Statistical Mechanics
Energetic footprints of irreversibility in the quantum regime (1907.06559v1)
M. H. Mohammady, A. Aufféves, J. Anders
2019-07-15
The unavoidable presence of irreversibility in classical thermodynamic processes carries two energetic footprints - the reduction of extractable work from the optimal, reversible case, and the generation of a surplus of heat that is irreversibly dissipated to the environment. Optimal thermodynamic protocols hence attempt to minimize irreversibility, quantified by the entropy production, subject to practical constraints. Recently it has been shown that in the quantum regime an additional quantum entropy production occurs, that can be linked to the fundamental irreversibility of a quantum system decohering into the energy basis. Here we employ quantum trajectories to construct distributions for classical heat and quantum heat exchanges, and show that the heat footprint of quantum irreversibility differs markedly from the classical case. We also quantify how the occurrence of quantum irreversibility reduces the amount of work that can be extracted from a state with coherences. Our results show that decoherence leads to both entropic and energetic footprints which play an important role in the optimization of controlled quantum operations at low temperature, including quantum processors.
Analogue of Hamilton-Jacobi theory for the time-evolution operator (1902.07237v3)
Michael Vogl, Pontus Laurell, Aaron D. Barr, Gregory A. Fiete
2019-02-19
In this paper we develop an analogue of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the time-evolution operator, and also provides a unified framework and starting point for many well-known approximations to the time-evolution operator. In the important special case of periodically driven systems at stroboscopic times, we find relatively simple equations for the coupling constants of the Floquet Hamiltonian, where a straightforward truncation of the couplings leads to a powerful class of approximations. Using our theory, we construct a flow chart that illustrates the connection between various common approximations, which also highlights some missing connections and associated approximation schemes. These missing connections turn out to imply an analytically accessible approximation that is the "inverse" of a rotating frame approximation and thus has a range of validity complementary to it. We numerically test the various methods on the one-dimensional Ising model to confirm the ranges of validity that one would expect from the approximations used. The theory provides a map of the relations between the growing number of approximations for the time-evolution operator. We describe these relations in a table showing the limitations and advantages of many common approximations, as well as the new approximations introduced in this paper.
An alternative flow equation for the functional renormalization group (1907.06503v1)
Elizabeth Alexander, Peter Millington, Jordan Nursey, Paul M. Saffin
2019-07-15
We derive an alternative to the Wetterich-Morris-Ellwanger equation by means of the two-particle irreducible (2PI) effective action, exploiting the method of external sources due to Garbrecht and Millington. The latter allows the two-point source of the 2PI effective action to be associated consistently with the regulator of the renormalization group flow. We show that this procedure leads to a flow equation that differs from that obtained in the standard approach based on the average one-particle irreducible effective action.
Capturing strong correlations in spin, electron and local moment systems (1906.08251v2)
Eoin Quinn
2019-06-19
We address the question of identifying degrees of freedom for quantum systems. Typically, quasi-particle descriptions of correlated matter are based upon the canonical algebras of bosons or fermions. Here we highlight that a special class of non-canonical algebras also offer useful quantum degrees of freedom, allowing for the development of quasi-particle descriptions which go beyond the weakly correlated paradigm. We give a broad overview of such algebras for spin, electron and local moment systems, and outline important test problems upon which to develop the framework.
Emergence of a bicritical end point in the random crystal field Blume-Capel model (1907.06454v1)
Sumedha, Soheli Mukherjee
2019-07-15
We obtain the phase diagram for the Blume-Capel model with bimodal distribution for random crystal fields, in the space of three fields: temperature, crystal field and magnetic field. We find that three critical lines meet at a tricritical point, but only for weak disorder. As disorder strength increases there is no tricritical point in the phase diagram. We instead find a bicritical end point, where only two of the critical lines meet on a first order surface in the H=0 plane. For intermediate strengths of disorder, the phase diagram has critical end points along with the bicritical end point. One needs to look at the phase diagram in the space of three fields to identify various such multicritical points.
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