Statistical Mechanics
Quantum quenches in isolated quantum glasses out of equilibrium (1904.03147v1)
S. J. Thomson, P. Urbani, M. Schiro
2019-04-05
In this work, we address the question of how a closed quantum system thermalises in the presence of a random external potential. By investigating the quench dynamics of the isolated quantum spherical
-spin model, a paradigmatic model of a mean-field glass, we aim to shed new light on this complex problem. Employing a closed-time Schwinger-Keldysh path integral formalism, we first initialise the system in a random, infinite-temperature configuration and allow it to equilibrate in contact with a thermal bath before switching off the bath and performing a quench. We find evidence that increasing the strength of either the interactions or the quantum fluctuations can act to lower the effective temperature of the isolated system and stabilise glassy behaviour.
Non-negative Wigner-like distributions and Renyi-Wigner entropies of arbitrary non-Gaussian quantum states: The thermal state of the one-dimensional box problem (1904.03145v1)
Ilki Kim
2019-04-05
In this work, we consider the phase-space picture of quantum mechanics. We then introduce non-negative Wigner-like distributions \widetilde{W}{\rho;\alpha}(x,p)'s corresponding to the density operator \hat{\rho} and being proportional to {W{\rho^{\alpha/2}}(x,p)}^2, where {W_{\rho}(x,p)}^2 denotes the Wigner function. In doing so, we utilize the formal symmetry between the purity measure Tr({\rho}^2) and its Wigner representation (2\pi\hbar \int dx dp {W_{\rho}(x,p)}^2 and then consider, as a generalization, such symmetry between the fractional moments Tr(\hat{\rho}^{\alpha}) and their Wigner representations 2\pi\hbar \int dx dp {W_{\rho^{\alpha/2}}(x,p)}^2. Next, we build up a framework that enables to explicitly evaluate the Renyi-Wigner entropies for the classical-like distributions {\mathcal W}{\rho;\alpha}(x,p) in a compact way. We also discuss the relationship between the non-negative feature of \widetilde{\mathcal W}{\rho;\alpha}(x,p) and the x-p uncertainty relation with the help of the celebrated Bopp shift, as well as providing a well-defined evaluation scheme of expectation values of observables within this formulation. To illustrate the validity of our framework, we evaluate the distributions \widetilde{\mathcal W}{\beta;\alpha}(x,p) corresponding to the (non-Gaussian) thermal state \hat{\rho}{\beta} of a single particle confined by a one-dimensional infinite potential well with either Dirichlet or Neumann boundary condition and then analyze the resulting Renyi entropies. Our phase-space approach will contribute to a deeper understanding of non-Gaussian states and their transitions either in the semiclassical limit (\hbar \to 0) or in the high-temperature limit (\beta \to 0), as well as enabling to systematically discuss the quantal-classical Second Law of thermodynamics on the single footing.
Dynamical typicality for initial states with a preset measurement statistics of several commuting observables (1904.03105v1)
B. N. Balz, J. Richter, J. Gemmer, R. Steinigeweg, P. Reimann
2019-04-05
We consider all pure or mixed states of a quantum many-body system which exhibit the same, arbitrary but fixed measurement outcome statistics for several commuting observables. Taking those states as initial conditions, which are then propagated by the pertinent Schr"odinger or von Neumann equation up to some later time point, and invoking a few additional, fairly weak and realistic assumptions, we show that most of them still entail very similar expectation values for any given observable. This so-called dynamical typicality property thus corroborates the widespread observation that a few macroscopic features are sufficient to ensure the reproducibility of experimental measurements despite many unknown and uncontrollable microscopic details of the system. We also discuss and exemplify the usefulness of our general analytical result as a powerful numerical tool.
Assessing the accuracy of direct-coupling analysis for RNA contact prediction (1812.07630v2)
Francesca Cuturello, Guido Tiana, Giovanni Bussi
2018-12-18
Many non-coding RNAs are known to play a role in the cell directly linked to their structure. Structure prediction based on the sole sequence is however a challenging task. On the other hand, thanks to the low cost of sequencing technologies, a very large number of homologous sequences are becoming available for many RNA families. In the protein community, it has emerged in the last decade the idea of exploiting the covariance of mutations within a family to predict the protein structure using the direct-coupling-analysis (DCA) method. The application of DCA to RNA systems has been limited so far. We here perform an assessment of the DCA method on 17 riboswitch families, comparing it with the commonly used mutual information analysis and with state-of-the-art R-scape covariance method. We also compare different flavors of DCA, including mean-field, pseudo-likelihood, and a proposed stochastic procedure (Boltzmann learning) for solving exactly the DCA inverse problem. Boltzmann learning outperforms the other methods in predicting contacts observed in high resolution crystal structures.
Particle-resolved lattice Boltzmann simulations of 3-dimensional active turbulence (1904.03069v1)
Dora Bardfalvy, Henrik Nordanger, Cesare Nardini, Alexander Morozov, Joakim Stenhammar
2019-04-05
Collective behaviour in suspensions of microswimmers is often dominated by the impact of long-ranged hydrodynamic interactions. These phenomena include active turbulence, where suspensions of pusher bacteria at sufficient densities exhibit large-scale, chaotic flows. To study this collective phenomenon, we use large-scale (up to
) particle-resolved lattice Boltzmann simulations of model microswimmers described by extended stresslets. Such system sizes enable us to obtain quantitative information about both the transition to active turbulence and characteristic features of the turbulent state itself. In the dilute limit, we test analytical predictions for a number of static and dynamic properties against our simulation results. For higher swimmer densities, where swimmer-swimmer interactions become significant, we numerically show that the length- and timescales of the turbulent flows increase steeply near the predicted finite-system transition density.
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