Biomedical subjects

Günter Mahler

Publications and source records attributed to Günter Mahler.

7 recordsLinked to original sources

PubMed2006

Application of the Hilbert space average method on heat conduction models.

We analyze closed one-dimensional chains of weakly coupled many level systems, by means of the so-called Hilbert space average method (HAM). Subject to some concrete conditions on the Hamiltonian of the system, our theory predicts energy diffusion with respect to a coarse-grained description for almost all initial states. Close to the respective equilibrium, we investigate this behavior in terms of heat transport and derive the heat conduction coefficient. Thus, we are able to show that both heat (energy) diffusive behavior as well as Fourier's law follows from and is compatible with a reversible Schrödinger dynamics on the complete level of description.

Journal Article↗

PubMed2005

Autonomous quantum thermodynamic machines.

We investigate the dynamics of a quantum system consisting of a single spin coupled to an oscillator and sandwiched between two thermal baths at different temperatures. By means of an adequately designed Lindblad equation, it is shown that this device can function as a thermodynamic machine exhibiting Carnot-type cycles. For the present model, this means that when run as a heat engine, coherent motion of the oscillator is amplified. Contrary to the quantum computer, such a machine has a quantum as well as a classical limit. Away from the classical limit, it asymptotically approaches a stationary transport scenario.

Journal Article↗

PubMed2005

Fourier's law from Schrödinger dynamics.

We consider a class of one-dimensional chains of weakly coupled many level systems. We present a theory which predicts energy diffusion within these chains for almost all initial states, if some concrete conditions on their Hamiltonians are met. By numerically solving the time dependent Schrödinger equation, we verify this prediction. Close to equilibrium we analyze this behavior in terms of heat conduction and compute the respective coefficient directly from the theory.

Journal Article↗

PubMed2005

Global and local relaxation of a spin chain under exact Schrödinger and master-equation dynamics.

We solve the Schrödinger equation for an interacting spin chain locally coupled to a quantum environment with a specific degeneracy structure. The reduced dynamics of the whole spin chain as well as of single spins is analyzed. We show that the total spin chain relaxes to a thermal equilibrium state independently of the internal interaction strength. In contrast, the asymptotic states of each individual spin are thermal for weak but nonthermal for stronger spin-spin coupling. The transition between both scenarios is found for couplings of the order of 0.1 x deltaE , with deltaE denoting the Zeeman splitting. We compare these results with a master-equation treatment; when time averaged, both approaches lead to the same asymptotic state and finally with analytical results.

Journal Article↗

PubMed2005

Control of local relaxation behavior in closed bipartite quantum systems.

We investigate the decoherence of a spin- 1/2 subsystem weakly coupled to an environment of many spins- 1/2 with and without mutual coupling. The total system is closed, its state is pure, and evolves under Schrödinger dynamics. Nevertheless, the considered spin typically reaches a quasistationary equilibrium state. Here we show that this state depends strongly on the coupling to the environment on the one hand and on the coupling within the environmental spins on the other. In particular we focus on spin star and spin ring-star geometries to investigate the effect of intra-environmental coupling on the central spin. By changing the spectrum of the environment, its effect as a bath on the central spin is also changed and may even be adjustable to some degree. We find that the relaxation behavior is related to the distribution of the energy eigenstates of the total system. For each of these relaxation modes, there is a dual mode for which the resulting subsystem approaches an inverted state occupation probability (negative temperature).

Journal Article↗

PubMed2004

Local versus global thermal states: correlations and the existence of local temperatures.

We consider a quantum system consisting of a regular chain of elementary subsystems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature T . We analyze under what condition the state factors into a product of canonical density matrices with respect to groups of n subsystems each, and when these groups have the same temperature T. While in classical mechanics the validity of this procedure only depends on the size of the groups n, in quantum mechanics the minimum group size n(min) also depends on the temperature T! As examples, we apply our analysis to a harmonic chain and different types of Ising spin chains. We discuss various features that show up due to the characteristics of the models considered. For the harmonic chain, which successfully describes thermal properties of insulating solids, our approach gives a quantitative estimate of the minimal length scale on which temperature can exist: This length scale is found to be constant for temperatures above the Debye temperature and proportional to T-3 below.

Journal Article↗

PubMed2004

Existence of temperature on the nanoscale.

We consider a regular chain of quantum particles with nearest neighbor interactions in a canonical state with temperature T. We analyze the conditions under which the state factors into a product of canonical density matrices with respect to groups of n particles each and under which these groups have the same temperature T. In quantum mechanics the minimum group size n(min) depends on the temperature T, contrary to the classical case. We apply our analysis to a harmonic chain and find that n(min)=const for temperatures above the Debye temperature and n(min) proportional to T(-3) below.

Journal Article↗