Topological Schr\"odinger cats: Non-local quantum superpositions of topological defects

Topological defects (such as monopoles, vortex lines, or domain walls) mark locations where disparate choices of a broken symmetry vacuum elsewhere in the system lead to irreconcilable differences. They are energetically costly (the energy density in their core reaches that of the prior symmetric vacuum) but topologically stable (the whole manifold would have to be rearranged to get rid of the defect). We show how, in a paradigmatic model of a quantum phase transition, a topological defect can be put in a non-local superposition, so that - in a region large compared to the size of its core - the order parameter of the system is "undecided" by being in a quantum superposition of conflicting choices of the broken symmetry. We demonstrate how to exhibit such a "Schr\"odinger kink" by devising a version of a double-slit experiment suitable for topological defects. Coherence detectable in such experiments will be suppressed as a consequence of interaction with the environment. We analyze environment-induced decoherence and discuss its role in symmetry breaking.Comment: 7 pages, 4 figure

Decoherence, Re-coherence, and the Black Hole Information Paradox

We analyze a system consisting of an oscillator coupled to a field. With the field traced out as an environment, the oscillator loses coherence on a very short {\it decoherence timescale}; but, on a much longer {\it relaxation timescale}, predictably evolves into a unique, pure (ground) state. This example of {\it re-coherence} has interesting implications both for the interpretation of quantum theory and for the loss of information during black hole evaporation. We examine these implications by investigating the intermediate and final states of the quantum field, treated as an open system coupled to an unobserved oscillator.Comment: 23 pages, 2 figures included, figures 3.1 - 3.3 available at http://qso.lanl.gov/papers/Papers.htm

Decoherence, Chaos, and the Second Law

We investigate implications of decoherence for quantum systems which are classically chaotic. We show that, in open systems, the rate of von Neumann entropy production quickly reaches an asymptotic value which is: (i) independent of the system-environment coupling, (ii) dictated by the dynamics of the system, and (iii) dominated by the largest Lyapunov exponent. These results shed a new light on the correspondence between quantum and classical dynamics as well as on the origins of the ``arrow of time.''Comment: 13 Pages, 2 Figures available upon request, Preprint LA-UR-93-, The new version contains the text, the previous one had only the Macros: sorry

Quantum Approach to a Derivation of the Second Law of Thermodynamics

We re-interprete the microcanonical conditions in the quantum domain as constraints for the interaction of the "gas-subsystem" under consideration and its environment ("container"). The time-average of a purity-measure is found to equal the average over the respective path in Hilbert-space. We then show that for typical (degenerate or non-degenerate) thermodynamical systems almost all states within the allowed region of Hilbert-space have a local von Neumann-entropy S close to the maximum and a purity P close to its minimum, respectively. Typically thermodynamical systems should therefore obey the second law.Comment: 4 pages. Accepted for publication in Phys. Rev. Let

Adiabatic-Impulse approximation for avoided level crossings: from phase transition dynamics to Landau-Zener evolutions and back again

We show that a simple approximation based on concepts underlying the Kibble-Zurek theory of second order phase transition dynamics can be used to treat avoided level crossing problems. The approach discussed in this paper provides an intuitive insight into quantum dynamics of two level systems, and may serve as a link between the theory of dynamics of classical and quantum phase transitions. To illustrate these ideas we analyze dynamics of a paramagnet-ferromagnet quantum phase transition in the Ising model. We also present exact unpublished solutions of the Landau-Zener like problems.Comment: 12 pages & 6 figures, minor corrections, version accepted in Phys. Rev.

Sub-Planck spots of Schroedinger cats and quantum decoherence

Heisenberg's principle$^1$ states that the product of uncertainties of position and momentum should be no less than Planck's constant $\hbar$. This is usually taken to imply that phase space structures associated with sub-Planck ($\ll \hbar$) scales do not exist, or, at the very least, that they do not matter. I show that this deeply ingrained prejudice is false: Non-local "Schr\"odinger cat" states of quantum systems confined to phase space volume characterized by `the classical action' $A \gg \hbar$ develop spotty structure on scales corresponding to sub-Planck $a = \hbar^2 / A \ll \hbar$. Such structures arise especially quickly in quantum versions of classically chaotic systems (such as gases, modelled by chaotic scattering of molecules), that are driven into nonlocal Schr\"odinger cat -- like superpositions by the quantum manifestations of the exponential sensitivity to perturbations$^2$. Most importantly, these sub-Planck scales are physically significant: $a$ determines sensitivity of a quantum system (or of a quantum environment) to perturbations. Therefore sub-Planck $a$ controls the effectiveness of decoherence and einselection caused by the environment$^{3-8}$. It may also be relevant in setting limits on sensitivity of Schr\"odinger cats used as detectors.Comment: Published in Nature 412, 712-717 (2001

PTOLEMY: A Proposal for Thermal Relic Detection of Massive Neutrinos and Directional Detection of MeV Dark Matter

We propose to achieve the proof-of-principle of the PTOLEMY project to directly detect the Cosmic Neutrino Background (CNB). Each of the technological challenges described in [1,2] will be targeted and hopefully solved by the use of the latest experimental developments and profiting from the low background environment provided by the LNGS underground site. The first phase will focus on the graphene technology for a tritium target and the demonstration of TES microcalorimetry with an energy resolution of better than 0.05 eV for low energy electrons. These technologies will be evaluated using the PTOLEMY prototype, proposed for underground installation, using precision HV controls to step down the kinematic energy of endpoint electrons to match the calorimeter dynamic range and rate capabilities. The second phase will produce a novel implementation of the EM filter that is scalable to the full target size and which demonstrates intrinsic triggering capability for selecting endpoint electrons. Concurrent with the CNB program, we plan to exploit and develop the unique properties of graphene to implement an intermediate program for direct directional detection of MeV dark matter [3,4]. This program will evaluate the radio-purity and scalability of the graphene fabrication process with the goal of using recently identified ultra-high radio-purity CO2 sources. The direct detection of the CNB is a snapshot of early universe dynamics recorded by the thermal relic neutrino yield taken at a time that predates the epochs of Big Bang Nucleosynthesis, the Cosmic Microwave Background and the recession of galaxies (Hubble Expansion). Big Bang neutrinos are believed to have a central role in the evolution of the Universe and a direct measurement with PTOLEMY will unequivocally establish the extent to which these predictions match present-day neutrino densities

The Luminous Erupting Dwarf Nova CV1 in the Dense Globular Cluster M15

Despite decades-old predictions of the expected presence of dozens of cataclysmic variables in the cores of globular clusters, the number of irrefutable, out-bursting candidates is still barely a handful. Using multi-wavelength, multi-epoch HST images we have produced outburst and quiescence light curves for the recently discovered large amplitude variable CV1 in the core of the post core-collapse globular cluster M15. The light curves and blue colors show that the object is a bona fide dwarf nova, with absolute magnitude at maximum light rivaling that of the most luminous known dwarf novae.Comment: 17 pages, 5 figures. Submitted to A

Relational physics with real rods and clocks and the measurement problem of quantum mechanics

The use of real clocks and measuring rods in quantum mechanics implies a natural loss of unitarity in the description of the theory. We briefly review this point and then discuss the implications it has for the measurement problem in quantum mechanics. The intrinsic loss of coherence allows to circumvent some of the usual objections to the measurement process as due to environmental decoherence.Comment: 19 pages, RevTex, no figure