reproduces the expectation values of local observables in a thermal mixed state. Our results imply more generally that the distribution of quantum states themselves becomes indistinguishable from those of uniformly random ones, i.e. the ensemble forms a quantum state-design in the parlance of quantum information theory. Our work establishes bridges between quantum many-body physics, quantum information and random matrix theory, by showing that pseudo-random states can arise from isolated quantum dynamics, opening up new ways to design applications for quantum state tomography and benchmarking.
We study the fate of an impurity in an ultracold heteronuclear Bose mixture, focusing on the experimentally relevant case of a $^{41}$K-$^{87}$Rb mixture, with the impurity in a $^{41}$K hyperfine state. Our work provides a comprehensive description
of an impurity in a BEC mixture with contact interactions across its phase diagram. We present results for the miscible and immiscible regimes, as well as for the impurity in a self-bound quantum droplet. Here, varying the interactions, we find novel, exotic states where the impurity localizes either at the center or at the surface of the droplet.
