Restricted Path Integral Formalism Research Articles

Accurate Exchange-Correlation Energies for the Warm Dense Electron Gas.

The density matrix quantum MonteCarlo (DMQMC) method is used to sample exact-on-average N-body density matrices for uniform electron gas systems of up to 10^{124} matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the k-space configuration path-integral formalism disagree by up to ∼10% at certain reduced temperatures T/T_{F}≤0.5 and densities r_{s}≤1. Our calculations confirm the accuracy of the configuration path-integral MonteCarlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that the DMQMC method can calculate free energies directly and present exact free energies for T/T_{F}≥1 and r_{s}≤2.

Continuous Quantum Nondemolition Measurements of a Particlein Electromagnetic and GravitationalFields**The project supported by National Natural ScienceFoundation of China under Grant No. 10265003

The detection of a particle in electromagnetic plus gravitationalfields is investigated. We obtain a set of quantum nondemolitionvariables. The continuous measurements of these nondemolitionparameters are analyzed in the framework of restricted pathintegral formalism. We manipulate the corresponding propagators,and deduce the probabilities associated with the possible measurement outputs.

Quantum measurements and the κ-Poincaré group

The possible description of the vacuum of quantum gravity through the so called kappa--Poincare group is analyzed considering some of the consequences of this symmetry in the path integral formulation of nonrelativistic quantum theory. This study is carried out with two cases, firstly, a free particle, and finally, the situation of a particle immersed in a homogeneous gravitational field. It will be shown that the kappa--Poincare group implies the loss of some of the basic properties associated to Feynman's path integral. For instance, loss of the group characteristic related to the time dependence of the evolution operator, or the breakdown of the composition law for amplitudes of events occurring successively in time. Additionally some similarities between the present idea and the so called restricted path integral formalism will be underlined. These analogies advocate the claim that if the kappa--Poincare group contains some of the physical information of the quantum gravity vacuum, then this vacuum could entail decoherence. This last result will also allow us to consider the possibility of analyzing the continuous measurement problem of quantum theory from a group--theoretical point of view, but now taking into account the kappa--Poincare symmetries.

QUANTUM MEASUREMENTS AND PAUL TRAPS IN GRAVITATIONAL BACKGROUNDS

In the present work we solve the motion equations of a particle in a Paul trap embedded in the gravitational field of a spherically symmetric mass. One of the ideas behind this work concerns the analysis of the effects that the gravity-induced quantum noise, stemming from the bodies in the neighborhood of the Paul trap, could have upon the enhancement of the quantum behavior of this system. This will be done considering a series expansion for the gravitational field of the source, and including in the Hamiltonian of the Paul trap only the first two terms. Higher-order contributions will be introduced as part of the environment of the system, and in consequence will not appear in the Hamiltonian. In other words, we put forward an argument that allows us to differentiate those gravitational degrees of freedom that will appear as an uncontrollable influence on the Paul trap. Along the ideas of the so-called restricted path integral formalism, we take into account the continuous monitoring of the position of our particle, and in consequence the corresponding propagators and probabilities, associated with the different measurements outputs, are obtained. Afterwards, the differential equation related to a quantum nondemolition variable is posed and solved, i.e., a family of quantum nondemolition parameters is obtained. Finally, a qualitative analysis of the effects on the system, of the gravity-induced environment, will be done.

QUANTUM NONDEMOLITION MEASUREMENTS OF A PARTICLE IN ELECTRIC AND GRAVITATIONAL FIELDS

In this work we obtain a nondemolition variable for the case in which a charged particle moves in the electric and gravitational fields of a spherical body. Afterwards we consider the continuous monitoring of this nondemolition parameter, and calculate, along the ideas of the so called restricted path integral formalism, the corresponding propagator. Using these results the probabilities associated with the possible measurement outputs are evaluated. The limit of our results, as the resolution of the measuring device goes to zero, is analyzed, and the dependence of the corresponding propagator upon the strength of the electric and gravitational fields is commented. The role that mass plays in the corresponding results, and its possible connection with the equivalence principle at quantum level, are studied.

QUANTUM-MECHANICAL DETECTION OF NON-NEWTONIAN GRAVITY

In this work the possibility of detecting the presence of a Yukawa term, as an additional contribution to the usual Newtonian gravitational potential, is introduced. The central idea is to analyze the effects at quantum level employing interference patterns (at this respect the present proposal resembles the Colella, Overhauser and Werner experiment), and deduce from it the possible effects that this Yukawa term could have. We will prove that the corresponding interference pattern depends on the phenomenological parameters that define this kind of terms. Afterwards, using the so-called restricted path integral formalism, the case of a particle whose position is being continuously monitored, is analyzed, and the effects that this Yukawa potential could have on the measurement outputs are obtained. This allows us to obtain another scheme that could lead to the detection of these terms. This last part also renders new theoretical predictions that could enable us to confront the restricted path integral formalism against some future experiments.

