arXiv subjects

G. Bimonte

Publications and source records attributed to G. Bimonte.

At least 37 records · Page 2Linked to original sources

arXiv2003

Comment on "Quantitative wave-particle duality in multibeam interferometers"

In a recent paper [Phys. Rev. {\bf A64}, 042113 (2001)] S. Dürr proposed an interesting multibeam generalization of the quantitative formulation of interferometric wave-particle duality, discovered by Englert for two-beam interferometers. The proposed generalization is an inequality that relates a generalized measure of the fringe visibility, to certain measures of the maximum amount of which-way knowledge that can be stored in a which-way detector. We construct an explicit example where, with three beams in a pure state, the scheme proposed by Dürr leads to the possibility of an ideal which-way detector, that can achieve a better path-discrimination, at the same time as a better fringe visibility. In our opinion, this seems to be in contrast with the intuitive idea of complementarity, as it is implemented in the two-beams case, where an increase in path discrimination always implies a decrease of fringe visibility, if the beams and the detector are in pure states.

quant-ph↗

arXiv2003

New classical brackets for dissipative systems

A set of brackets for classical dissipative systems, subject to external random forces, are derived. The method is inspired to the old procedure found by Peierls, for deriving the canonical brackets of conservative systems, starting from an action principle. It is found that an adaptation of Peierls' method is applicable also to dissipative systems, when the friction term can be described by a linear functional of the coordinates, as is the case in the classical Langevin equation, with an arbitrary memory function. The general expression for the brackets satisfied by the coordinates, as well as by the external random forces, at different times, is determined, and it turns out that they all satisfy the Jacobi identity. Upon quantization, these classical brackets are found to coincide with the commutation rules for the quantum Langevin equation, that have been obtained in the past, by appealing to microscopic conservative quantum models for the friction mechanism.

hep-th↗

arXiv2002

Complementarity, measurement and information in interference experiments

Different criteria (Shannon's entropy, Bayes' average cost, Durr's normalized rms spread) have been introduced to measure the "which-way" information present in interference experiments where, due to non-orthogonality of the detector states, the path determination is incomplete. For each of these criteria, we determine the optimal measurement to be carried on the detectors, in order to read out the maximum which-way information. We show that, while in two-beam experiments, the optimal measurement is always provided by an observable involving the detector only, in multibeam experiments, with equally populated beams and two-state detectors, this is the case only for the Durr criterion, as the other two require the introduction of an ancillary quantum system, as part of the read-out apparatus.

quant-ph↗

arXiv1999

Bicovariant Calculus in Quantum Theory and a Generalization of the Gauss Law

We construct a deformation of the quantum algebra Fun(T^*G) associated with Lie group G to the case where G is replaced by a quantum group G_q which has a bicovariant calculus. The deformation easily allows for the inclusion of the current algebra of left and right invariant one forms. We use it to examine a possible generalization of the Gauss law commutation relations for gauge theories based on G_q.

hep-th↗

arXiv1999

Inverse Symmetry Breaking on the lattice: an accurate MC study

We present here a new MC study of ISB at finite temperature in a $Z_2\times Z_2$ $λϕ^4$ model in four dimensions. The results of our simulations, even if not conclusive, are favourable to ISB. Detection of the effect required measuring some critical couplings with six-digits precision, a level of accuracy that could be achieved only by a careful use of FSS techniques. The gap equations for the Debye masses, resulting from the resummation of the ring diagrams, seem to provide a qualitatively correct description of the data, while the simple one-loop formulae appear to be inadequate.

hep-lat↗

arXiv1998

Current Oscillations, Interacting Hall Discs and Boundary CFTs

In this paper, we discuss the behavior of conformal field theories interacting at a single point. The edge states of the quantum Hall effect (QHE) system give rise to a particular representation of a chiral Kac-Moody current algebra. We show that in the case of QHE systems interacting at one point we obtain a ``twisted'' representation of the current algebra. The condition for stationarity of currents is the same as the classical Kirchoff's law applied to the currents at the interaction point. We find that in the case of two discs touching at one point, since the currents are chiral, they are not stationary and one obtains current oscillations between the two discs. We determine the frequency of these oscillations in terms of an effective parameter characterizing the interaction. The chiral conformal field theories can be represented in terms of bosonic Lagrangians with a boundary interaction. We discuss how these one point interactions can be represented as boundary conditions on fields, and how the requirement of chirality leads to restrictions on the interactions described by these Lagrangians. By gauging these models we find that the theory is naturally coupled to a Chern-Simons gauge theory in 2+1 dimensions, and this coupling is completely determined by the requirement of anomaly cancellation.

hep-th↗

arXiv1998

Comments on the Non-Commutative Description of Classical Gravity

We find a one-parameter family of Lagrangian descriptions for classical general relativity in terms of tetrads which are not c-numbers. Rather, they obey exotic commutation relations. These noncommutative properties drop out in the metric sector of the theory, where the Christoffel symbols and the Riemann tensor are ordinary commuting objects and they are given by the usual expression in terms of the metric tensor. Although the metric tensor is not a c-number, we argue that all measurements one can make in this theory are associated with c-numbers, and thus that the common invariant sector of our one--parameter family of deformed gauge theories (for the case of zero torsion) is physically equivalent to Einstein's general relativity.

