Relaxation into equilibrium under pure Schr\"odinger dynamics

We consider bipartite quantum systems that are described completely by a state vector $|\Psi(t)>$ and the fully deterministic Schr\"odinger equation. Under weak constraints and without any artificially introduced decoherence or irreversibility, the smaller of the two subsystems shows thermodynamic behaviour like relaxation into an equilibrium, maximization of entropy and the emergence of the Boltzmann energy distribution. This generic behaviour results from entanglement.Comment: 5 pages, 9 figure

Pattern formation in quantum Turing machines

We investigate the iteration of a sequence of local and pair unitary transformations, which can be interpreted to result from a Turing-head (pseudo-spin $S$) rotating along a closed Turing-tape ($M$ additional pseudo-spins). The dynamical evolution of the Bloch-vector of $S$, which can be decomposed into $2^{M}$ primitive pure state Turing-head trajectories, gives rise to fascinating geometrical patterns reflecting the entanglement between head and tape. These machines thus provide intuitive examples for quantum parallelism and, at the same time, means for local testing of quantum network dynamics.Comment: Accepted for publication in Phys.Rev.A, 3 figures, REVTEX fil

On the concept of pressure in quantum mechanics

Heat and work are fundamental concepts for thermodynamical systems. When these are scaled down to the quantum level they require appropriate embeddings. Here we show that the dependence of the particle spectrum on system size giving rise to a formal definition of pressure can, indeed, be correlated with an external mechanical degree of freedom, modelled as a spatial coordinate of a quantum oscillator. Under specific conditions this correlation is reminiscent of that occurring in the classical manometer.Comment: 7 pages, 3 figure

Local effective dynamics of quantum systems: A generalized approach to work and heat

By computing the local energy expectation values with respect to some local measurement basis we show that for any quantum system there are two fundamentally different contributions: changes in energy that do not alter the local von Neumann entropy and changes that do. We identify the former as work and the latter as heat. Since our derivation makes no assumptions on the system Hamiltonian or its state, the result is valid even for states arbitrarily far from equilibrium. Examples are discussed ranging from the classical limit to purely quantum mechanical scenarios, i.e. where the Hamiltonian and the density operator do not commute.Comment: 5 pages, 1 figure, published versio

Cavity-induced temperature control of a two-level system

We consider a two-level atom interacting with a single mode of the electromagnetic field in a cavity within the Jaynes-Cummings model. Initially, the atom is thermal while the cavity is in a coherent state. The atom interacts with the cavity field for a fixed time. After removing the atom from the cavity and applying a laser pulse the atom will be in a thermal state again. Depending on the interaction time with the cavity field the final temperature can be varied over a large range. We discuss how this method can be used to cool the internal degrees of freedom of atoms and create heat baths suitable for studying thermodynamics at the nanoscale

Direct carrier detection by in situ suppression hybridization with cosmid clones of the Duchenne/Becker muscular dystrophy locus

A basic problem in genetic counseling of families with Duchenne/Becker muscular dystrophy (DMD/BMD) concerns the carrier status of female relatives of an affected male. In about 60% of these patients, deletions of one or more exons of the dystrophin gene can be identified. These deletions preferentially include exon 45, which can be detected by multiplex polymerase chain reaction (PCR) and Southern blot analysis of genomic cosmid clones that map to this critical region. As a new approach for definitive carrier detection, we have performed chromosomal in situ suppression (CISS) hybridization with these cosmid clones in female relatives of four unrelated patients. In normal females, most metaphases showed signals on both×chromosomes, whereas only one×chromosome was labeled in carriers. Our results demonstrate that CISS hybridization can define the carrier status in female relatives of DMD patients exhibiting a deletion in the dystrophin gene

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 first 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.Comment: 12 pages, 5 figures, discussion of results extended, accepted for publication in Phys. Rev.