Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature

Abstract

This work concerns the theoretical description of the quantum dynamics of molecular junctions with thermal fluctuations and probability losses. To this end, we propose a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. Along the lines discussed in [A. Sergi et al., Symmetry 10 518 (2018)], we adopt the operator-valued Wigner formulation of quantum mechanics (wherein the density matrix depends on the points of the Wigner phase space associated to the system) and derive a non-linear equation of motion. Moreover, we introduce a model for a non-Hermitian quantum single-molecule junction (nHQSMJ). In this model the leads are mapped to a tunneling two-level system, which is in turn coupled to a harmonic mode (i.e., the molecule). A decay operator acting on the two-level system describes phenomenologically probability losses. Finally, the temperature of the molecule is controlled by means of a Nosé-Hoover chain thermostat. A numerical study of the quantum dynamics of this toy model at different temperatures is reported. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction. The possibility that the formalism here presented can be extended to treat both more quantum states (∼10) and many more classical modes or atomic particles (∼103−105) is highlighted.

Quantum–Classical Hybrid Systems and Ehrenfest’s Theorem

“…When a quantum many-body system comprises light and heavy particles, approximation as a QCH can enable efficient numerical calculations [ 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 ]. Our theoretical approach uses an operator-valued Wigner function [ 9 , 10 , 11 , 12 , 13 , 14 ], thus enabling a suitable representation of mixed states and making the theory amenable to the derivation of controllable approximations of numerical algorithms [ 75 , 76 ].…”

Classical Limit of Quantum Mechanics for Damped Driven Oscillatory Systems: Quantum–Classical Correspondence

“…As n increases, the form of the obtained sawtooth driving force becomes more exact. [35][36][37][38], non-Hermitian Hamiltonian dynamics [39][40][41], and the Schwinger action method [15,42]. Let's look into the relatively well-known Lindblad dynamics here.…”

Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian

“…We mention, incidentally, that in the literature time-dependent SU(2) models have been considered which can be solved exactly without resorting to the Lewis and Riesenfeld theory [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67]. It should also be emphasized that recent studies have usefully leveraged on the knowledge of the evolution operator for time-dependent single spin 1/2 models to derive the exact dynamics of quite general multi-spin time-dependent models [68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85].…”