Skip to main content

E. Verdaguer

Followers

6

Following

2

Co-authors

2

Public Views

Interests

Uploads

Papers by E. Verdaguer

Master equation for quantum Brownian motion derived by stochastic methods

International Journal of Theoretical Physics, 2001

The master equation for a linear open quantum system in a general environment is derived using a ... more The master equation for a linear open quantum system in a general environment is derived using a stochastic approach. This is an alternative derivation to that of Hu, Paz and Zhang, which was based on the direct computation of path integrals, or to that of Halliwell and Yu, based on the evolution of the Wigner function for a linear closed quantum system. We first show by using the influence functinal formalism that the reduced Wigner function for the open system coincides with a distribution function resulting from averaging both over the initial conditions and the stochastic source of a formal Langevin equation. The master equation for the reduced Wigner function can then be deduced as a Fokker-Planck equation obtained from the formal Langevin equation.

format_quoteThe reduced Wigner function is formalized as a stochastic process, leading to a master equation derived from the Fokker-Planck equation.format_quote

1 Inverse scattering technique in gravity

The purpose of this chapter is to describe the Inverse Scattering Method (ISM) for the gravitatio... more The purpose of this chapter is to describe the Inverse Scattering Method (ISM) for the gravitational field. We begin in section 1.1 with a brief overview of the ISM in nonlinear physics. In a nutshell the procedure involves two main steps. The first step consists of finding for a given nonlinear equation a set of linear differential equations (spectral equations) whose integrability conditions are just the nonlinear equation to be solved. The second step consists of finding the class of solutions known as soliton solutions. It turns out that given a particular solution of the nonlinear equation new soliton solutions can be generated by purely algebraic operations, after an integration of the linear differential equations for the particular solution. We consider in particular some of the best known equations that admit the ISM such as the Korteweg–de Vries and the sine-Gordon equations. In section 1.2 we write Einstein equations in vacuum for spacetimes that admit an orthogonally tra...

Radiative isotropic cosmologies with extra dimensions

Physical Review D, 1986

Cosmic Strings and Einstein-Rosen Soliton Waves

Physical Review D, 1987

Gravitational-Field of Superconducting Cosmic Strings

Physical Review Letters, 1988

Spacelike fluctuations of the stress tensor for de Sitter vacuum

International Journal of Theoretical Physics, 1999

The two-point function characterizing the stress tensor fluctuations of a massless minimally coup... more The two-point function characterizing the stress tensor fluctuations of a massless minimally coupled field for an invariant vacuum state in de Sitter spacetime is discussed. This two-point function is explicitly computed for spacelike separated points which are geodesically connected. We show that these fluctuations are as important as the expectation value of the stress tensor itself. These quantum field fluctuations will induce fluctuations in the geometry of de Sitter spacetime. This paper is a first step towards the computation of such metric fluctuations, which may be of interest for large-scale structure formation in cosmology. The relevance of our results in this context is briefly discussed.

Imprints of cosmic strings on the cosmological GW background

The equation which governs the temporal evolution of a gravitational wave (GW) in curved space- t... more The equation which governs the temporal evolution of a gravitational wave (GW) in curved space- time can be treated as the Schrodinger equation for a particle moving in the presence of an effective potential. When GWs propagate in an expanding Universe with constant effective potential, there is a critical value (kc) of the comoving wave-number which discriminates the metric perturbations into oscillating (k > kc) and non-oscillating (k < kc) modes. As a consequence, if the non-oscillatory modes are outside the horizon they do not freeze out. The effective potential is reduced to a non- vanishing constant in a cosmological model which is driven by a two-component fluid, consisting of radiation (dominant) and cosmic strings (sub-dominant). It is known that the cosmological evolution gradually results in the scaling of a cosmic-string network and, therefore, after some time (��) the Universe becomes radiation-dominated. The evolution of the non-oscillatory GW modes during �� (wh...

