arXiv subjects

Wojciech H. Zurek

Publications and source records attributed to Wojciech H. Zurek.

94 records · Page 6Linked to original sources

arXiv1997

Critical Dynamics of Symmetry Breaking: Quenches, Dissipation and Cosmology

Symmetry-breaking phase transitions may leave behind topological defects \cite{Kibble} with a density dependent on the quench rate \cite{Zurek}. We investigate the dynamics of such quenches for the one-dimensional, Landau-Ginzburg case and show that the density of kinks, $n$, scales differently with the quench timescale, $τ_Q$, depending on whether the dynamics in the vicinity of the critical point is overdamped ($n \propto τ_Q^{-1/4}$) or underdamped ($n \propto τ_Q^{-1/3}$). Either of these cases may be relevant to the early Universe, and we derive bounds on the initial density of topological defects in cosmological phase transitions.

hep-ph↗

arXiv1997

Resilient Quantum Computation: Error Models and Thresholds

Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical quantum computation requires overcoming the problems of environmental noise and operational errors, problems which appear to be much more severe than in classical computation due to the inherent fragility of quantum superpositions involving many degrees of freedom. Here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value. The result is obtained by combining quantum error-correction, fault tolerant state recovery, fault tolerant encoding of operations and concatenation. It holds under physically realistic assumptions on the errors.

quant-ph↗

arXiv1995

COSMOLOGICAL EXPERIMENTS IN SUPERFLUIDS AND SUPERCONDUCTORS

Evolution of the order parameter in condensed matter analogues of cosmological phase transitions is discussed. It is shown that the density of the frozen-out topological defects is set by the competition between the quench rate -- the rate at which the phase transition is taking place -- and the relaxation rate of the order parameter. More specifically, the characteristic domain size which determines the typical distance separating topological defects in the new broken symmetry phase (and, therefore, their density) is determined by the correlation length at the instant at which the relaxation timescale of the order parameter is equal to the time from the phase transition. This scenario shares with the Kibble mechanism the idea that topological defects will appear ``in between'' domains with independently chosen broken symmetry vacuum. However, it differs from the original proposal in estimating the size of such domains through the non-equilibrium aspects of the transition (quench rate), rather than through the Ginzburg temperature at which thermally activated symmetry restoration can still occur in the correlation - length sized volumes of the broken symmetry phase. This scenario can be employed to analyze recent superfluid quench experiments carried out in bulk He$^4$ to study the analogue of the ``cosmological'' prediction of significant vortex line production. It can be also applied to superfluid quenches in annular geometry, as well as to the rapid phase transition from the normal metal to superconductor, where the symmetry breaking occurs in the order parameter with the local (rather than a global) gauge. Cosmological implications of the revised defect formation scenario with the critical domain size set by the freeze-out time rather than by the Ginzburg temperature are also briefly considered.

cond-mat↗

arXiv1994

Preferred Observables, Predictability, Classicality, and the Environment-Induced Decoherence

Selection of the preferred classical set of states in the process of decoherence -- so important for cosmological considerations -- is discussed with an emphasis on the role of information loss and entropy. {\it Persistence of correlations} between the observables of two systems (for instance, a record and a state of a system evolved from the initial conditions described by that record) in the presence of the environment is used to define classical behavior. From the viewpoint of an observer (or any system capable of maintaining records) {\it predictability} is a measure of such persistence. {\it Predictability sieve} -- a procedure which employs both the statistical and algorithmic entropies to systematically explore all of the Hilbert space of an open system in order to eliminate the majority of the unpredictable and non-classical states and to locate the islands of predictability including the preferred {\it pointer basis} is proposed. Predictably evolving states of decohering systems along with the time-ordered sequences of records of their evolution define the effectively classical branches of the universal wavefunction in the context of the ``Many Worlds Interpretation". The relation between the consistent histories approach and the preferred basis is considered. It is demonstrated that histories of sequences of events corresponding to projections onto the states of the pointer basis are consistent.

gr-qc↗