Statistical Mechanics
The Effects of Intrinsic Dynamical Ghost Modes in Discrete-Time Langevin Simulations (1902.02338v1)
Lucas Frese Grønbech Jensen, Niels Grønbech-Jensen
2019-02-06
Using the recently published GJF-2GJ Langevin thermostat, which can produce time-step-independent statistical measures even for large time steps, we analyze and discuss the causes for abrupt deviations in statistical data as the time step is increased for some simulations of nonlinear oscillators. Exemplified by the pendulum, we identify a couple of discrete-time dynamical modes in the purely damped pendulum equation as the cause of the observed discrepancies in statistics. The existence, stability and kinetics of the modes are consistent with the acquired velocity distribution functions from Langevin simulations, and we conclude that the simulation deviations from physical expectations are not due to normal, systematic algorithmic time-step errors, but instead due to the inherent properties of discrete time in nonlinear dynamics.
Entanglement and spectra in topological many-body localized phases (1902.02259v1)
K. S. C. Decker, D. M. Kennes, J. Eisert, C. Karrasch
2019-02-06
Many-body localized systems in which interactions and disorder come together defy the expectations of quantum statistical mechanics: In contrast to ergodic systems, they do not thermalize when undergoing non-equilibrium dynamics. What is less clear, however, is how topological features interplay with many-body localized phases as well as the nature of the transition between a topological and a trivial state within the latter. In this work, we numerically address these questions, using a combination of extensive tensor network calculations, specifically DMRG-X, as well as exact diagonalization, leading to a comprehensive characterization of Hamiltonian spectra and eigenstate entanglement properties. We advocate that the scaling properties of entanglement features characterize many-body localized systems both in topological and trivial situations, but that no longer the entanglement entropy, but mixed-state entanglement measures such as the negativity - a concept inherited from quantum information - can meaningfully be made use of, due to the close to degenerate energy levels.
Bipartite fidelity of critical dense polymers (1902.02246v1)
G. Parez, A. Morin-Duchesne, P. Ruelle
2019-02-06
We investigate the bipartite fidelity
for a lattice model described by a logarithmic CFT: the model of critical dense polymers. We define this observable in terms of a partition function on the pants geometry, where
defects enter at the top of the pants lattice and exit in one of the legs. Using the correspondence with the XX spin chain, we obtain an exact closed-form expression for
asymptotic expansion as a function of
, where
is the lattice width at the top of the pants and
is the width of the leg where the defects exit. We find an agreement with the results of St'ephan and Dubail for rational CFTs, with the central charge and conformal weights specialised to
and
. We compute a second instance
of the bipartite fidelity for
by imposing a different rule for the connection of the defects. In the conformal setting, this choice corresponds to inserting two boundary condition changing fields of weight
that are logarithmic instead of primary. We compute the asymptotic expansion in this case as well and find a simple additive correction compared to
, of the form
. We confirm this lattice result with a CFT derivation and find that this correction term is identical for all logarithmic theories, independently of
and
.
Thermodynamics of precision in quantum non equilibrium steady states (1901.10428v2)
Giacomo Guarnieri, Gabriel T. Landi, Stephen R. Clark, John Goold
2019-01-29
Autonomous engines operating at the nano-scale can be prone to deleterious fluctuations in the heat and particle currents which increase, for fixed power output, the more reversible the operation regime is. This fundamental trade-off between current fluctuations and entropy production forms the basis of the recently formulated thermodynamic uncertainty relations (TURs). However, these relations have so far only been derived for classical Markovian systems and can be violated in the quantum regime. In this paper we show that the geometry of quantum non-equilibrium steady-states alone, already directly implies the existence of a TUR, but with a looser bound. The geometrical nature of this result makes it extremely general, establishing a fundamental limit for the thermodynamics of precision. Our proof is based on the McLennan-Zubarev ensemble, which provides an exact description of non-equilibrium steady-states. We first prove that the entropy production of this ensemble can be expressed as a quantum relative entropy. The TURs are then shown to be a direct consequence of the quantum Cramer-Rao bound, a fundamental result from parameter estimation theory. By combining techniques from many-body physics and information sciences, our approach also helps to shed light on the delicate relationship between quantum effects and current fluctuations in autonomous machines.
Fluctuation-Induced Quantum Zeno Effect (1809.09085v2)
Heinrich Fröml, Alessio Chiocchetta, Corinna Kollath, Sebastian Diehl
2018-09-24
An isolated quantum gas with a localized loss features a non-monotonic behavior of the particle loss rate as an incarnation of the quantum Zeno effect, as recently shown in experiments with cold atomic gases. While this effect can be understood in terms of local, microscopic physics, we show that novel many-body effects emerge when non-linear gapless quantum fluctuations become important. To this end, we investigate the effect of a local dissipative impurity on a one-dimensional gas of interacting fermions. We show that the escape probability for modes close to the Fermi energy vanishes for an arbitrary strength of the dissipation. In addition, transport properties across the impurity are qualitatively modified, similarly to the Kane-Fisher barrier problem. We substantiate these findings using both a microscopic model of spinless fermions and a Luttinger liquid description.
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