The Schwinger Model on a circle: relation between Path Integral and Hamiltonian approaches

We solve the massless Schwinger model exactly in Hamiltonian formalism on a circle. We construct physical states explicitly and discuss the role of the spectral flow and nonperturbative vacua. Different thermodynamical correlation functions are calculated and after performing the analytical continuation are compared with the corresponding expressions obtained for the Schwinger model on the torus in Euclidean Path Integral formalism obtained before.Comment: 40 page

Relativistic Harmonic Oscillator Revisited

The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example as part of string theory, is insufficient to describe all the states of the relativistic oscillator. We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators. These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers. Two of these Fock spaces include negative norm ghosts (as in string theory) while the third one is completely free of ghosts. We discuss a gauge symmetry in a worldline theory approach that supplies appropriate constraints to remove all the ghosts from all Fock sectors of the single oscillator. The resulting ghost free quantum spectrum in d+1 dimensions is then classified in unitary representations of the Lorentz group SO(d,1). Moreover all states of the single oscillator put together make up a single infinite dimensional unitary representation of a hidden global symmetry SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these new results in string theory and other areas of physics and mathematics are briefly mentioned.Comment: 41 pages, 2 figures, LaTe

Loschmidt echo with a non-equilibrium initial state: early time scaling and enhanced decoherence

We study the Loschmidt echo (LE) in a central spin model in which a central spin is globally coupled to an environment (E) which is subjected to a small and sudden quench at $t=0$ so that its state at $t=0^+$, remains the same as the ground state of the initial environmental Hamiltonian before the quench; this leads to a non-equilibrium situation. This state now evolves with two Hamiltonians, the final Hamiltonian following the quench and its modified version which incorporates an additional term arising due to the coupling of the central spin to the environment. Using a generic short-time scaling of the decay rate, we establish that in the early time limit, the rate of decay of the LE (or the overlap between two states generated from the initial state evolving through two channels) close to the quantum critical point (QCP) of E is independent of the quenching. We do also study the temporal evolution of the LE and establish the presence of a crossover to a situation where the quenching becomes irrelevant. In the limit of large quench amplitude the non-equilibrium initial condition is found to result in a drastic increase in decoherence at large times, even far away from a QCP. These generic results are verified analytically as well as numerically, choosing E to be a transverse Ising chain where the transverse field is suddenly quenched.Comment: 5 pages, 6 figures; New results, figures and references added, title change

Reduced coherence in double-slit diffraction of neutrons

In diffraction experiments with particle beams, several effects lead to a fringe visibility reduction of the interference pattern. We theoretically describe the intensity one can measure in a double-slit setup and compare the results with the experimental data obtained with cold neutrons. Our conclusion is that for cold neutrons the fringe visibility reduction is due not to decoherence, but to initial incoherence.Comment: 4 pages LaTeX, 2 figure

The General Correlation Function in the Schwinger Model on a Torus

In the framework of the Euclidean path integral approach we derive the exact formula for the general N-point chiral densities correlator in the Schwinger model on a torusComment: 17 pages, misprints corrected, references adde

On the precise connection between the GRW master-equation and master-equations for the description of decoherence

We point out that the celebrated GRW master-equation is invariant under translations, reflecting the homogeneity of space, thus providing a particular realization of a general class of translation-covariant Markovian master-equations. Such master-equations are typically used for the description of decoherence due to momentum transfers between system and environment. Building on this analogy we show the exact relationship between the GRW master-equation and decoherence master-equations, further providing a collisional decoherence model formally equivalent to the GRW master-equation. This allows for a direct comparison of order of magnitudes of relevant parameters. This formal analogy should not lead to confusion on the utterly different spirit of the two research fields, in particular it has to be stressed that the decoherence approach does not lead to a solution of the measurement problem. Building on this analogy however the feasibility of the extension of spontaneous localization models in order to avoid the infinite energy growth is discussed. Apart from a particular case considered in the paper, it appears that the amplification mechanism is generally spoiled by such modifications.Comment: 9 pages, latex, no figures, to appear on J. Phys.

Quantum decoherence of the damped harmonic oscillator

In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations.Comment: Talk at the XI International Conference on Quantum Optics (ICQO'2006), May 2006, Minsk (Belarus), 9 page