Benefits of Objective Collapse Models for Cosmology and Quantum Gravity

We display a number of advantages of objective collapse theories for the resolution of long-standing problems in cosmology and quantum gravity. In particular, we examine applications of objective reduction models to three important issues: the origin of the seeds of cosmic structure, the problem of time in quantum gravity and the information loss paradox; we show how reduction models contain the necessary tools to provide solutions for these issues. We wrap up with an adventurous proposal, which relates the spontaneous collapse events of objective collapse models to microscopic virtual black holes.     

Spacetime Coarse Grainings and the Problem of Time in the Decoherent Histories Approach to Quantum Theory

We investigate the possibility of assigning consistent probabilities to sets of histories characterized by whether they enter a particular subspace of the Hilbert space of a closed system during a given time interval. In particular we investigate the case that this subspace is a region of the configuration space. This corresponds to a particular class of coarse grainings of spacetime regions. We consider the arrival time problem, as a warm up, to deal with the problem of time in reparametrization invariant theories (as for example in canonical quantum gravity) which subsequently we examine. Decoherence conditions and probabilities for those application are derived. The resulting decoherence condition does not depend on the explicit form of the restricted propagator that was problematic for generalizations such as application in quantum cosmology. Closely related to our results, is the problem of tunnelling time as well as the quantum Zeno effect. Some interpretational comments conclude, and we discuss the applicability of this formalism to deal with the arrival time problem and the problem of time in general.     

Frequency Spectra and Probability Distributions for Quantum Fluctuations

This paper discusses two distinct, but related issues in quantum fluctuation effects. The first is the frequency spectrum which can be assigned to one loop quantum processes. The formal spectrum is a flat one, but the finite quantum effects can be associated with a rapidly oscillating spectrum, as in the case of the Casimir effect. The leads to the speculation that one might be able to dramatically change the final answer by upsetting the delicate cancellation which usually occurs. The second issue is the probability distribution for quantum fluctuations. It is well known that quantities which are linear in a free quantum field have a Gaussian distribution. Here it will be argued that quadratic quantities, such as the quantum stress tensor, must have a skewed distribution. Some possible implications of this result for inflationary cosmology will be discussed. In particular, this might be a source for non-Gaussianity.     

Background independent duals of the harmonic oscillator

We show that a class of topological field theories are quantum duals of the harmonic oscillator. This is demonstrated by establishing a correspondence between the creation and annihilation operators and nonlocal gauge invariant observables of the topological field theory. The example is used to discuss some issues concerning background independence and the relation of vacuum energy to the problem of time in quantum gravity.     

Particle creation,classicality and related issues in quantum field theory: I. Formalism and toy models

The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is straightforward, several conceptual issues arise in such a study. We present a general formalism to address some of the conceptual issues like the emergence of classicality, definition of particle content, back reaction etc. In particular, we parameterize the wave function in terms of a complex number (which we call excitation parameter) and express all physically relevant quantities in terms it. Many of the notions—like those of particle number density, effective Lagrangian etc., which are usually defined using asymptotic in–out states—are generalized as time-dependent concepts and we show that these generalized definitions lead to useful and reasonable results. Having developed the general formalism we apply it to several examples. Exact analytic expressions are found for a particular toy model and approximate analytic solutions are obtained in the extreme cases of adiabatic and highly non-adiabatic evolution. We then work out the exact results numerically for a variety of models and compare them with the analytic results and approximations. The formalism is useful in addressing the question of emergence of classicality of the quantum state, its relation to particle production and to clarify several conceptual issues related to this. In Paper II which is a sequel to this, the formalism will be applied to analyze the corresponding issues in the context of quantum field theory in background cosmological models and electric fields.     

On Decaying Rate of Quantum States

The survival amplitude of a quantum state (wave function) under the Schrödinger evolution can be expressed as the Fourier transform of the probability density induced by the wave function in the energy representation. In particular, the first zero of the survival amplitude is a fundamental quantity in characterizing the decaying rate of the quantum state. A basic problem in quantum mechanics is to study how fast the survival amplitude can fall. We present a general estimation of the decaying rate of a quantum state in terms of a moment of any order. The result is established by integrating an inequality which involves controlling trigonometric sums by power functions. This inequality is of independent interest in estimating exponential sums.     

On the information completeness of quantum tomograms

We address the problem of information completeness of quantum measurements in connection to quantum state tomography and with particular concern to quantum symplectic tomography. We put forward some non-trivial situations where informatively incomplete set of tomograms allows as well the state reconstruction provided to have some a priori information on the state or its dynamics. We then introduce a measure of information completeness and apply it to symplectic quantum tomograms.     

Quantum coherence,evolution of the Wigner function,and transition from quantum to classical dynamics for a chaotic system

The paper deals with dynamics of a quantum chaotic system under influence of an environment. The effect of an environment is known to destroy the quantum coherence and can convert the quantum dynamics of a system to classical. We use a semiclassical technique for studying the process of decoherence. The condition for transition from quantum to classical dynamics is obtained in general form and checked numerically for a particular chaotic system, known as quantum the standard map on a torus. The relevance of the obtained results to the problem of correspondence between quantum and classical mechanics is briefly discussed. (c) 1996 American Institute of Physics.     

Non-Markovian relaxation of a three-level system: quantum trajectory approach

The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schr?dinger equation called the time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.     

