arXiv subjects

Tatsuhiko N. Ikeda

Publications and source records attributed to Tatsuhiko N. Ikeda.

44 records · Page 3Linked to original sources

arXiv2016

Entanglement Pre-thermalization in an Interaction Quench between Two Harmonic Oscillators

Entanglement pre-thermalization (EP) is a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble, which incorporates nonlocal conserved quantities, exactly describes the total system. In the presence of a symmetry-breaking perturbation, EP is quasi-stationary and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.

cond-mat.stat-mech↗

arXiv2016

Conductivity bounds in probe brane models

We discuss upper and lower bounds on the electrical conductivity of finite temperature strongly coupled quantum field theories, holographically dual to probe brane models, within linear response. In a probe limit where disorder is introduced entirely through an inhomogeneous background charge density, we find simple lower and upper bounds on the electrical conductivity in arbitrary dimensions. In field theories in two spatial dimensions, we show that both bounds persist even when disorder is included in the bulk metric. We discuss the challenges with finding sharp lower bounds on conductivity in three or more spatial dimensions when the metric is inhomogeneous.

hep-th↗

arXiv2015

How accurately can the microcanonical ensemble describe small isolated quantum systems?

We numerically investigate quantum quenches of a nonintegrable hard-core Bose-Hubbard model to test the accuracy of the microcanonical ensemble in small isolated quantum systems. We show that, in a certain range of system size, the accuracy increases with the dimension of the Hilbert space $D$ as $1/D$. We ascribe this rapid improvement to the absence of correlations between many-body energy eigenstates as well as to the eigenstate thermalization. Outside of that range, the accuracy is found to scale as $1/\sqrt{D}$ and improves algebraically with the system size.

cond-mat.stat-mech↗

arXiv2014

Entanglement prethermalization: Locally thermal but non-locally non-thermal states in a one-dimensional Bose gas

A well-isolated system often shows relaxation to a quasi-stationary state before reaching thermal equilibrium. Such a prethermalization has attracted considerable interest recently in association with closely related fundamental problems of relaxation and thermalization of isolated quantum systems. Motivated by the recent experiment in ultracold atoms, we study the dynamics of a one-dimensional Bose gas which is split into two subsystems, and find that individual subsystems relax to Gibbs states, yet the entire system does not due to quantum entanglement. In view of recent experimental realization on a small well-defined number of ultracold atoms, our prediction based on exact few-body calculations is amenable to experimental test.

cond-mat.quant-gas↗

arXiv2014

Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis

We ask whether the Eigenstate Thermalization Hypothesis (ETH) is valid in a strong sense: in the limit of an infinite system, {\it every} eigenstate is thermal. We examine expectation values of few-body operators in highly-excited many-body eigenstates and search for `outliers', the eigenstates that deviate the most from ETH. We use exact diagonalization of two one-dimensional nonintegrable models: a quantum Ising chain with transverse and longitudinal fields, and hard-core bosons at half-filling with nearest- and next-nearest-neighbor hopping and interaction. We show that even the most extreme outliers appear to obey ETH as the system size increases, and thus provide numerical evidences that support ETH in this strong sense. Finally, periodically driving the Ising Hamiltonian, we show that the eigenstates of the corresponding Floquet operator obey ETH even more closely. We attribute this better thermalization to removing the constraint of conservation of the total energy.

cond-mat.stat-mech↗

arXiv2014

The Second Law of Thermodynamics under Unitary Evolution and External Operations

A microscopic definition of the thermodynamic entropy in an isolated quantum system must satisfy (i) additivity, (ii) extensivity and (iii) the second law of thermodynamics. We show that the diagonal entropy, which is the Shannon entropy in the energy eigenbasis at each instant of time, meets the first two requirements and that the third requirement is satisfied if an arbitrary external operation is performed at typical times. In terms of the diagonal entropy, thermodynamic irreversibility follows from the facts that the Hamiltonian dynamics restricts quantum trajectories under unitary evolution and that the external operation is performed without referring to any particular information about the microscopic state of the system.

cond-mat.stat-mech↗

arXiv2012

Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas

By calculating correlation functions for the Lieb-Liniger model based on the algebraic Bethe ansatz method, we conduct a finite-size scaling analysis of the eigenstate thermalization hypothesis (ETH) which is considered to be a possible mechanism of thermalization in isolated quantum systems. We find that the ETH in the weak sense holds in the thermodynamic limit even for an integrable system although it does not hold in the strong sense. Based on the result of the finite-size scaling analysis, we compare the contribution of the weak ETH to thermalization with that of yet another thermalization mechanism, the typicality, and show that the former gives only a logarithmic correction to the latter.

cond-mat.stat-mech↗

arXiv2011

Eigenstate Randomization Hypothesis: Why Does the Long-Time Average Equal the Microcanonical Average?

We derive an upper bound on the difference between the long-time average and the microcanonical ensemble average of observables in isolated quantum systems. We propose, numerically verify, and analytically support a new hypothesis, eigenstate randomization hypothesis (ERH), which implies that in the energy eigenbasis the diagonal elements of observables fluctuate randomly. We show that ERH includes eigenstate thermalization hypothesis (ETH) and makes the aforementioned bound vanishingly small. Moreover, ERH is applicable to integrable systems for which ETH breaks down. We argue that the range of the validity of ERH determines that of the microcanonical description.

cond-mat.stat-mech↗