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

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 We also present exact unpublished solutions of the Landau-Zener like problems.Comment: 12 pages & 6 figures, minor corrections, version accepted in Phys.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

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

Following a "Collapsing" Wavefunction

I study the quantum mechanics of a spin interacting with an ``apparatus''. Although the evolution of the whole system is unitary, the spin evolution is not. The system is chosen so that the spin exhibits loss of quantum coherence, or ``wavefunction collapse'', of the sort usually associated with a quantum measurement. The system is analyzed from the point of view of the spin density matrix (or ``Schmidt paths''), and also using the consistent histories approach. These two points of view are contrasted with each other. Connections between the results and the form of the Hamiltonian are discussed in detail.Comment: 30 pages, plain LaTex, 3 figures in a separate uuencoded fil

Critical dynamics of decoherence

We study decoherence induced by a dynamic environment undergoing a quantum phase transition. Environment's susceptibility to perturbations - and, consequently, efficiency of decoherence - is amplified near a critical point. Over and above this near-critical susceptibility increase, we show that decoherence is dramatically enhanced by non-equilibrium critical dynamics of the environment. We derive a simple expression relating decoherence to the universal critical exponents exhibiting deep connections with the theory of topological defect creation in non-equilibrium phase transitions.Comment: 8 pages; version accepted in PR

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

Finite-Time Disentanglement via Spontaneous Emission

We show that under the influence of pure vacuum noise two entangled qubits become completely disentangled in a finite time, and in a specific example we find the time to be given by $\ln \Big(\frac{2 +\sqrt 2}{2}\Big)$ times the usual spontaneous lifetime.Comment: revtex, 4 pages, 2 figure