9,606 research outputs found
Exact relaxation in a class of non-equilibrium quantum lattice systems
A reasonable physical intuition in the study of interacting quantum systems
says that, independent of the initial state, the system will tend to
equilibrate. In this work we study a setting where relaxation to a steady state
is exact, namely for the Bose-Hubbard model where the system is quenched from a
Mott quantum phase to the strong superfluid regime. We find that the evolving
state locally relaxes to a steady state with maximum entropy constrained by
second moments, maximizing the entanglement, to a state which is different from
the thermal state of the new Hamiltonian. Remarkably, in the infinite system
limit this relaxation is true for all large times, and no time average is
necessary. For large but finite system size we give a time interval for which
the system locally "looks relaxed" up to a prescribed error. Our argument
includes a central limit theorem for harmonic systems and exploits the finite
speed of sound. Additionally, we show that for all periodic initial
configurations, reminiscent of charge density waves, the system relaxes
locally. We sketch experimentally accessible signatures in optical lattices as
well as implications for the foundations of quantum statistical mechanics.Comment: 8 pages, 3 figures, replaced with final versio
A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states
We prove that quantum many-body systems on a one-dimensional lattice locally
relax to Gaussian states under non-equilibrium dynamics generated by a bosonic
quadratic Hamiltonian. This is true for a large class of initial states - pure
or mixed - which have to satisfy merely weak conditions concerning the decay of
correlations. The considered setting is a proven instance of a situation where
dynamically evolving closed quantum systems locally appear as if they had truly
relaxed, to maximum entropy states for fixed second moments. This furthers the
understanding of relaxation in suddenly quenched quantum many-body systems. The
proof features a non-commutative central limit theorem for non-i.i.d. random
variables, showing convergence to Gaussian characteristic functions, giving
rise to trace-norm closeness. We briefly relate our findings to ideas of
typicality and concentration of measure.Comment: 27 pages, final versio
Partial-measurement back-action and non-classical weak values in a superconducting circuit
We realize indirect partial measurement of a transmon qubit in circuit
quantum electrodynamics by interaction with an ancilla qubit and projective
ancilla measurement with a dedicated readout resonator. Accurate control of the
interaction and ancilla measurement basis allows tailoring the measurement
strength and operator. The tradeoff between measurement strength and qubit
back-action is characterized through the distortion of a qubit Rabi oscillation
imposed by ancilla measurement in different bases. Combining partial and
projective qubit measurements, we provide the solid-state demonstration of the
correspondence between a non-classical weak value and the violation of a
Leggett-Garg inequality.Comment: 5 pages, 4 figures, and Supplementary Information (8 figures
An analysis of the acoustic cavitation noise spectrum: The role of periodic shock waves
Research on applications of acoustic cavitation is often reported in terms of the features within the spectrum of the emissions gathered during cavitation occurrence. There is, however, limited understanding as to the contribution of specific bubble activity to spectral features, beyond a binary interpretation of stable versus inertial cavitation. In this work, laser-nucleation is used to initiate cavitation within a few millimeters of the tip of a needle hydrophone, calibrated for magnitude and phase from 125 kHz to 20 MHz. The bubble activity, acoustically driven at f0 = 692 kHz, is resolved with high-speed shadowgraphic imaging at 5 × 106 frames per second. A synthetic spectrum is constructed from component signals based on the hydrophone data, deconvolved within the calibration bandwidth, in the time domain. Cross correlation coefficients between the experimental and synthetic spectra of 0.97 for the f 0/2 and f 0/3 regimes indicate that periodic shock waves and scattered driving field predominantly account for all spectral features, including the sub-harmonics and their over-harmonics, and harmonics of f 0
Men Are from Mars, Women Are from Venus: Evaluation and Modelling of Verbal Associations
We present a quantitative analysis of human word association pairs and study
the types of relations presented in the associations. We put our main focus on
the correlation between response types and respondent characteristics such as
occupation and gender by contrasting syntagmatic and paradigmatic associations.
Finally, we propose a personalised distributed word association model and show
the importance of incorporating demographic factors into the models commonly
used in natural language processing.Comment: AIST 2017 camera-read
New CP-violation and preferred-frame tests with polarized electrons
We used a torsion pendulum containing polarized
electrons to search for CP-violating interactions between the pendulum's
electrons and unpolarized matter in the laboratory's surroundings or the sun,
and to test for preferred-frame effects that would precess the electrons about
a direction fixed in inertial space. We find and for AU. Our preferred-frame constraints, interpreted in
the Kosteleck\'y framework, set an upper limit on the parameter eV that should be compared to the benchmark
value eV.Comment: 4 figures, accepted for publication in Physical Review Letter
Correlations, spectral gap, and entanglement in harmonic quantum systems on generic lattices
We investigate the relationship between the gap between the energy of the
ground state and the first excited state and the decay of correlation functions
in harmonic lattice systems. We prove that in gapped systems, the exponential
decay of correlations follows for both the ground state and thermal states.
Considering the converse direction, we show that an energy gap can follow from
algebraic decay and always does for exponential decay. The underlying lattices
are described as general graphs of not necessarily integer dimension, including
translationally invariant instances of cubic lattices as special cases. Any
local quadratic couplings in position and momentum coordinates are allowed for,
leading to quasi-free (Gaussian) ground states. We make use of methods of
deriving bounds to matrix functions of banded matrices corresponding to local
interactions on general graphs. Finally, we give an explicit entanglement-area
relationship in terms of the energy gap for arbitrary, not necessarily
contiguous regions on lattices characterized by general graphs.Comment: 26 pages, LaTeX, published version (figure added
Joint density-functional theory for electronic structure of solvated systems
We introduce a new form of density functional theory for the {\em ab initio}
description of electronic systems in contact with a molecular liquid
environment. This theory rigorously joins an electron density-functional for
the electrons of a solute with a classical density-functional theory for the
liquid into a single variational principle for the free energy of the combined
system. A simple approximate functional predicts, without any fitting of
parameters to solvation data, solvation energies as well as state-of-the-art
quantum-chemical cavity approaches, which require such fitting.Comment: Fixed typos and minor updates to tex
Parametric instability in dark molecular clouds
The present work investigates the parametric instability of parallel
propagating circularly polarized Alfven(pump) waves in a weakly ionized
molecular cloud. It is shown that the relative drift between the plasma
particles gives rise to the Hall effect resulting in the modified pump wave
characteristics. Although the linearized fluid equations with periodic
coefficients are difficult to solve analytically, it is shown that a linear
transformation can remove the periodic dependence. The resulting linearized
equations with constant coefficients are used to derive an algebraic dispersion
relation. The growth rate of the parametric instability is a sensitive function
of the amplitude of the pump wave as well as to the ratio of the pump and the
modified dust-cyclotron frequencies. The instability is insensitive to the
plasma-beta The results are applied to the molecular clouds.Comment: 27 page, 5 figures, accepted in Ap
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