Quantum-classical transitions in Lifshitz tails with magnetic fields

We consider Lifshitz's model of a quantum particle subject to a repulsive Poissonian random potential and address various issues related to the influence of a constant magnetic field on the leading low-energy tail of the integrated density of states. In particular, we propose the magnetic analog of a 40-year-old landmark result of Lifshitz for short-ranged single-impurity potentials U. The Lifshitz tail is shown to change its character from purely quantum, through quantum classical, to purely classical with an increasing range of U. This systematics is explained by the increasing importance of the classical fluctuations of the particle's potential energy in comparison to the quantum fluctuations associated with its kinetic energy.     

Is quantum mechanics compatible with a deterministic universe? Two interpretations of quantum probabilities

Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical probabilities. Our analysis will be focused, as a particular example, on the Aspect-type EPR experiment. It will be shown that the quantum mechanical probabilities appearing in this experiment can be consistently understood as conditional probabilities without any paradoxical consequences. Therefore, nothing implies in the Aspect experiment that quantum theory is incompatible with a deterministic universe.     

Strong chaos of fast scrambling yields order: Emergence of decoupled quantum information capsules

The information loss problem in black hole evaporation is one of fundamental issues. Its resolution requires more profound understanding of information storage mechanism in quantum systems. In this Letter, we argue that when multiple unknown parameters are stored in large entangled qudits, strong chaos generated by fast scrambling in high temperature limit yields an ordered information storage structure with decoupled quantum information capsules (QICs). A rotational isometry emerges in the quantum Fisher information metric. The isometry is expected to be observed in future experiments on cold atoms in a pure entangled state. We provide a QIC speculation of black hole evaporation.     

Heuristic approach to non-abelian quantum kinematics and dynamics in configuration spacetime

New plausible kinematic foundations of quantum dynamics are discussed in a heuristic manner in which the quantum rule stems directly from the non-Abelian configuration symmetries of a system. Upon quantizing the ‘complete’ configuration symmetry group itself, irreducible generalized configuration-state representations can be calculated, whose transition amplitudes yield the propagation kernel. These states results from solving a set of ‘generalized Schrödinger equations’ corresponding to the superselection rules dictated by the quantized group. The propagation kernel of the system is thus obtained as an invariant Hurwitz integral, defined over the manifold of the complete symmetry group. A heuristic argument is given in favor of this approach to non-Abelian quantum kinematics, in which sums over physical world lines are evaluated instead of sums over arbitrary paths, for obtaining the propagation kernel of quantum systems having a classical Lagrangian analog. The attained quantum kinematic formalism, however, is completely general and does not depend on this particular interpretation. Nevertheless, the heuristic argument strongly suggests that non-Abelian quantum kinematics contains the formalism of standard nonrelativistic quantum mechanics as a very special case. No examples of the issues involved are presented in this paper.     

Quantum Gravity from the Point of View of Locally Covariant Quantum Field Theory

We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin–Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales.     

An Introduction to Many Worlds in Quantum Computation

The interpretation of quantum mechanics is an area of increasing interest to many working physicists. In particular, interest has come from those involved in quantum computing and information theory, as there has always been a strong foundational element in this field. This paper introduces one interpretation of quantum mechanics, a modern ‘many-worlds’ theory, from the perspective of quantum computation. Reasons for seeking to interpret quantum mechanics are discussed, then the specific ‘neo-Everettian’ theory is introduced and its claim as the best available interpretation defended. The main objections to the interpretation, including the so-called “problem of probability” are shown to fail. The local nature of the interpretation is demonstrated, and the implications of this both for the interpretation and for quantum mechanics more generally are discussed. Finally, the consequences of the theory for quantum computation are investigated, and common objections to using many worlds to describe quantum computing are answered. We find that using this particular many-worlds theory as a physical foundation for quantum computation gives several distinct advantages over other interpretations, and over not interpreting quantum theory at all.     

Characterization of Sequential Quantum Machines

We further investigate some properties of sequential quantum machines (SQMs) and introduce so-called quantum sequential machines (QSMs). In particular, the equivalence between SQMs and QSMs is also presented. We give a counterexample to answer an open problem proposed by S. Gudder recently.     

Quantum theory of nonlinear processes

Principles of development of the quantum theory of nonlinear processes on the basis of Lagrangian formulation are discussed. It is shown that in the framework of this formulation it is possible to preserve succession from the classical theory and, in particular, use these methods for studies of quantum systems. The quantum dispersion of a nonlinear oscillator excited by an external source and of a parametric generator is calculated. Its role is established in the solution of the problem of stability of oscillations.     

Vacuum energy: Quantum hydrodynamics vs. quantum gravity

We compare quantum hydrodynamics and quantum gravity. They share many common features. In particular, both have quadratic divergences, and both lead to the problem of the vacuum energy, which, in quantum gravity, transforms to the cosmological constant problem. We show that, in quantum liquids, the vacuum energy density is not determined by the quantum zero-point energy of the phonon modes. The energy density of the vacuum is much smaller and is determined by the classical macroscopic parameters of the liquid, including the radius of the liquid droplet. In the same manner, the cosmological constant is not determined by the zero-point energy of quantum fields. It is much smaller and is determined by the classical macroscopic parameters of the Universe dynamics: the Hubble radius, the Newton constant, and the energy density of matter. The same may hold for the Higgs mass problem: the quadratically divergent quantum correction to the Higgs potential mass term is also cancelled by the microscopic (trans-Planckian) degrees of freedom due to the thermodynamic stability of the whole quantum vacuum.