arXiv subjects

Emil A. Yuzbashyan

Publications and source records attributed to Emil A. Yuzbashyan.

62 records · Page 4Linked to original sources

arXiv2005

Nonequilibrium Cooper pairing in the nonadiabatic regime

We obtain a complete solution for the mean-field dynamics of the BCS paired state with a large, but finite number of Cooper pairs in the non-adiabatic regime. We show that the problem reduces to a classical integrable Hamiltonian system and derive a complete set of its integrals of motion. The condensate exhibits irregular multi-frequency oscillations ergodically exploring the part of the phase-space allowed by the conservation laws. In the thermodynamic limit however the system can asymptotically reach a steady state.

cond-mat.supr-con↗

arXiv2005

Relaxation and persistent oscillations of the order parameter in the non-stationary BCS theory

We determine the limiting dynamics of a fermionic condensate following a sudden perturbation for various initial conditions. We demonstrate that possible initial states of the condensate fall into two classes. In the first case, the order parameter asymptotes to a constant value. The approach to a constant is oscillatory with an inverse square root decay. This happens, e.g., when the strength of pairing is abruptly changed while the system is in the paired ground state and more generally for any nonequilibrium state that is in the same class as the ground state. In the second case, the order parameter exhibits persistent oscillations with several frequencies. This is realized for nonequilibrium states that belong to the same class as excited stationary states. Our classification of initial states extends the concept of excitation spectrum to nonequilibrium regime and allows one to predict the evolution without solving equations of motion.

cond-mat.supr-con↗

arXiv2005

Integrable dynamics of coupled Fermi-Bose condensates

We study the mean-field dynamics of a fermionic condensate interacting with a single bosonic mode (a generalized Dicke model). This problem is integrable and can be mapped onto a corresponding BCS problem. We derive the general solution and a full set of integrals of motion for the time evolution of coupled Fermi-Bose condensates. The present paper complements our earlier study of the dynamics of the BCS model (cond-mat/0407501 and cond-mat/0505493). Here we provide a self-contained introduction to the variable separation method, which enables a complete analytical description of the evolution of the generalized Dicke, BCS, and other similar models.

cond-mat.supr-con↗

arXiv2005

Theory of superconducting pairing near the mobility edge

We develop a theory of a pseudogap state appearing near the superconductor-insulator transition in strongly disordered metals with attractive interaction. We show that such an interaction combined with the fractal nature of the single particle wave functions near the mobility edge leads to an anomalously large single particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem.

cond-mat.supr-con↗

arXiv2004

Solution for the dynamics of the BCS and central spin problems

We develop an explicit description of a time-dependent response of fermionic condensates to perturbations. The dynamics of Cooper pairs at times shorter than the energy relaxation time can be described by the BCS model. We obtain a general explicit solution for the dynamics of the BCS model. We also solve a closely related dynamical problem - the central spin model, which describes a localized spin coupled to a "spin bath". Here, we focus on presenting the solution and describing its general properties, but also mention some applications, e.g. to nonstationary pairing in cold Fermi gases and to the issue of electron spin decoherence in quantum dots. A typical dynamics of the BCS and central spin models is quasi-periodic with a large number of frequencies and stable under small perturbations. We show that for certain special initial conditions the number of frequencies decreases and the solution simplifies. In particular, periodic solutions correspond to the ground state and excitations of the BCS model.

cond-mat.supr-con↗

arXiv2004

Finite Size Corrections for the Pairing Hamiltonian

We study the effects of superconducting pairing in small metallic grains. We show that in the limit of large Thouless conductance one can explicitly determine the low energy spectrum of the problem as an expansion in the inverse number of electrons on the grain. The expansion is based on the formal exact solution of the Richardson model. We use this expansion to calculate finite size corrections to the ground state energy, Matveev-Larkin parameter, and excitation energies.

cond-mat.supr-con↗

arXiv2003

Strong Coupling Expansion for the Pairing Hamiltonian

The paper is devoted to the effects of superconducting pairing in small metallic grains. It turns out that at strong superconducting coupling and in the limit of large Thouless conductance one can explicitly determine the low energy spectrum of the problem. We start with the strong coupling limit and develop a systematic expansion in powers of the inverse coupling constant for the many-particle spectrum of the system. The strong coupling expansion is based on the formal exact solution of the Richardson model and converges for realistic values of the coupling constant. We use this expansion to study the low energy excitations of the system, in particular energy and spin gaps in the many-body spectrum.

cond-mat.str-el↗

arXiv2003

Extracting Hidden Symmetry from the Energy Spectrum

In this paper we revisit the problem of finding hidden symmetries in quantum mechanical systems. Our interest in this problem was renewed by nontrivial degeneracies of a simple spin Hamiltonian used to model spin relaxation in alkali-metal vapors. We consider this spin Hamiltonian in detail and use this example to outline a general approach to finding symmetries when eigenvalues and eigenstates of the Hamiltonian are known. We extract all nontrivial symmetries responsible for the degeneracy and show that the symmetry group of the Hamiltonian is SU(2). The symmetry operators have a simple meaning which becomes transparent in the limit of large spin. As an additional example we apply the method to the Hydrogen atom.

cond-mat↗