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arXiv2018

Two-species diffusion-annihilation process on the fully-connected lattice: probability distributions and extreme value statistics

We study the two-species diffusion-annihilation process, $A+B\rightarrow$ Ø, on the fully-connected lattice. Probability distributions for the number of particles and the reaction time are obtained for a finite-size system using a master equation approach. Mean values and variances are deduced from generating functions. When the reaction is far from complete, i.e., for a large number of particles of each species, mean-field theory is exact and the fluctuations are Gaussian. In the scaling limit the reaction time displays extreme-value statistics in the vicinity of the absorbing states. A generalized Gumbel distribution is obtained for unequal initial densities, $ρ_A>ρ_B$. For equal or almost equal initial densities, $ρ_A\simeqρ_B$, the fluctuations of the reaction time near the absorbing state are governed by a probability density involving derivatives of $\vartheta_4$, the Jacobi theta function.

cond-mat.stat-mech↗

arXiv2021

Scalar product for the XXZ spin chain with general integrable boundaries

We calculate the scalar product of Bethe states of the XXZ spin-$\frac{1}{2}$ chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer matrix and the off-shell Bethe vectors allow one to derive a linear system for the scalar product of off-shell and on-shell Bethe states. We show that this linear system can be solved in terms of a compact determinant formula that involves the Jacobian of the transfer matrix eigenvalue and certain q-Pochhammer polynomials of the boundary couplings.

math-ph↗

arXiv2021

A Yang-Baxter integrable cellular automaton with a four site update rule

We present a one dimensional reversible block cellular automaton, where the time evolution is dictated by a period 3 cycle of update rules. At each time step a subset of the cells is updated using a four site rule with two control bits and two action bits. The model displays rich dynamics. There are three types of stable particles, left movers, right movers and "frozen" bound states that only move as an effect of scattering with the left and right movers. Multi-particle scattering in the system is factorized. We embed the model into the canonical framework of Yang-Baxter integrability by rigorously proving the existence of a commuting set of diagonal-to-diagonal transfer matrices. The construction involves a new type of Lax operator.

cond-mat.stat-mech↗

arXiv2024

Nonequilibrium Phase Transition in a 2D Ferromagnetic Spins with Effective Interactions

The study of nonequilibrium steady-state (NESS) in the Ising model offers rich insights into the properties of complex systems far from equilibrium. This paper explores the nature of NESS phase transitions in two-dimensional (2D) ferromagnetic Ising model on a square lattice under effective interactions using Monte Carlo (MC) algorithms. This requires extensive MC simulations using the modified Metropolis and modified Glauber update rules. The qualification of the modified update rules is characterized by the definition of an effective parameter $h$. For $|h|>1$, it is analytically shown that the nature of the phase transition (including the critical temperature) is independent of $h$. Furthermore, for $-1<h<1$, we study the steady-state properties of phase transitions using numerical methods. Therefore, we performed simulations for different lattice sizes and measured relevant physical quantities. From the data, we determined the numerical results of the transition temperature and relevant critical exponents for various values of $h$ by applying finite-size scaling (FSS). We found that the FSS analysis of the exponents is consistent with the analytical values of the equilibrium 2D Ising model.

cond-mat.stat-mech↗

arXiv2012

Non-specific binding of Na$^+$ and Mg$^{2+}$ to RNA determined by force spectroscopy methods

RNA duplex stability depends strongly on ionic conditions, and inside cells RNAs are exposed to both monovalent and multivalent ions. Despite recent advances, we do not have general methods to quantitatively account for the effects of monovalent and multivalent ions on RNA stability, and the thermodynamic parameters for secondary structure prediction have only been derived at 1M [Na$^+$]. Here, by mechanically unfolding and folding a 20 bp RNA hairpin using optical tweezers, we study the RNA thermodynamics and kinetics at different monovalent and mixed monovalent/Mg$^{2+}$ salt conditions. We measure the unfolding and folding rupture forces and apply Kramers theory to extract accurate information about the hairpin free energy landscape under tension at a wide range of ionic conditions. We obtain non-specific corrections for the free energy of formation of the RNA hairpin and measure how the distance of the transition state to the folded state changes with force and ionic strength. We experimentally validate the Tightly Bound Ion model and obtain values for the persistence length of ssRNA. Finally, we test the approximate rule by which the non-specific binding affinity of divalent cations at a given concentration is equivalent to that of monovalent cations taken at 100 fold that concentration for small molecular constructs.

q-bio.BM↗

arXiv2024

Effectiveness of probabilistic contact tracing in epidemic containment: the role of super-spreaders and transmission path reconstruction

