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Juan Pablo Paz

Publications and source records attributed to Juan Pablo Paz.

70 records · Page 4Linked to original sources
arXiv2000

Decoherence and the rate of entropy production in chaotic quantum systems

We show that for an open quantum system which is classically chaotic (a quartic double well with harmonic driving coupled to a sea of harmonic oscillators) the rate of entropy production has, as a function of time, two relevant regimes: For short times it is proportional to the diffusion coefficient (fixed by the system--environment coupling strength). For longer times (but before equilibration) there is a regime where the entropy production rate is fixed by the Lyapunov exponent. The nature of the transition time between both regimes is investigated.

quant-ph↗
arXiv1997

Continuous Error Correction

We propose a new approach to study the evolution of a quantum state that is encoded in a system which is continuously subject to the operations required to implement a quantum error correcting code. In the limit of continuous error correction we introduce a Markovian master equation that includes the effects of: a) Hamiltonian evolution, b) errors caused by the interaction with an environment and c) error-correcting operations. The master equation is formally presented for all stabilizer codes and its solution is analyzed for the simplest such code.

quant-ph↗
arXiv1997

Quantum computation with phase drift errors

We present results of numerical simulations of the evolution of an ion trap quantum computer made out of 18 ions which are subject to a sequence of nearly 15000 laser pulses in order to find the prime factors of N=15. We analyze the effect of random and systematic phase drift errors arising from inaccuracies in the laser pulses which induce over (under) rotation of the quantum state. Simple analytic estimates of the tolerance for the quality of driving pulses are presented. We examine the use of watchdog stabilization to partially correct phase drift errors concluding that, in the regime investigated, it is rather inefficient.

quant-ph↗
arXiv1996

Why We Don't Need Quantum Planetary Dynamics: Decoherence and the Correspondence Principle for Chaotic Systems

Violation of correspondence principle may occur for very macroscopic byt isolated quantum systems on rather short timescales as illustrated by the case of Hyperion, the chaotically tumbling moon of Saturn, for which quantum and classical predictions are expected to diverge on a timescale of approximately 20 years. Motivated by Hyperion, we review salient features of ``quantum chaos'' and show that decoherence is the essential ingredient of the classical limit, as it enables one to solve the apparent paradox caused by the breakdown of the correspondence principle for classically chaotic systems.

quant-ph↗
arXiv1996

Decoherence and Initial Correlations in Quantum Brownian Motion

We analyze the evolution of a quantum Brownian particle starting from an initial state that contains correlations between this system and its environment. Using a path integral approach, we obtain a master equation for the reduced density matrix of the system finding relatively simple expressions for its time dependent coefficients. We examine the evolution of delocalized initial states (Schrödinger's cats) investigating the effectiveness of the decoherence process. Analytic results are obtained for an ohmic environment (Drude's model) at zero temperature.

quant-ph↗
arXiv1996

Perfect Quantum Error Correction Code

We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We give a simple circuit which takes the initial state with four extra qubits in the state |0> to the encoded state. The circuit can be converted into a decoding one by simply running it backward. Reading the extra four qubits at the decoder's output we learn which one of the sixteen alternatives (no error plus all fifteen possible 1-bit errors) was realized. The original state of the encoded qubit can then be restored by a simple unitary transformation.

quant-ph↗
arXiv1996

Factoring in a Dissipative Quantum Computer

We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders, etc) which are described in terms of elementary Toffoli gates. We present a simple analysis of the impact of losses and decoherence on the performance of this quantum factoring circuit. For that purpose, we simulate a quantum computer which is running the program to factor N = 15 while interacting with a dissipative environment. As a consequence of this interaction randomly selected qubits may spontaneously decay. Using the results of our numerical simulations we analyze the efficiency of some simple error correction techniques.

quant-ph↗
arXiv1995

Quantum Origin of Noise and Fluctuations in Cosmology

We address two basic issues in the theory of galaxy formation from fluctuations of quantum fields: 1) the nature and origin of noise and fluctuations and 2) the conditions for using a classical stochastic equation for their description. On the first issue, we derive the influence functional for a $λϕ^4 $ field in a zero-temperature bath in de Sitter universe and obtain the correlator for the colored noises of vacuum fluctuations. This exemplifies a new mechanism we propose for colored noise generation which can act as seeds for galaxy formation with non-Gaussian distributions. For the second issue, we present a (functional) master equation for the inflaton field in de Sitter universe. By examining the form of the noise kernel we study the decoherence of the long-wavelength sector and the conditions for it to behave classically.

