We study the real time dynamics of a quantum system with a potential barrier coupled to a heat-bath environment. The time evolution of the density matrix starting from a general initial state is evaluated explicitly in the semiclassical approximation. As the temperature is decreased below a critical temperature ${\mathit{T}}_{\mathit{c}}$ , large quantum fluctuations render the harmonic approximation near the barrier top insufficient and a caustic arises. As a consequence, anharmonicities of the potential become essential, even in the close vicinity of the barrier top, and the semiclassical density matrix has to be evaluated beyond the Gaussian approximation. The range of validity with respect to temperature and time of the semiclassical analytical results is discussed in detail. We illustrate the outcome of the theory with an explicit example.We study the real time dynamics of a quantum system with a potential barrier coupled to a heat-bath environment. The time evolution of the density matrix starting from a general initial state is evaluated explicitly in the semiclassical approximation. As the temperature is decreased below a critical temperature ${\mathit{T}}_{\mathit{c}}$, large quantum fluctuations render the harmonic approximation near the barrier top insufficient and a caustic arises. As a consequence, anharmonicities of the potential become essential, even in the close vicinity of the barrier top, and the semiclassical density matrix has to be evaluated beyond the Gaussian approximation. The range of validity with respect to temperature and time of the semiclassical analytical results is discussed in detail. We illustrate the outcome of the theory with an explicit example.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsNov 1, 199513 citations

Dissipative quantum systems with a potential barrier. III. Steady state nonequilibrium flux and reaction rate

Joachim Ankerhold, Hermann Grabert

We study the real time dynamics of a dissipative quantum system in a metastable state which may decay by crossing a potential barrier. Starting from an initial state where the system is in thermal equilibrium on one side of the barrier, the time evolution of the density matrix is evaluated analytically in the semiclassical approximation for coordinates near the barrier top. In a region about a critical temperature ${\mathrm{T}}_{\mathrm{c}}$ large quantum fluctuations render the harmonic approximation of the potential insufficient and anharmonicities become essential. Accounting for non-Gaussian fluctuation modes, we show that the density matrix approaches a quasistationary state with a constant flux across the barrier. This extends our earlier results [Phys. Rev. E 51, 4267 (1995)] on the quantum generalization of the Kramers flux state to the region about ${\mathrm{T}}_{\mathrm{c}}$ . By matching the flux state onto the equilibrium state on one side of the barrier, we determine the decay rate out of the metastable state. The rate constant shows a changeover from thermally activated decay to quantum tunneling for temperatures below ${\mathrm{T}}_{\mathrm{c}}$ .We study the real time dynamics of a dissipative quantum system in a metastable state which may decay by crossing a potential barrier. Starting from an initial state where the system is in thermal equilibrium on one side of the barrier, the time evolution of the density matrix is evaluated analytically in the semiclassical approximation for coordinates near the barrier top. In a region about a critical temperature ${\mathrm{T}}_{\mathrm{c}}$ large quantum fluctuations render the harmonic approximation of the potential insufficient and anharmonicities become essential. Accounting for non-Gaussian fluctuation modes, we show that the density matrix approaches a quasistationary state with a constant flux across the barrier. This extends our earlier results [Phys. Rev. E 51, 4267 (1995)] on the quantum generalization of the Kramers flux state to the region about ${\mathrm{T}}_{\mathrm{c}}$. By matching the flux state onto the equilibrium state on one side of the barrier, we determine the decay rate out of the metastable state. The rate constant shows a changeover from thermally activated decay to quantum tunneling for temperatures below ${\mathrm{T}}_{\mathrm{c}}$.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsFeb 1, 19979 citations

Tunnelling through a dynamical barrier in dissipative quantum systems

D. Boosé, J. Richert, Uzy Smilansky

Quantum tunnelling induces transitions not only through potential barriers, but also through energy barriers of dynamical origin. The coupling to a noisy environment introduces dissipation which affects tunnelling. This effect is studied by an analytic non-perturbative solution of a problem involving tunnelling through a dynamical barrier in the presence of a noisy environment. The accessibility to the classically forbidden energy region above the dynamical barrier is reduced (enhanced) by the friction(diffusion) effect. The occupation of each level above the dynamical barrier is characterized by the succession in time of two different regimes. The transition between both regimes is ruled by an energy criterion which is discussed.Quantum tunnelling induces transitions not only through potential barriers, but also through energy barriers of dynamical origin. The coupling to a noisy environment introduces dissipation which affects tunnelling. This effect is studied by an analytic non-perturbative solution of a problem involving tunnelling through a dynamical barrier in the presence of a noisy environment. The accessibility to the classically forbidden energy region above the dynamical barrier is reduced (enhanced) by the friction(diffusion) effect. The occupation of each level above the dynamical barrier is characterized by the succession in time of two different regimes. The transition between both regimes is ruled by an energy criterion which is discussed.

Journal of Physics A Mathematical and GeneralNov 21, 19921 citation

Dissipative Quantum Systems

WORLD SCIENTIFIC eBooksOct 1, 200813 citations

{\mathit{T}}_{\mathit{c}}

, large quantum fluctuations render the harmonic approximation near the barrier top insufficient and a caustic arises. As a consequence, anharmonicities of the potential become essential, even in the close vicinity of the barrier top, and the semiclassical density matrix has to be evaluated beyond the Gaussian approximation. The range of validity with respect to temperature and time of the semiclassical analytical results is discussed in detail. We illustrate the outcome of the theory with an explicit example.

{\mathrm{T}}_{\mathrm{c}}

large quantum fluctuations render the harmonic approximation of the potential insufficient and anharmonicities become essential. Accounting for non-Gaussian fluctuation modes, we show that the density matrix approaches a quasistationary state with a constant flux across the barrier. This extends our earlier results [Phys. Rev. E 51, 4267 (1995)] on the quantum generalization of the Kramers flux state to the region about

{\mathrm{T}}_{\mathrm{c}}

. By matching the flux state onto the equilibrium state on one side of the barrier, we determine the decay rate out of the metastable state. The rate constant shows a changeover from thermally activated decay to quantum tunneling for temperatures below

{\mathrm{T}}_{\mathrm{c}}