The recent COVID-19 pandemic underscores the significance of early-stage non-pharmacological intervention strategies. The widespread use of masks and the systematic implementation of contact tracing strategies provide a potentially equally effective and socially less impactful alternative to more conventional approaches, such as large-scale mobility restrictions. However, manual contact tracing faces strong limitations in accessing the network of contacts, and the scalability of currently implemented protocols for smartphone-based digital contact tracing becomes impractical during the rapid expansion phases of the outbreaks, due to the surge in exposure notifications and associated tests. A substantial improvement in digital contact tracing can be obtained through the integration of probabilistic techniques for risk assessment that can more effectively guide the allocation of new diagnostic tests. In this study, we first quantitatively analyze the diagnostic and social costs associated with these containment measures based on contact tracing, employing three state-of-the-art models of SARS-CoV-2 spreading. Our results suggest that probabilistic techniques allow for more effective mitigation at a lower cost. Secondly, our findings reveal a remarkable efficacy of probabilistic contact-tracing techniques in performing backward and multi-step tracing and capturing super-spreading events.

q-bio.PE↗

arXiv2013

Jet-induced jammed states of granular jet impacts

The impacts of granular jets for both frictional and frictionless grains in two dimensions are numerically investigated. A dense flow with a dead zone emerges during the impact. From our two-dimensional simulation, we evaluate the equations of state and the con- stitutive equations of the flow. The asymptotic divergences of pressure and shear stress similar to the situation near the jamming transition appear for the frictionless case, while their exponents are smaller than those of the sheared granular systems, and are close to the extrapolation from the kinetic theoretical regime. In a similar manner to the jam- ming for frictional grains, the critical density decreases as the friction constant of grains increases. For bi-disperse systems, the effective friction constant defined as the ratio of shear stress to normal stress, monotonically increases from near zero, as the strain rate increases. On the other hand, the effective friction constant has two metastable branches for mono-disperse systems because of the coexistence of a crystallized state and a liquid state.

cond-mat.stat-mech↗

arXiv2014

Ising model on random networks and the canonical tensor model

We introduce a statistical system on random networks of trivalent vertices for the purpose of studying the canonical tensor model, which is a rank-three tensor model in the canonical formalism. The partition function of the statistical system has a concise expression in terms of integrals, and has the same symmetries as the kinematical ones of the canonical tensor model. We consider the simplest non-trivial case of the statistical system corresponding to the Ising model on random networks, and find that its phase diagram agrees with what is implied by regrading the Hamiltonian vector field of the canonical tensor model with N = 2 as a renormalization group flow. Along the way, we obtain an explicit exact expression of the free energy of the Ising model on random networks in the thermodynamic limit by the Laplace method. This paper provides a new example connecting a model of quantum gravity and a random statistical system.

hep-th↗

arXiv2014

Analytical estimates of the locations of phase transition points in the ground state for the bimodal Ising spin glass model in two dimensions

We analytically estimate the locations of phase transition points in the ground state for the $\pm J$ random bond Ising model with asymmetric bond distributions on the square lattice. We propose and study the percolation transitions for two types of bond shared by two non-frustrated plaquettes. The present method indirectly treats the sizes of clusters of correlated spins for the ferromagnetic and spin glass orders. We find two transition points. The first transition point is the phase transition point for the ferromagnetic order, and the location is obtained as $p_c^{(1)} \approx 0.895 \, 399 \, 54$ as the solution of $[p^2 + 3 (1-p)^2 ]^2 \, p^3 - \frac{1}{2} = 0$. The second transition point is the phase transition point for the spin glass order, and the location is obtained as $p_c^{(2)} = \frac{1}{4} [2 + \sqrt{2 (\sqrt{5} - 1)}] \approx 0.893 \, 075 \, 69$. Here, $p$ is the ferromagnetic bond concentration, and $1 - p$ is the antiferromagnetic bond concentration. The obtained locations are reasonably close to the previously estimated locations. This study suggests the presence of the intermediate phase between $p_c^{(1)}$ and $p_c^{(2)}$; however, since the present method produces remarkable values but has no mathematical proof for accuracy yet, no conclusions are drawn in this article about the presence of the intermediate phase.

cond-mat.dis-nn↗

arXiv2013

Calculation of multifractal dimensions in spin chains

It was demonstrated in [Phys. Rev. E 86, 021104, (2012)], that the ground-state wave functions for a large variety of one-dimensional spin-1/2 models are multifractals in the natural spin-z basis. We present here the details of analytical derivations and numerical confirmations of these results.

nlin.CD↗

arXiv2025

Rise and fall of nonstabilizerness via random measurements

We investigate the dynamics of nonstabilizerness - also known as `magic' - in monitored quantum circuits composed of random Clifford unitaries and local projective measurements. For measurements in the computational basis, we derive an analytical model for dynamics of the stabilizer nullity, showing that it decays in quantized steps and requires exponentially many measurements to vanish, which reveals the strong protection through Clifford scrambling. On the other hand, for measurements performed in rotated non-Clifford bases, measurements can both create and destroy nonstabilizerness. Here, the dynamics leads to a steady-state with non-trivial nonstabilizerness, independent of the initial state. We find that Haar-random states equilibrate in constant time, whereas stabilizer states exhibit linear-in-size relaxation time. While the stabilizer nullity is insensitive to the rotation angle, Stabilizer Rényi Entropies expose a richer structure in their dynamics. Our results uncover sharp distinctions between coarse and fine-grained nonstabilizerness diagnostics and demonstrate how measurements can both suppress and sustain quantum computational resources.

