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

TASI 2009 Lectures: Searching for Unexpected Physics at the LHC

These TASI lectures consider low mass hidden sectors from Hidden Valleys, Quirks and Unparticles. We show how each corresponds to a different limit of the same class of models: hidden sectors with non-abelian gauge groups with mass gaps well below a TeV that communicate to the Standard Model through weak scale suppressed higher dimension operators. We provide concrete examples of such models and discuss LHC signatures. Lastly we turn to discussing the application of Hidden Valleys to dark matter sectors.Comment: 35 pages, 21 figure

Quantum Theory of the Classical: Quantum Jumps, Born's Rule, and Objective Classical Reality via Quantum Darwinism

Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with derivation of preferred sets of states that help define what exists - our everyday classical reality. They emerge as a result of breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification - of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection. Pointer states obtained this way determine what can happen - define events - without appealing to Born's rule for probabilities. Therefore, Born's rule can be now deduced from the entanglement-assisted invariance, or envariance - a symmetry of entangled quantum states. With probabilities at hand one also gains new insights into foundations of quantum statistical physics. Moreover, one can now analyze information flows responsible for decoherence. These information flows explain how perception of objective classical reality arises from the quantum substrate: Effective amplification they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment - through quantum Darwinism

Eliminating Ensembles from Equilibrium Statistical Physics: Maxwell's Demon, Szilard's Engine, and Thermodynamics via Entanglement

A system in equilibrium does not evolve -- time independence is its telltale characteristic. However, in Newtonian physics the microstate of an individual system (a point in its phase space) evolves incessantly in accord with its equations of motion. Ensembles were introduced in XIX century to bridge that chasm between continuous motion of phase space points in Newtonian dynamics and stasis of thermodynamics: While states of individual classical systems inevitably evolve, a phase space distribution of such states -- an ensemble -- can be time-independent. I show that entanglement (e.g., with the environment) can yield a time-independent equilibrium in an individual quantum system. This allows one to eliminate ensembles -- an awkward stratagem introduced to reconcile thermodynamics with Newtonian mechanics -- and use an individual system interacting and therefore entangled with its heat bath to represent equilibrium and to elucidate the role of information and measurements in physics. Thus, in our quantum Universe one can practice statistical physics without ensembles -- hence, in a sense, without statistics. The elimination of ensembles uses ideas that led to the recent derivation of Born's rule from the symmetries of entanglement, and I start with a review of that derivation. I then review and discuss difficulties related to the reliance on ensembles and illustrate the need for ensembles with the classical Szilard's engine. A similar quantum engine -- a single system interacting with the thermal heat bath environment -- is enough to establish thermodynamics. The role of Maxwell's demon (which in this quantum context resembles Wigner's friend) is also discussed.Comment: to appear in Physics Report

Topological relics of symmetry breaking: Winding numbers and scaling tilts from random vortex-antivortex pairs

I show that random distributions of vortex-antivortex pairs (rather than of individual vortices) lead to scaling of typical winding numbers W trapped inside a loop of circumference C with the square root of C when the expected winding numbers are large. Such scaling is consistent with the Kibble-Zurek mechanism (KZM). By contrast, distribution of individual vortices with randomly assigned topological charges would result in the dispersion of W scaling with the square root of the area inside C. Scaling of the dispersion of W and of the probability of detection of non-zero W with C can be also studied for loops so small that non-zero windings are rare. In this case I show a doubling of the scaling of dispersion with C when compared to the scaling of dispersion in the large W regime. Moreover, probability of trapping of a non-zero W becomes, in this case, proportional to the area subtended by C (hence, to the square of circumference). This quadruples, as compared with large winding numbers regime, the exponent in the power law dependence of the frequency of trapping of W=+1 or W=-1 on C. Such change of the power law exponent by a FACTOR OF FOUR implies quadrupling of the scaling of the frequency of winding number trapping with the quench rate, and is of key importance for experimental tests of KZM.Comment: Improvements in the presentation (including extended title) throughout. Conclusions (e.g., scalings in Fig. 2) unchange

The classical-statistical limit of quantum mechanics

The classical-statistical limit of quantum mechanics is studied. It is proved that the limit $\hbar \to 0$ is the good limit for the operators algebra but it si not so for the state compact set. In the last case decoherence must be invoked to obtain the classical-statistical limit.Comment: 9 page

Quench from Mott Insulator to Superfluid

We study a linear ramp of the nearest-neighbor tunneling rate in the Bose-Hubbard model driving the system from the Mott insulator state into the superfluid phase. We employ the truncated Wigner approximation to simulate linear quenches of a uniform system in 1,2, and 3 dimensions, and in a harmonic trap in 3 dimensions. In all these setups the excitation energy decays like one over third root of the quench time. The -1/3 scaling arises from an impulse-adiabatic approximation - a variant of the Kibble-Zurek mechanism - describing a crossover from non-adiabatic to adiabatic evolution when the system begins to keep pace with the increasing tunneling rate.Comment: 10 pages, 13 figures; version published in Phys. Rev.