Is the dynamics of open quantum systems always linear?

We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system density matrix and a bath density matrix the time evolution generally is no longer governed by a linear map nor is this map affine. Put differently, the evolution is truly nonlinear and cannot be cast into the form of a linear map plus a term that is independent of the initial density matrix of the open quantum system. As a consequence, the inhomogeneity that emerges in formally exact generalized master equations is in fact a nonlinear term that vanishes for a factorizing initial state. The general results are elucidated with the example of two interacting spins prepared at thermal equilibrium with one spin subjected to an external field. The second spin represents the environment. The field allows the preparation of mixed density matrices of the first spin that can be represented as a convex combination of two limiting pure states, i.e. the preparable reduced density matrices make up a convex set. Moreover, the map from these reduced density matrices onto the corresponding density matrices of the total system is affine only for vanishing coupling between the spins. In general, the set of the accessible total density matrices is nonconvex.Comment: 19 pages, 3 figures, minor changes to improve readability, discussion on Mori's linear regime and references adde

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.Comment: 4 pages REVTeX, incl 3 figures, to appear in Europhys.Let

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.Comment: 4 pages REVTeX, incl one figure, to appear in Phys.Rev.Let

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.Comment: 29 pages + 1 figure as compressed ps-file (uufiles) to appear in Phys. Rev.

Microsecond resolution of quasiparticle tunneling in the single-Cooper-pair-transistor

We present radio-frequency measurements on a single-Cooper-pair-transistor in which individual quasiparticle poisoning events were observed with microsecond temporal resolution. Thermal activation of the quasiparticle dynamics is investigated, and consequently, we are able to determine energetics of the poisoning and un-poisoning processes. In particular, we are able to assign an effective quasiparticle temperature to parameterize the poisoning rate.Comment: 4 pages, 4 fig

Quantum-Dot Cellular Automata using Buried Dopants

The use of buried dopants to construct quantum-dot cellular automata is investigated as an alternative to conventional electronic devices for information transport and elementary computation. This provides a limit in terms of miniaturisation for this type of system as each potential well is formed by a single dopant atom. As an example, phosphorous donors in silicon are found to have good energy level separation with incoherent switching times of the order of microseconds. However, we also illustrate the possibility of ultra-fast quantum coherent switching via adiabatic evolution. The switching speeds are numerically calculated and found to be 10's of picoseconds or less for a single cell. The effect of decoherence is also simulated in the form of a dephasing process and limits are estimated for operation with finite dephasing. The advantages and limitations of this scheme over the more conventional quantum-dot based scheme are discussed. The use of a buried donor cellular automata system is also discussed as an architecture for testing several aspects of buried donor based quantum computing schemes.Comment: Minor changes in response to referees comments. Improved section on scaling and added plot of incoherent switching time

Quantum Brownian Motion With Large Friction

Quantum Brownian motion in the strong friction limit is studied based on the exact path integral formulation of dissipative systems. In this limit the time-nonlocal reduced dynamics can be cast into an effective equation of motion, the quantum Smoluchowski equation. For strongly condensed phase environments it plays a similar role as master equations in the weak coupling range. Applications for chemical, mesoscopic, and soft matter systems are discussed and reveal the substantial role of quantum fluctuations.Comment: 11 pages, 6 figures, to appear in: Chaos: "100 years of Brownian motion

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.Comment: to be published in Phys. Rev.

Strong friction limit in quantum mechanics: the Quantum Smoluchowski equation

For a quantum system coupled to a heat bath environment the strong friction limit is studied starting from the exact path integral formulation. Generalizing the classical Smoluchowski limit to low temperatures a time evolution equation for the position distribution is derived and the strong role of quantum fluctuations in this limit is revealed.Comment: 4 pages, PRL in pres