arXiv subjects

Hermann Grabert

Publications and source records attributed to Hermann Grabert.

66 records · Page 4Linked to original sources

arXiv1997

Coulomb charging energy for arbitrary tunneling strength

The Coulomb energy of a small metallic island coupled to an electrode by a tunnel junction is investigated. We employ Monte Carlo simulations to determine the effective charging energy for arbitrary tunneling strength. For small tunneling conductance, the data agree with analytical results based on a perturbative treatment of electron tunneling, while for very strong tunneling recent semiclassical results for large conductance are approached. The data allow for an identification of the range of validity of various analytical predictions.

cond-mat↗

arXiv1997

High temperature anomaly of the conductance of a tunnel junction

The linear conductance of a tunnel junction in series with an ohmic resistor is determined in the high temperature limit. The tunneling current is treated nonperturbatively by means of path integral techniques. Due to quantum effects the conductance is smaller than the classical series conductance. The reduction factor is found to be nonanalytic in the environmental resistance for vanishing resistance. This behavior is a high temperature manifestation of the Coulomb blockade effect.

cond-mat↗

arXiv1997

Crossover from coherent to incoherent dynamics in damped quantum systems

The destruction of quantum coherence by environmental influences is investigated taking the damped harmonic oscillator and the dissipative two-state system as prototypical examples. It is shown that the location of the coherent-incoherent transition depends to a large degree on the dynamical quantity under consideration.

cond-mat.stat-mech↗

arXiv1997

Charging effects in quantum wires

We investigate the role of charging effects in a voltage-biased quantum wire. Both the finite range of the Coulomb interaction and the long-ranged nature of the Friedel oscillation imply a finite capacitance, leading to a charging energy. While observable Coulomb blockade effects are absent for a single impurity, they are crucial if islands are present. For a double barrier, we give the resonance condition, fully taking into account the charging of the island.

cond-mat.mes-hall↗

arXiv1996

Exact time evolution and master equations for the damped harmonic oscillator

Using the exact path integral solution for the damped harmonic oscillator it is shown that in general there does not exist an exact dissipative Liouville operator describing the dynamics of the oscillator for arbitrary initial bath preparations. Exact non-stationary Liouville operators can be found only for particular preparations. Three physically meaningful examples are examined. An exact new master equation is derived for thermal initial conditions. Second, the Liouville operator governing the time-evolution of equilibrium correlations is obtained. Third, factorizing initial conditions are studied. Additionally, one can show that there are approximate Liouville operators independent of the initial preparation describing the long time dynamics under appropriate conditions. The general form of these approximate master equations is derived and the coefficients are determined for special cases of the bath spectral density including the Ohmic, Drude and weak coupling cases. The connection with earlier work is discussed.

physics.atom-ph↗

arXiv1996

Voltage-biased quantum wire with impurities

The bosonization technique to describe correlated electrons in a one-dimensional quantum wire containing impurities is extended to include an applied voltage source. The external reservoirs are shown to lead to a boundary condition for the boson phase fields. We use the formalism to investigate the channel conductance, electroneutrality, and charging effects.

cond-mat↗

arXiv1996

Friedel oscillations in Luttinger liquids

We study the density disturbance of a correlated 1D electron liquid in the presence of a scatterer or a barrier. The 2k_F-periodic density profile away from the barrier (Friedel oscillation) is computed for arbitrary electron--electron interaction and arbitrary impurity strength. We find that in presence of correlations, the Friedel oscillation decays slower than predicted by Fermi liquid theory. In the case of a spinless Luttinger liquid characterized by an interaction constant g<1, the asymptotic decay of the Friedel oscillation is x^-g. For a weak scatterer, the decay is even slower at small-to-intermediate distances from the impurity, with a crossover to the asymptotic x^-g law.

cond-mat↗

arXiv1996

Exact and Semiclassical Density Matrix of a Particle Moving in a Barrier Potential with Bound States

We present a barrier potential with bound states that is exactly solvable and determine the eigenfunctions and eigenvalues of the Hamiltonian. The equilibrium density matrix of a particle moving at temperature T in this nonlinear barrier potential field is determined. The exact density matrix is compared with the result of the path integral approach in the semiclassical approximation. For opaque barriers the simple semiclassical approximation is found to be sufficient at high temperatures while at low temperatures the fluctuation paths may have a caustic depending on temperature and endpoints. Near the caustics the divergence of the simple semiclassical approximation of the density matrix is removed by a nonlinear fluctuation potential. For opaque barriers the improved semiclassical approximation is again in agreement with the exact result. In particular, bound states and the form of resonance states are described accurately by the semiclassical approach.

chem-ph↗

arXiv1995

Quantum Effects in Barrier Dynamics

The dynamics near the top of a potential barrier is studied in the temperature region where quantum effects become important. The time evolution of the density matrix of a system that deviates initially from equilibrium in the vicinity of the barrier top but is in local equilibrium away from the barrier top is determined. Explicit results are given for a range of parameters where the nonequilibrium state is not affected by anharmonicities of the barrier potential except for the barrier height. In particular, for a system confined initially to one side of the barrier the relaxation to a quasi--stationary flux state is determined. The associated rate constant is evaluated and the relation to other rate formulas is discussed in detail.

chem-ph↗

arXiv1995

Coulomb Charging at Large Conduction

We discuss the suppression of Coulomb charging effects on a small metallic island coupled to an electrode by a tunnel junction. At high temperatures the quantum corrections to the classical charging energy $E_c=e^2/2C$, where $C$ is the island capacitance, are evaluated. At low temperatures the large quantum fluctuations of the island charge cause a strong reduction of the effective $E_c$ which is determined explicitly in the limit of a large tunneling conductance.

cond-mat↗

arXiv1995

Friedel oscillations for interacting fermions in one dimension

We study Friedel oscillations in one-dimensional electron liquid for arbitrary electron-electron interaction and arbitrary impurity strength. For Luttinger liquid leads, the Friedel oscillations decay as x^-g far away from the impurity, where g is the interaction constant. For a weak scatterer, a slower decay is found at intermediate distances from the impurity, with a crossover to the asymptotic x^-g law.

cond-mat↗

arXiv1995

Dissipative Quantum Systems with Potential Barrier. General Theory and Parabolic Barrier

We study the real time dynamics of a quantum system with potential barrier coupled to a heat-bath environment. Employing the path integral approach an evolution equation for the time dependent density matrix is derived. The time evolution is evaluated explicitly near the barrier top in the temperature region where quantum effects become important. It is shown that there exists a quasi-stationary state with a constant flux across the potential barrier. This state generalizes the Kramers flux solution of the classical Fokker-Planck equation to the quantum regime. In the temperature range explored the quantum flux state depends only on the parabolic approximation of the anharmonic barrier potential near the top. The parameter range within which the solution is valid is investigated in detail. In particular, by matching the flux state onto the equilibrium state on one side of the barrier we gain a condition on the minimal damping strength. For very high temperatures this condition reduces to a known result from classical rate theory. Within the specified parameter range the decay rate out of a metastable state is calculated from the flux solution. The rate is shown to coincide with the result of purely thermodynamic methods. The real time approach presented can be extended to lower temperatures and smaller damping.

quant-ph↗