Induced quantum metric fluctuations and the validity of semiclassical gravity

Physical Review D, 2004

We propose a criterion for the validity of semiclassical gravity ͑SCG͒ which is based on the stab... more We propose a criterion for the validity of semiclassical gravity ͑SCG͒ which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equation obtained in the framework of stochastic gravity. Specifically, the Einstein-Langevin equation yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. The homogeneous solutions of the Einstein-Langevin equation are equivalent to the solutions of the perturbed semiclassical equation, which describe the evolution of the expectation value of the quantum metric perturbations. The information on the intrinsic fluctuations, which are connected to the initial fluctuations of the metric perturbations, can also be retrieved entirely from the homogeneous solutions. However, the induced metric fluctuations proportional to the noise kernel can only be obtained from the Einstein-Langevin equation ͑the inhomogeneous term͒. These equations exhibit runaway solutions with exponential instabilities. A detailed discussion about different methods to deal with these instabilities is given. We illustrate our criterion by showing explicitly that flat space is stable and a description based on SCG is a valid approximation in that case.

Scattering of quantum particles by gravitational plane waves

Physical Review D, 1991

Stochastic gravity: beyond semiclassical gravity

Journal of Physics: Conference Series, 2007

The back-reaction of a classical gravitational field interacting with quantum matter fields is de... more The back-reaction of a classical gravitational field interacting with quantum matter fields is described by the semiclassical Einstein equation, which has the expectation value of the quantum matter fields stress tensor as a source. The semiclassical theory may be obtained from the quantum field theory of gravity interacting with N matter fields in the large N limit. This theory breaks down when the fields quantum fluctuations are important. Stochastic gravity goes beyond the semiclassical limit and allows for a systematic and self-consistent description of the metric fluctuations induced by these quantum fluctuations. The correlation functions of the metric fluctuations obtained in stochastic gravity reproduce the correlation functions in the quantum theory to leading order in an 1/N expansion. Two main applications of stochastic gravity are discussed. The first, in cosmology, to obtain the spectrum of primordial metric perturbations induced by the inflaton fluctuations, even beyond the linear approximation. The second, in black hole physics, to study the fluctuations of the horizon of an evaporating black hole.

format_quoteSemiclassical equations break down with large stress tensor fluctuations; a stochastic framework is proposed to better describe interactions.format_quote

Cosmological Einstein-Rosen metrics and generalised soliton solutions

Classical and Quantum Gravity, 1987

The authors consider all generalised soliton solutions for the cosmological Einstein-Rosen metric... more The authors consider all generalised soliton solutions for the cosmological Einstein-Rosen metrics generated by transforming the Kasner metric. Besides some new solutions, several well known cosmological solutions, as well as the recently discussed composite universes, are seen to fall within this class of soliton solutions. The properties of the solutions are briefly explained.

Generalised soliton solutions of the Weyl class

Classical and Quantum Gravity, 1989

The whole family of generalised soliton solutions of the Weyl class for Einstein's equations in v... more The whole family of generalised soliton solutions of the Weyl class for Einstein's equations in vacuum is considered. A classification scheme for the distinct types of metrics belonging to this family is given and emphasis is placed on the asymptotically flat solutions. The physical interpretation of the occurring parameters is also briefly considered.

Dissipation, Noise, and Vacuum Decay in Quantum Field Theory

Physical Review Letters, 2001

We study the process of vacuum decay in quantum field theory focusing on the stochastic aspects o... more We study the process of vacuum decay in quantum field theory focusing on the stochastic aspects of the interaction between long-and short-wavelength modes. This interaction results in a diffusive behavior of the reduced Wigner function describing the state of long-wavelength modes, and thereby to a finite activation rate even at zero temperature. This effect can make a substantial contribution to the total decay rate.

