A Langevin Canonical Approach to the Dynamics of Chiral Systems: Populations and Coherences

Abstract

A canonical framework for chiral two-level systems coupled to a bath of harmonic oscillators is developed to extract, from a stochastic dynamics, the thermodynamic equilibrium values of both the population difference and coherences. The incoherent and coherent tunneling regimes are analyzed for an Ohmic environment in terms of a critical temperature defined by the maximum of the heat capacity. The corresponding numerical results issued from solving a non-linear coupled system of equations are fitted to approximate path-integral analytical expressions beyond the so-called non-interacting blip approximation in order to determine the different time scales governing both regimes.

A Langevin Canonical Approach to the Study of Quantum Stochastic Resonance in Chiral Molecules

“…In these cases, the time evolution of each individual trajectory is not possible, and a previous stability analysis is mandatory. However, in the stable case, a satisfactory description of population differences and coherences, average energies, and heat capacity have been achieved by running up to 10 4 trajectories (as previously used) [21,22]. The friction coefficient used is finally γ = 0.1 (dimensionless rate), and a canonical (Maxwell-Boltzmann) distribution is assumed, only classical noise being considered.…”

“…The average energy in the normalized |Ψ(t) state is given by Ψ|Ĥ|Ψ = −2δ √ 1 − z 2 cos Φ + 2 z ≡ H 0 , where H 0 represents a Hamiltonian function. Furthermore, the Heisenberg equations of motion can be easily derived fromż = −∂H 0 /∂Φ andΦ = ∂H 0 /∂z, leading to the following non-linear coupled equations for an isolated chiral TLS [19][20][21][22]…”

“…In previous works, we have applied this formalism to study the dissipative and stochastic dynamics of chiral systems by analyzing the population difference and coherences [19,21], thermal averages and heat capacity [22], the geometric phase [33], as well as the decoherence process [20]. The obtained thermodynamical results agree very well with the standard results issued from a previous work devoted to the study of the thermodynamics of an ensemble of non-interacting chiral molecules [34], which was carried out with an alternative methodology.…”

“…In a series of papers [19][20][21][22], the authors have studied a chiral TLS in the presence of an environment (harmonic bath) leading to a more realistic analysis of chiral dynamics. The TLS is modeled by a two-well (asymmetric) potential within the Born-Oppenheimer approximation.…”

A Langevin Canonical Approach to the Dynamics of Chiral Systems: Thermal Averages and Heat Capacity

“…This work can be considered as a step forward (as a follow‐up of a previous work) into a more complete stochastic dynamical analysis of this open quantum system by focusing on different thermodynamic quantities such as average energies, phase differences, and heat capacities. We are not going to consider here a very important topic about anomalies of the heat capacity and refer the reader to some pertinent works .…”