Latest Research Papers In Condensed Matter Physics | (Cond-Mat.Stat-Mech) 2019-07-09
Statistical Mechanics
Optimal cycles for low-dissipation heat engines (1907.02939v1)
Paolo Abiuso, Martí Perarnau-Llobet
2019-07-05
We consider the optimization of a finite-time Carnot engine characterized by small dissipations. We show with a simple inequality that the optimal strategy is to perform infinitesimal cycles around a given working point, which can be thus chosen optimally. Remarkably, this optimal point is independent of the figure of merit combining power and efficiency that is being maximised. Furthermore, in the corresponding cycle the power output becomes proportional to the heat capacity of the working substance. Since the heat capacity can scale supra-extensively with the number of constituents of the engine (e.g. in a phase transition point), this enables us to design many-body heat engines reaching Carnot efficiency at finite power per constituent in the thermodynamic limit.
Action principle and weak invariants (1903.02302v2)
Sumiyoshi Abe, Congjie Ou
2019-03-06
A weak invariant associated with a master equation is characterized in such a way that its spectrum is not constant in time but its expectation value is conserved under time evolution generated by the master equation. Here, an intriguing relationship between the concept of weak invariants and the action principle for master equations based on the auxiliary operator formalism is revealed. It is shown that the auxiliary operator can be thought of as a weak invariant.
Boundary TBA, trees and loops (1809.05705v2)
Ivan Kostov, Didina Serban, Dinh-Long Vu
2018-09-15
We derive a graph expansion for the thermal partition function of solvable two-dimensional models with boundaries. This expansion of the integration measure over the virtual particles winding around the time cycle is obtained with the help of the matrix-tree theorem. The free energy is a sum over all connected graphs, which can be either trees or trees with one loop. The generating function for the connected trees satisfies a non-linear integral equation, which is equivalent to the TBA equation. The sum over connected graphs gives the bulk free energy as well as the exact g-functions for the two boundaries. We reproduced the integral formula conjectured by Dorey, Fioravanti, Rim and Tateo, and proved subsequently by Pozsgay. The method is easily extended to the case of non-diagonal bulk scattering and diagonal reflection matrices. As an example we consider a system with two types of particles solved by nested Bethe Ansatz
Open XXZ chain and boundary modes at zero temperature (1901.10932v4)
Sebastian Grijalva, Jacopo De Nardis, Veronique Terras
2019-01-30
We study the open XXZ spin chain in the anti-ferromagnetic regime and for generic longitudinal magnetic fields at the two boundaries. We discuss the ground state via the Bethe ansatz and we show that, for a chain of even length L and in a regime where both boundary magnetic fields are equal and bounded by a critical field, the spectrum is gapped and the ground state is doubly degenerate up to exponentially small corrections in L. We connect this degeneracy to the presence of a boundary root, namely an excitation localized at one of the two boundaries. We compute the local magnetization at the left edge of the chain and we show that, due to the existence of a boundary root, this depends also on the value of the field at the opposite edge, even in the half-infinite chain limit. Moreover we give an exact expression for the large time limit of the spin autocorrelation at the boundary, which we explicitly compute in terms of the form factor between the two quasi-degenerate ground states. This, as we show, turns out to be equal to the contribution of the boundary root to the local magnetization. We finally discuss the case of chains of odd length.
The free energy of compressed lattice knots (1903.00441v4)
EJ Janse van Rensburg
2019-03-01
A compressed knotted ring polymer in a confining cavity is modelled by a knotted lattice polygon confined in a cube in
. The GAS algorithm [17] is used to sample lattice polygons of fixed knot type in a confining cube and to estimate the free energy of confined lattice knots. Lattice polygons of knot types the unknot, the trefoil knot, and the figure eight knot, are sampled and the free energies are estimated as functions of the concentration of monomers in the confining cube. The data show that the free energy is a function of knot type at low concentrations, and (mean-field) Flory-Huggins theory [12,15] is used to model the free energy as a function of monomer concentration. The Flory interaction parameter of knotted lattice polygons in
Don't forget to Follow and Resteem. @arxivsanity
Keeping everyone inform.