Noise-induced transition in a quantum system

We examine the noise-induced transition in a fluctuating bistable potential of a driven quantum system in thermal equilibrium. Making use of a Wigner canonical thermal distribution for description of the statistical properties of the thermal bath, we explore the generic effects of quantization like vacuum field fluctuation and tunneling in the characteristic stationary probability distribution functions undergoing transition from unimodal to bimodal nature and in signal-to-noise ratio characterizing the co-operative effect among the noise processes and the weak periodic signal.Comment: To appear on Physics Letters

Numerical simulation of transmission coefficient using c-number Langevin equation

We numerically implement the reactive flux formalism on the basis of a recently proposed c-number Langevin equation [Barik \textit{et al}, J. Chem. Phys. {\bf 119}, 680 (2003); Banerjee \textit{et al}, Phys. Rev. E {\bf 65}, 021109 (2002)] to calculate transmission coefficient. The Kramers' turnover, the $T^2$ enhancement of the rate at low temperatures and other related features of temporal behaviour of the transmission coefficient over a range of temperature down to absolute zero, noise correlation and friction are examined for a double well potential and compared with other known results. This simple method is based on canonical quantization and Wigner quasiclassical phase space function and takes care of quantum effects due to the system order by order

Noise-induced quantum transport

We analyze the problem of directed quantum transport induced by external exponentially correlated telegraphic noise. In addition to quantum nature of the heat bath, nonlinearity of the periodic system potential brings in quantum contribution. We observe that quantization, in general, enhances classical current at low temperature, while the differences become insignificant at higher temperature. Interplay of quantum diffusion and quantum correction to system potential is analyzed for various ranges of temperature, correlation time and strength of external noise and asymmetry parameters. A possible experimental realization of the observed quantum effects in a superionic conductor placed in a random asymmetric dichotomous electric field has been suggested.Comment: 23 pages and 5 figures. To be published in Physical Review

Anharmonic quantum contribution to vibrational dephasing

Based on a quantum Langevin equation and its corresponding Hamiltonian within a c-number formalism we calculate the vibrational dephasing rate of a cubic oscillator. It is shown that leading order quantum correction due to anharmonicity of the potential makes a significant contribution to the rate and the frequency shift. We compare our theoretical estimates with those obtained from experiments for small diatomics $N_2$, $O_2$ and $CO$.Comment: 21 pages, 1 figure and 1 tabl

Quantum escape kinetics over a fluctuating barrier

The escape rate of a particle over a fluctuating barrier in a double well potential exhibits resonance at an optimum value of correlation time of fluctuation. This has been shown to be important in several variants of kinetic model of chemical reactions . We extend the analysis of this phenomenon of resonant activation to quantum domain to show how quantization significantly enhances resonant activation at low temperature due to tunneling

Quantum phase-space function formulation of reactive flux theory

On the basis of a coherent-state representation of the quantum noise operator and an ensemble averaging procedure a scheme for quantum Brownian motion has been proposed recently [Banerjee et al., Phys. Rev. E 65, 021109 (2002); 66, 051105 (2002)]. We extend this approach to formulate reactive flux theory in terms of quantum phase space distribution functions and to derive a time-dependent quantum transmission coefficient-a quantum analog of the classical Kramers-Grote-Hynes coefficient in the spirit of Kohen and Tannor's classical formulation. The theory is valid for arbitrary noise correlation and temperature. The specific forms of this coefficient in the Markovian as well as in the non-Markovian limits have been worked out in detail for the intermediate to strong damping regimes with an analysis of quantum effects. While the classical transmission coefficient is independent of temperature, its quantum counterpart has significant temperature dependence particularly in the low-temperature regime