The real-time dynamics of a particle in a slightly asymmetric double-well potential in the presence of ohmic dissipation is analysed by using standard quantum-statistical methods. At zero temperature, the particle eventually goes towards the lower potential well; the relaxation has an overall exponential character with possibly small oscillations; at finite temperature, the particle thermalizes over the two wells; two successive exponential regimes are observed in this case. The results about the final average position of the particle agree with the detailed balance principle and are in fact independent of the ohmic assumption. For an ohmic dissipation law, the localization phenomenon which occurs in the perfectly symmetric double-well potential at zero temperature disappears when an asymmetry is present, although a precursor behaviour is displayed for very low values of the asymmetry.The real-time dynamics of a particle in a slightly asymmetric double-well potential in the presence of ohmic dissipation is analysed by using standard quantum-statistical methods. At zero temperature, the particle eventually goes towards the lower potential well; the relaxation has an overall exponential character with possibly small oscillations; at finite temperature, the particle thermalizes over the two wells; two successive exponential regimes are observed in this case. The results about the final average position of the particle agree with the detailed balance principle and are in fact independent of the ohmic assumption. For an ohmic dissipation law, the localization phenomenon which occurs in the perfectly symmetric double-well potential at zero temperature disappears when an asymmetry is present, although a precursor behaviour is displayed for very low values of the asymmetry.

Journal de physiqueJan 1, 198628 citations

Friction and dissipative phenomena in quantum mechanics

Morton D. Kostin

Journal of Statistical PhysicsFeb 1, 1975114 citations

Continuum limit frozen Gaussian approximation for the reduced thermal density matrix of dissipative systems

Riccardo Conte, Eli Pollak

A continuum limit frozen Gaussian approximation is formulated for the reduced thermal density matrix for dissipative systems. The imaginary time dynamics is obtained from a novel generalized Langevin equation for the system coordinates. The method is applied to study the thermal density in a double well potential in the presence of Ohmic-like friction. We find that the approximation describes correctly the delocalization of the density due to quantization of the vibrations in the well. It also accounts for the friction induced reduction of the tunneling density in the barrier region.A continuum limit frozen Gaussian approximation is formulated for the reduced thermal density matrix for dissipative systems. The imaginary time dynamics is obtained from a novel generalized Langevin equation for the system coordinates. The method is applied to study the thermal density in a double well potential in the presence of Ohmic-like friction. We find that the approximation describes correctly the delocalization of the density due to quantization of the vibrations in the well. It also accounts for the friction induced reduction of the tunneling density in the barrier region.

The Journal of Chemical PhysicsMar 1, 201218 citations

Dissipation and friction of a quantum spin system

Yang Wang, Yu Jia

The European Physical Journal BApr 1, 20222 citations

Dissipative Quantum Tunneling in a Biased Double-Well System at Finite Temperatures

Matthew P. A. Fisher, Alan T. Dorsey

We study quantum tunneling in a biased double-well potential in the presence of Ohmic dissipation with a friction coefficient $\ensuremath{\alpha}>1$. The tunneling rate out of the metastable well is calculated in real time as a function of the temperature $T$ and bias energy $\ensuremath{\epsilon}$. The $T=0$ result agrees with a droplet-model calculation in imaginary time. At low temperatures we find an enhancement to the $T=0$ rate varying as ${(\frac{T}{\ensuremath{\epsilon}})}^{2}$.We study quantum tunneling in a biased double-well potential in the presence of Ohmic dissipation with a friction coefficient $\ensuremath{\alpha}>1$. The tunneling rate out of the metastable well is calculated in real time as a function of the temperature $T$ and bias energy $\ensuremath{\epsilon}$. The $T=0$ result agrees with a droplet-model calculation in imaginary time. At low temperatures we find an enhancement to the $T=0$ rate varying as ${(\frac{T}{\ensuremath{\epsilon}})}^{2}$.

Physical Review LettersApr 15, 1985159 citations

Non-Markovian Quantum Dissipation in the Presence of External Fields

Rui‐Xue Xu, Yan Mo, Ping Cui +2 more

Progress in theoretical chemistry and physicsJan 1, 200314 citations

T

and bias energy $\ensuremath{\epsilon}$. The

T=0

result agrees with a droplet-model calculation in imaginary time. At low temperatures we find an enhancement to the

T=0

rate varying as ${(\frac{T}{\ensuremath{\epsilon}})}^{2}$.