Einstein–Maxwell fields

Gravitational Solitons

We consider the class of regular (in a certain precise sense) null vector fields, which have the ... more We consider the class of regular (in a certain precise sense) null vector fields, which have the following properties; they are (1) tangent to geodesies, (2) diverging, (3) shear free, (4) twist (or curl) free. It is well known that the vacuum Einstein fields whose principle null vector field (pnvf) satisfies are the Robinson-Trautman (1962) (RT) metrics and those which satisfy (l)-(3) are the algebraically special twisting metrics, (Kerr, 1963). To understand these metrics better we ask for those Maxwell fields (in flat space) whose pnvf also satisfy conditions (l)-{4) and (l)-(3)-It can be shown that (l)-{4) imply (and are implied by) that the Maxwell field is a Lienard-Wiechart (LW) field. (This establishes the analogy between the RT metrics and the LW fields.) Conditions (l}-(3) imply that the Maxwell field is a complex LW field. (We mean by this that if the Maxwell equations are complexified (Newman, 1973) (in complex Minkowski space) then the real solution in question is induced from the complex solution which is associated with a charged particle moving along an arbitrary complex world line.) Finally it can be shown that the Einstein equations can be complexified and that the algebraically special twisting metrics can be inter preted as if they had a point source moving in the complex manifold and are thus analogous to the complex LW fields. References

THEORY : From Mean Values to Fluctuations 1 From Semiclassical to Stochastic Gravity

Stochastic semiclassical gravity of the 90’s is a theory naturally evolved from semiclassical gra... more Stochastic semiclassical gravity of the 90’s is a theory naturally evolved from semiclassical gravity of the 70’s and 80’s. It improves on the semiclassical Einstein equation with source given by the expectation value of the stress-energy tensor of quantum matter fields in curved spacetimes by incorporating an additional source due to their fluctuations. In stochastic semiclassical gravity the main object of interest is the noise kernel, the vacuum expectation value of the (operator-valued) stress-energy bi-tensor, and the centerpiece is the (stochastic) EinsteinLangevin equation. We describe this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the energy momentum tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh close-time-path effe...

Recent Advances in Stochastic Gravity: Theory and Issues

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given ... more Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein- Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the expectation value of the stress-energy bi-tensor which describes the fluctuations of quantum matter fields. Here, we first give an axiomatic derivation of the Einstein-Langevin equations and then show how they can also be derived by the original method based on the influence functional. As a first application we solve these equations and compute the two- point correlation functions for the linearized Einstein tensor and for the metric perturbations in a Minkowski background. We then turn to the important issue of the validity of semiclassical gravity by examining the criteria based on the ratio of the variance of fluctuations of the stress-energy tensor of a quan...

Quantum Noise and Fluctuations in Gravitation and Cosmology

We give a short update of our research program on nonequilibrium statistical field theory applied... more We give a short update of our research program on nonequilibrium statistical field theory applied to quantum processes in the early universe and black holes, as well as the development of stochastic gravity theory as an extension of semiclassical gravity and an intermediary in the 'bottom-up' approach to quantum gravity.

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given ... more Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black hole

Transverse Fierz-Pauli symmetry

We consider some flat space theories for spin 2 gravitons, with less invariance than full diffeom... more We consider some flat space theories for spin 2 gravitons, with less invariance than full diffeomorphisms. For the massless case, classical stability and absence of ghosts require invariance under transverse diffeomorphisms (TDiff). Generic TDiff invariant theories contain a propagating scalar, which disappears if the symmetry is enhanced in one of two ways. One possibility is to consider full diffeomorphisms (Diff). The other (which we denote WTDiff) adds a Weyl symmetry, by which the Lagrangian becomes independent of the trace. The first possibility corresponds to General Relativity, whereas the second corresponds to "unimodular" gravity (in a certain gauge). Phenomenologically, both options are equally acceptable. For massive gravitons, the situation is more restrictive. Up to field redefinitions, classical stability and absence of ghosts lead directly to the standard Fierz-Pauli Lagrangian. In this sense, the WTDiff theory is more rigid against deformations than linear...

International Journal of Theoretical Physics: Preface