Quantum nondemolition measurements in a Paul trap

In this Letter a family of quantum nondemolition variables for the case of a particle caught in a Paul trap is obtained. Afterwards, in the context of the so called restricted path integral formalism, a continuous measuring process for this family of parameters is considered, and then the corresponding propagators are calculated. In other words, the time evolution of a particle in a Paul trap, when the corresponding quantum nondemolition parameter is being continuously monitored, is deduced. The probabilities associated with the possible measurement outputs are also obtained, and in this way new theoretical results emerge, which could allow us to confront the predictions of this restricted path integral formalism with the readouts of some future experiments.

GROUP-THEORETICAL STRUCTURE OF QUANTUM MEASUREMENTS AND EQUIVALENCE PRINCIPLE

The transverse group associated to some continuous quantum measuring processes is analyzed in the presence of nonvanishing gravitational fields. This is done considering, as an example, the case of a particle whose coordinates are being monitored. Employing the so-called restricted path integral formalism, it will be shown that the measuring process could always contain information concerning the gravitational field. In other words, it seems that with the presence of a measuring process the equivalence principle may, in some cases, break down. The relation between the breakdown of the equivalence principle, at quantum level, and the fact that the gravitational field could always act as a decoherence environment, is also analyzed. The phenomena of quantum beats of quantum optics will allow us to consider the possibility that the experimental corroboration of the equivalence principle at quantum level could be taken as an indirect evidence in favor of the quantization of the gravitational field, i.e. the quantum properties of this field avoid the violation of the equivalence principle.

Gravity-induced interference and continuous quantum measurements

Gravity-induced quantum interference is a remarkable effect that has already been confirmed experimentally, and it is a phenomenon in which quantum mechanics and gravity play simultaneously an important role. Additionally, a generalized version of this interference experiment could offer the possibility to confront against measurement outputs one of the formalisms that claim to give an explanation to the so called quantum measurement problem, namely the restricted path integral formalism. In this work we will analyze a possible extension of Colella, Overhauser, and Werner experiment and find that in the context of the restricted path integral formalism we obtain new interference terms that could be measured in an extended version of this experimental construction. These new terms not only show, as in the first experiment, that at the quantum level gravity is not a purely geometric effect, it still depends on mass, but also show that interference does depend on some parameters that appear in the restricted path integral formalism, thus offering the possibility to have a testing framework for its theoretical predictions.

ON A QUANTUM EQUIVALENCE PRINCIPLE

The logical consistency of a description of quantum theory in the context of general relativity, which includes minimal coupling principle, is analyzed from the point of view of Feynman's formulation in terms of path integrals. We will argue from this standpoint and use an argument that claims the incompleteness of the general relativistic description of gravitation, which emerges as a consequence of the gravitationally induced phases of the so-called flavor-oscillation clocks, that the postulates of quantum theory are logically incompatible with the usual minimal coupling principle. It will be shown that this inconsistency could emerge from the fact that the required geometrical information to calculate the probability of finding a particle at any point of the respective manifold does not lie in a region with finite volume. Then we put forth a new quantum minimal coupling principle in terms of a restricted path integral, and along the ideas of this model not only the propagator of a free particle is calculated but also the conditions under which we recover Feynman's case for a free particle are deduced. The effect on diatomic interstellar molecules is also calculated. The already existing relation between restricted path integral formalism and decoherence model will enable us to connect the issue of a quantum minimal coupling principle with the collapse of the wave function. From this last remark we will claim that the geometrical structure of the involved manifold acts as, always present, a measuring device on a quantum particle. In other words, in this proposal we connect the issue of a quantum minimal coupling principle with a claim which states that gravity could be one of the physical entities which results in the collapse of the wave function.

Continuous quantum measurements of a particle in a Paul trap

We calculate the propagator of a particle caught in a Paul trap and subject to the continuous quantum measurement of its position. The probabilities of the measurement outputs, the possible trajectories of the particle, are also found. This enables us to propose a series of experiments that would allow us to compare the predictions of one of the models that describe the interaction between a measured quantum system and measuring device, namely the so-called restricted path-integral formalism, with the experiment.