58,818 research outputs found
Geodesic Paths for Quantum Many-Body Systems
We propose a method to obtain optimal protocols for adiabatic ground-state
preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak
and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum
non-dissipative systems. The space of controllable parameters of isolated
quantum many-body systems is endowed with a Riemannian quantum metric
structure, which can be exploited when such systems are driven adiabatically.
Here, we use this metric structure to construct optimal protocols in order to
accomplish the task of adiabatic ground-state preparation in a fixed amount of
time. Such optimal protocols are shown to be geodesics on the parameter
manifold, maximizing the local fidelity. Physically, such protocols minimize
the average energy fluctuations along the path. Our findings are illustrated on
the Landau-Zener model and the anisotropic XY spin chain. In both cases we show
that geodesic protocols drastically improve the final fidelity. Moreover, this
happens even if one crosses a critical point, where the adiabatic perturbation
theory fails.Comment: 5 pages, 2 figures + 4 pages supplemen
Geodesic paths for quantum many-body systems
We propose a method to obtain optimal protocols for adiabatic ground-state preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum non-dissipative systems. The space of controllable parameters of isolated quantum many-body systems is endowed with a Riemannian quantum metric structure, which can be exploited when such systems are driven adiabatically. Here, we use this metric structure to construct optimal protocols in order to accomplish the task of adiabatic ground-state preparation in a fixed amount of time. Such optimal protocols are shown to be geodesics on the parameter manifold, maximizing the local fidelity. Physically, such protocols minimize the average energy fluctuations along the path. Our findings are illustrated on the Landau-Zener model and the anisotropic XY spin chain. In both cases we show that geodesic protocols drastically improve the final fidelity. Moreover, this happens even if one crosses a critical point, where the adiabatic perturbation theory fails.http://meetings.aps.org/link/BAPS.2016.MAR.F50.9First author draf
Classical and Quantum Fluctuation Theorems for Heat Exchange
The statistics of heat exchange between two classical or quantum finite
systems initially prepared at different temperatures are shown to obey a
fluctuation theorem.Comment: 4 pages, 1 included figure, to appear in Phys Rev Let
On the Quantum Jarzynski Identity
In this note, we will discuss how to compactly express and prove the
Jarzynski identity for an open quantum system with dissipative dynamics. We
will avoid explicitly measuring the work directly, which is tantamount to
continuously monitoring the system, and instead measure the heat flow from the
environment. We represent the measurement of heat flow with Hermitian map
superoperators that act on the system density matrix. Hermitian maps provide a
convenient and compact representation of sequential measurement and correlation
functions.Comment: 4 page
Temperature-extended Jarzynski relation: Application to the numerical calculation of the surface tension
We consider a generalization of the Jarzynski relation to the case where the
system interacts with a bath for which the temperature is not kept constant but
can vary during the transformation. We suggest to use this relation as a
replacement to the thermodynamic perturbation method or the Bennett method for
the estimation of the order-order surface tension by Monte Carlo simulations.
To demonstrate the feasibility of the method, we present some numerical data
for the 3D Ising model
Non-equilibrium Relations for Spin Glasses with Gauge Symmetry
We study the applications of non-equilibrium relations such as the Jarzynski
equality and fluctuation theorem to spin glasses with gauge symmetry. It is
shown that the exponentiated free-energy difference appearing in the Jarzynski
equality reduces to a simple analytic function written explicitly in terms of
the initial and final temperatures if the temperature satisfies a certain
condition related to gauge symmetry. This result is used to derive a lower
bound on the work done during the non-equilibrium process of temperature
change. We also prove identities relating equilibrium and non-equilibrium
quantities. These identities suggest a method to evaluate equilibrium
quantities from non-equilibrium computations, which may be useful to avoid the
problem of slow relaxation in spin glasses.Comment: 8 pages, 2 figures, submitted to JPS
Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis
In this paper we present a first-principles analysis of the nonequilibrium
work distribution and the free energy difference of a quantum system
interacting with a general environment (with arbitrary spectral density and for
all temperatures) based on a well-understood micro-physics (quantum Brownian
motion) model under the conditions stipulated by the Jarzynski equality [C.
Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)] and Crooks' fluctuation theorem
[G. E. Crooks, Phys. Rev. E 60, 2721 (1999)] (in short FTs). We use the
decoherent history conceptual framework to explain how the notion of
trajectories in a quantum system can be made viable and use the
environment-induced decoherence scheme to assess the strength of noise which
could provide sufficient decoherence to warrant the use of trajectories to
define work in open quantum systems. From the solutions to the Langevin
equation governing the stochastic dynamics of such systems we were able to
produce formal expressions for these quantities entering in the FTs, and from
them prove explicitly the validity of the FTs at the high temperature limit. At
low temperatures our general results would enable one to identify the range of
parameters where FTs may not hold or need be expressed differently. We explain
the relation between classical and quantum FTs and the advantage of this
micro-physics open-system approach over the phenomenological modeling and
energy-level calculations for substitute closed quantum systems
Posterior probability and fluctuation theorem in stochastic processes
A generalization of fluctuation theorems in stochastic processes is proposed.
The new theorem is written in terms of posterior probabilities, which are
introduced via the Bayes theorem. In usual fluctuation theorems, a forward path
and its time reversal play an important role, so that a microscopically
reversible condition is essential. In contrast, the microscopically reversible
condition is not necessary in the new theorem. It is shown that the new theorem
adequately recovers various theorems and relations previously known, such as
the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the
Hatano-Sasa relation, when adequate assumptions are employed.Comment: 4 page
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