Statistical Mechanics
Slow scrambling and hidden integrability in a random rotor model (1903.10499v1)
Dan Mao, Debanjan Chowdhury, T. Senthil
2019-03-25
We analyze the out-of-time-order correlation functions of a solvable model of a large number,
, of
-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. We focus on the growth of commutators of operators at a temperature
above the zero temperature quantum critical point separating the spin-glass and paramagnetic phases. In the large
limit, the squared commutators of the rotor fields do not display any exponential growth of commutators, in spite of the absence of any sharp quasiparticle-like excitations in the disorder-averaged theory. We show that in this limit, the problem is integrable and point out interesting connections to random-matrix theory. At leading order in
, there are no modifications to the critical behavior but an irrelevant term in the fixed-point action leads to a small exponential growth of the squared commutator. We also introduce and comment on a generalized model involving
-pair rotor interactions.
Systematic construction of scarred many-body dynamics in 1D lattice models (1903.10491v1)
Kieran Bull, Ivar Martin, Z. Papić
2019-03-25
We introduce a family of non-integrable 1D lattice models that feature robust periodic revivals under a global quench from certain initial product states, thus generalizing the phenomenon of many-body scarring recently observed in Rydberg atom quantum simulators. Our construction is based on a systematic embedding of the single-site unitary dynamics into a kinetically-constrained many-body system. We numerically demonstrate that this construction yields optimal models with the highest amplitude of the wave-function revivals, and it captures all local 1D lattice models that support scars for the fixed choice of the kinetic constraint. We show that general scarring models have a simple interpretation in terms of quantum clock operators, which allows to decompose their dynamics into a period of nearly free clock precession and an interacting bottleneck, shedding light on their anomalously slow thermalization when quenched from special initial states.
Active Learning of Spin Network Models (1903.10474v1)
Jialong Jiang, David A. Sivak, Matt Thomson
2019-03-25
Complex networks can be modeled as a probabilistic graphical model, where the interactions between binary variables, "spins", on nodes are described by a coupling matrix that is inferred from observations. The inverse statistical problem of finding direct interactions is difficult, especially for large systems, because of the exponential growth in the possible number of states and the possible number of networks. In the context of the experimental sciences, well-controlled perturbations can be applied to a system, shedding light on the internal structure of the network. Therefore, we propose a method to improve the accuracy and efficiency of inference by iteratively applying perturbations to a network that are advantageous under a Bayesian framework. The spectrum of the empirical Fisher information can be used as a measure for the difficulty of the inference during the training process. We significantly improve the accuracy and efficiency of inference in medium-sized networks based on this strategy with a reasonable number of experimental queries. Our method could be powerful in the analysis of complex networks as well as in the rational design of experiments.
Thermogeometric study of van der Waals like phase transition in black holes: an alternative approach (1903.10370v1)
Krishnakanta Bhattacharya, Bibhas Ranjan Majhi
2019-03-25
It is well-known that the non-extremal anti-de-Sitter (AdS) black holes show various van der Waals type criticalities, such as the
,
,
,
\etc~In these cases, the phase space diagram of the relevant quantities are similar in behaviour to the isotherms on
Stochastic Thermodynamics with Odd Controlling Parameters (1903.05324v2)
Geng Li, Z. C. Tu
2019-03-13
Stochastic thermodynamics extends the notions and relations of classical thermodynamics to small systems with strong fluctuations. The definition of work and heat and the microscopically reversible condition are two key concepts in the current framework of stochastic thermodynamics. Here, we apply the stochastic thermodynamics to small systems with odd controlling parameters and find that the definition of heat and the microscopically reversible condition are incompatible. Such a contraction also leads to a revision to the fluctuation theorems and nonequilibrium work relations. Through introducing an adjoint dynamics, we find that the total entropy production can be separated into three parts and two of them respectively satisfy the integral and the detailed fluctuation theorem. By revising the definition of heat and the microscopically reversible condition respectively, we can derive two sets of modified nonequilibrium work relations, including the Jarzynski equality, the detailed Crooks work relation, and the integral Crooks work relation. We take the strategy of shortcuts to isothermality as an example and give a more sophisticated explanation to the Jarzynski-like equality derived from shortcuts to isothermality.
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