Bounds to unitary evolution

Upper and lower bounds are established for the survival probability $||^{2}$ of a quantum state, in terms of the energy moments $$. Introducing a cut-off in the energy generally enables considerable improvement in these bounds and allows the method to be used where the exact energy moments do not exist.Comment: 5 pages, 8 figure

Gauge transformation through an accelerated frame of reference

The Schr\"{o}dinger equation of a charged particle in a uniform electric field can be specified in either a time-independent or a time-dependent gauge. The wave-function solutions in these two gauges are related by a phase-factor reflecting the gauge symmetry of the problem. In this article we show that the effect of such a gauge transformation connecting the two wave-functions can be mimicked by the effect of two successive extended Galilean transformations connecting the two wave-function. An extended Galilean transformation connects two reference frames out of which one is accelerating with respect to the other.Comment: 7 Pages, Latex fil

A fast and robust approach to long-distance quantum communication with atomic ensembles

Quantum repeaters create long-distance entanglement between quantum systems while overcoming difficulties such as the attenuation of single photons in a fiber. Recently, an implementation of a repeater protocol based on single qubits in atomic ensembles and linear optics has been proposed [Nature 414, 413 (2001)]. Motivated by rapid experimental progress towards implementing that protocol, here we develop a more efficient scheme compatible with active purification of arbitrary errors. Using similar resources as the earlier protocol, our approach intrinsically purifies leakage out of the logical subspace and all errors within the logical subspace, leading to greatly improved performance in the presence of experimental inefficiencies. Our analysis indicates that our scheme could generate approximately one pair per 3 minutes over 1280 km distance with fidelity (F>78%) sufficient to violate Bell's inequality.Comment: 10 pages, 4 figures, 5 tables (Two appendixes are added to justify two claims used in the maintext.

Role of the relative phase in the merging of two independent Bose-Einstein condensates

We study the merging of two independent Bose-Einstein condensates with arbitrary initial phase difference, in the framework of a one-dimensional time-dependent Gross-Pitaevskii model. The role of the initial phase difference in the process is discussed, and various types of phase-sensitive excitations are identified.Comment: 19 Pages, 7 figure

Delay Time in Quaternionic Quantum Mechanics

In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex quantum mechanics.Comment: 9 pages, 5 figure

Classical and Quantum Fluctuation Theorems for Heat Exchange

The statistics of heat exchange between two classical or quantum finite systems initially prepared at different temperatures are shown to obey a fluctuation theorem.Comment: 4 pages, 1 included figure, to appear in Phys Rev Let

Disentanglement and Decoherence without dissipation at non-zero temperatures

Decoherence is well understood, in contrast to disentanglement. According to common lore, irreversible coupling to a dissipative environment is the mechanism for loss of entanglement. Here, we show that, on the contrary, disentanglement can in fact occur at large enough temperatures $T$ even for vanishingly small dissipation (as we have shown previously for decoherence). However, whereas the effect of $T$ on decoherence increases exponentially with time, the effect of $T$ on disentanglement is constant for all times, reflecting a fundamental difference between the two phenomena. Also, the possibility of disentanglement at a particular $T$ increases with decreasing initial entanglement.Comment: 3 page

Smooth double barriers in quantum mechanics

Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle energy, and their dependence on the barrier parameters are obtained for various cases. We also discuss the tunneling time, for which we obtain generalizations of the known results for rectangular barriers.Comment: 23 pages, 8 figures, a slightly reduced version to appear in American Journal of Physics, references correcte

Mapping of strongly correlated steady-state nonequilibrium to an effective equilibrium

By mapping steady-state nonequilibrium to an effective equilibrium, we formulate nonequilibrium problems within an equilibrium picture where we can apply existing equilibrium many-body techniques to steady-state electron transport problems. We study the analytic properties of many-body scattering states, reduce the boundary condition operator in a simple form and prove that this mapping is equivalent to the correct linear-response theory. In an example of infinite-U Anderson impurity model, we approximately solve for the scattering state creation operators, based on which we derive the bias operator Y to construct the nonequilibrium ensemble in the form of the Boltzmann factor exp(-beta(H-Y)). The resulting Hamiltonian is solved by the non-crossing approximation. We obtain the Kondo anomaly conductance at zero bias, inelastic transport via the charge excitation on the quantum dot and significant inelastic current background over a wide range of bias. Finally, we propose a self-consistent algorithm of mapping general steady-state nonequilibrium.Comment: 15 pages, 9 figure

A scaling theory of quantum breakdown in solids

We propose a new scaling theory for general quantum breakdown phenomena. We show, taking Landau-Zener type breakdown as a particular example, that the breakdown phenomena can be viewed as a quantum phase transition for which the scaling theory is developed. The application of this new scaling theory to Zener type breakdown in Anderson insulators, and quantum quenching has been discussed.Comment: 3 page