gr-qc↗
arXiv1995

Dissipation and Decoherence in Mean Field Theory

The time evolution of a closed system of mean fields and fluctuations is Hamiltonian, with the canonical variables parameterizing the general time-dependent Gaussian density matrix of the system. Yet, the evolution manifests both quantum decoherence and apparent irreversibility of energy flow from the coherent mean fields to fluctuating quantum modes. Using scalar QED as an example we show how this collisionless damping and decoherence may be understood as the result of {\em dephasing} of the rapidly varying fluctuations and particle production in the time varying mean field.

hep-ph↗
arXiv1994

Non-Equilibrium Quantum Fields in the Large N Expansion

An effective action technique for the time evolution of a closed system consisting of one or more mean fields interacting with their quantum fluctuations is presented. By marrying large $N$ expansion methods to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured and a systematic, energy conserving and gauge invariant expansion about the quasi-classical mean field(s) in powers of $1/N$ developed. The general method is exposed in two specific examples, $O(N)$ symmetric scalar $ł\F^4$ theory and Quantum Electrodynamics (QED) with $N$ fermion fields. The $ł\F^4$ case is well suited to the numerical study of the real time dynamics of phase transitions characterized by a scalar order parameter. In QED the technique may be used to study the quantum non-equilibrium effects of pair creation in strong electric fields and the scattering and transport processes in a relativistic $e^+e^-$ plasma. A simple renormalization scheme that makes practical the numerical solution of the equations of motion of these and other field theories is described.

hep-ph↗
arXiv1994

Nonequilibrium Quantum Dynamics Of Disoriented Chiral Condensates

The nonequilibrium dynamics of the chiral phase transition expected during the expansion of the quark-qluon plasma produced in a high energy hadron or heavy ion collision is studied in the O(4) linear sigma model to leading order in a large $N$ expansion. Starting from an approximate equilibrium configuration at an initial proper time $τ$ in the disordered phase we study the transition to the ordered broken symmetry phase as the system expands and cools. We give results for the proper time evolution of the effective pion mass, the order parameter $<σ>$ as well as for the pion two point correlation function expressed in terms of a time dependent phase space number density and pair correlation density. We determine the phase space of initial conditions that lead to instabilities (exponentially growing long wave length modes) as the system evolves in time. These instabilities are what eventually lead to disoriented chiral condensates. In our simulations,we found that instabilities that are formed during the initial phases of the expansion exist for proper times that are at most $3 fm/c$ and lead to condensate regions that do not contain large numbers of particles. The damping of instabilities is a consequence of strong coupling.

hep-ph↗
arXiv1994

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.''

gr-qc↗
arXiv1994

Decoherence in Quantum Brownian Motion

We examine the dependence of decoherence on the spectral density of the environment as well as on the initial state of the system. We use two simple examples to illustrate some important effects. The simplest derivation of the general form of the master equation for a general quantum Brownian motion is outlined in an Appendix.

gr-qc↗
arXiv1993

Environment--Induced Decoherence, Classicality and Consistency of Quantum Histories

We prove that for an open system, in the Markovian regime, it is always possible to construct an infinite number of non trivial sets of histories that exactly satisfy the probability sum rules. In spite of being perfectly consistent, these sets manifest a very non--classical behavior: they are quite unstable under the addition of an extra instant to the list of times defining the history. To eliminate this feature --whose implications for the interpretation of the formalism we discuss-- and to achieve the stability that characterizes the quasiclassical domain, it is necessary to separate the instants which define the history by time intervals significantly larger than the typical decoherence time. In this case environment induced superselection is very effective and the quasiclassical domain is characterized by histories constructed with ``pointer projectors''.

gr-qc↗
arXiv1993

Minisuperspace as a Quantum Open System

We trace the development of ideas on dissipative processes in chaotic cosmology and on minisuperspace quantum cosmology from the time Misner proposed them to current research. We show 1) how the effect of quantum processes like particle creation in the early universe can address the issues of the isotropy and homogeneity of the observed universe, 2) how viewing minisuperspace as a quantum open system can address the issue of the validity of such approximations customarily adopted in quantum cosmology, and 3) how invoking statistical processes like decoherence and correlation when considered together can help to establish a theory of quantum fields in curved spacetime as the semiclassical limit of quantum gravity. {\it Dedicated to Professor Misner on the occasion of his sixtieth birthday, June 1992.} To appear in the Proceedings of a Symposium on {\it Directions in General Relativity}, College Park, May 1993, Volume 1, edited by B. L. Hu, M. P. Ryan and C. V. Vishveshwara (Cambridge University Press 1993)~~~~umdpp 93-60

gr-qc↗