quant-ph↗

arXiv2012

Quantum dynamics and entanglement of a 1D Fermi gas released from a trap

We investigate the entanglement properties of the nonequilibrium dynamics of one-dimensional noninteracting Fermi gases released from a trap. The gas of N particles is initially in the ground state within hard-wall or harmonic traps, then it expands after dropping the trap. We compute the time dependence of the von Neumann and Renyi entanglement entropies and the particle fluctuations of spatial intervals around the original trap, in the limit of a large number N of particles. The results for these observables apply to one-dimensional gases of impenetrable bosons as well. We identify different dynamical regimes at small and large times, depending also on the initial condition, whether it is that of a hard-wall or harmonic trap. In particular, we analytically show that the expansion from hard-wall traps is characterized by the asymptotic small-time behavior $S \approx (1/3)\ln(1/t)$ of the von Neumann entanglement entropy, and the relation $S\approx π^2 V/3$ where V is the particle variance, which are analogous to the equilibrium behaviors whose leading logarithms are essentially determined by the corresponding conformal field theory with central charge $c=1$. The time dependence of the entanglement entropy of extended regions during the expansion from harmonic traps shows the remarkable property that it can be expressed as a global time-dependent rescaling of the space dependence of the initial equilibrium entanglement entropy.

cond-mat.stat-mech↗

arXiv2013

Dependence of a quantum mechanical system on its own initial state and the initial state of the environment it interacts with

We present a unifying framework to the understanding of when and how quantum mechanical systems become independent of their initial conditions and adapt macroscopic properties (like temperature) of the environment.By viewing this problem from an quantum information theory perspective, we are able to simplify it in a very natural and easy way. We first show that for any interaction between the system and the environment, and almost all initial states of the system, the question of how long the system retains memory of its initial conditions can be answered by studying the temporal evolution of just one special initial state. This special state thereby depends only on our knowledge of macroscopic parameters of the system. We provide a simple entropic inequality for this state that can be used to determine whether mosts states of the system have, or have not become independent of their initial conditions after time $t$. We discuss applications of our entropic criterion to thermalization times in systems with an effective light-cone and to quantum memories suffering depolarizing noise. We make a similar statement for almost all initial states of the environment, and finally provide a sufficient condition for which a system never thermalizes, but remains close to its initial state for all times.

quant-ph↗

arXiv2013

Approximating random quantum optimization problems

We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-QSAT on large random graphs. As an approximation strategy, we optimize the solution space over `classical' product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are: (i) The derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment. (ii) A demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects structure of the solution space of random $k$-QSAT. Simulated annealing exhibits metastability in similar `hard' regions of parameter space. (iii) A generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy `landscape' of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random $k$-QSAT in a two-dimensional energy-density--clause-density space.

cond-mat.stat-mech↗

arXiv2013

Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence

We show that the phenomenon of frozen discord, exhibited by specific classes of two-qubit states under local nondissipative decoherent evolutions, is a common feature of all known bona fide measures of general quantum correlations. All those measures, despite inducing typically inequivalent orderings on the set of nonclassically correlated states, return a constant value in the considered settings. Every communication protocol which relies on quantum correlations as resource will run with a performance completely unaffected by noise in the specified dynamical conditions. We provide a geometric interpretation of this

quant-ph↗

arXiv2013

Unidirectional quantum walks: evolution and exit times

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in place or move in a fixed direction, e.g., rightward or upward. While both formulations are essentially equivalent, the present approach leads to consider Discrete Fourier Transforms, which eventually results in obtaining explicit expressions for the wave functions in terms of finite sums, and allows the use of efficient algorithms based on the Fast Fourier Transform. The wave functions here obtained govern the probability of finding the particle at any given location, but determine as well the exit-time probability of the walker from a fixed interval, which is also analyzed.

quant-ph↗

arXiv2013

Thermalized polarization dynamics of a discrete optical waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line $T=\infty$ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.

cond-mat.stat-mech↗

arXiv2013

Action principle for continuous quantum measurement

We present a stochastic path integral formalism for continuous quantum measurement that enables the analysis of rare events using action methods. By doubling the quantum state space to a canonical phase space, we can write the joint probability density function of measurement outcomes and quantum state trajectories as a phase space path integral. Extremizing this action produces the most-likely paths with boundary conditions defined by preselected and postselected states as solutions to a set of ordinary differential equations. As an application, we analyze continuous qubit measurement in detail and examine the structure of a quantum jump in the Zeno measurement regime.

quant-ph↗