gr-qc↗

arXiv1998

New Tetrads for General Relativity

Using the tools of q--differential calculus and quantum Lie algebras associated to quantum groups, we find a one--parameter family of q-gauge theories associated to the quantum group $ISO_q(3,1)$. Although the gauge fields, that is the spin--connection and the vierbeins are non--commuting objects depending on a deformation parameter, $q$, it is possible to construct out of them a metric theory which is insensitive to the deformation. The Christoffel symbols and the Riemann tensor are ordinary commuting objects. Hence it is argued that torsionless Einstein's General Relativity is the common invariant sector of a one--parameter family of deformed gauge theories.

hep-th↗

arXiv1998

A Monte Carlo study of Inverse Symmetry Breaking

We make a Monte Carlo study of the coupled two-scalar $λϕ^2_1ϕ^2_2$ model in four dimensions at finite temperature. We find no trace of Inverse Symmetry Breaking for values of the renormalized parameters for which perturbation theory predicts this phenomenon.

hep-lat↗

arXiv1998

A lattice Monte Carlo study of Inverse Symmetry Breaking in a two-scalar model in three dimensions

We carry a Monte Carlo study of the coupled two-scalar $λϕ^2_1 ϕ^2_2$ model in three dimensions. We find no trace of Inverse Symmetry Breaking in the region of negative $λ$'s for which the one-loop effective potential predicts this phenomenon. Moreover, for $λ$'s negative enough, but still in the stability region for the potential, one of the transitions turns out to be of first order, both for zero and finite temperature.

hep-lat↗

arXiv1997

Cosmological waveguides for gravitational waves

We study the linearized equations describing the propagation of gravitational waves through dust. In the leading order of the WKB approximation, dust behaves as a non-dispersive, non-dissipative medium. Taking advantage of these features, we explore the possibility that a gravitational wave from a distant source gets trapped by the gravitational field of a long filament of galaxies of the kind seen in the large scale structure of the Universe. Such a waveguiding effect may lead to a huge magnification of the radiation from distant sources, thus lowering the sensitivity required for a successful detection of gravitational waves by detectors like VIRGO, LIGO and LISA.

gr-qc↗

arXiv1997

Hidden Quantum Group Structure in Einstein's General Relativity

A new formal scheme is presented in which Einstein's classical theory of General Relativity appears as the common, invariant sector of a one-parameter family of different theories. This is achieved by replacing the Poincare` group of the ordinary tetrad formalism with a q-deformed Poincare` group, the usual theory being recovered at q=1. Although written in terms of noncommuting vierbein and spin-connection fields, each theory has the same metric sector leading to the ordinary Einstein-Hilbert action and to the corresponding equations of motion. The Christoffel symbols and the components of the Riemann tensor are ordinary commuting numbers and have the usual form in terms of a metric tensor built as an appropriate bilinear in the vierbeins. Furthermore we exhibit a one-parameter family of Hamiltonian formalisms for general relativity, by showing that a canonical formalism a` la Ashtekar can be built for any value of q. The constraints are still polynomial, but the Poisson brackets are not skewsymmetric for q different from 1.

hep-th↗

arXiv1997

2+1 Einstein Gravity as a Deformed Chern-Simons Theory

The usual description of 2+1 dimensional Einstein gravity as a Chern-Simons (CS) theory is extended to a one parameter family of descriptions of 2+1 Einstein gravity. This is done by replacing the Poincare' gauge group symmetry by a q-deformed Poincare' gauge group symmetry, with the former recovered when q-> 1. As a result, we obtain a one parameter family of Hamiltonian formulations for 2+1 gravity. Although formulated in terms of noncommuting dreibeins and spin-connection fields, our expression for the action and our field equations, appropriately ordered, are identical in form to the ordinary ones. Moreover, starting with a properly defined metric tensor, the usual metric theory can be built; the Christoffel symbols and space-time curvature having the usual expressions in terms of the metric tensor, and being represented by c-numbers. In this article, we also couple the theory to particle sources, and find that these sources carry exotic angular momentum. Finally, problems related to the introduction of a cosmological constant are discussed.

hep-th↗

arXiv1997

Deformed Chern-Simons Theories

We construct a Chern-Simons action for q-deformed gauge theory which is a simple and straightforward generalization of the usual one. Space-time continues to be an ordinary (commuting) manifold, while the gauge potentials and the field strengths become q-commuting fields. Our approach, which is explicitly carried out for the case of `minimal' deformations, has the advantage of leading naturally to a consistent Hamiltonian structure that has essentially all of the features of the undeformed case. For example, using the new Poisson brackets, the constraints form a closed algebra and generate q-deformed gauge transformations.

hep-th↗

arXiv1996

Lattice Gauge Fields and Noncommutative Geometry

Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its fields. In this paper, we develop a formulation which tries to remedy this defect. It starts from a cubical decomposition of the supporting manifold (compactified spacetime or spatial slice) interpreting it as a finite topological approximation in the sense of Sorkin. This finite space is entirely described by the algebra of cochains with the cup product. The methods of Connes and Lott are then used to develop gauge theories on this algebra and to derive Wilson's actions for the gauge and Dirac fields therefrom which can now be given geometrical meaning. We also describe very natural candidates for the QCD theta term and Chern-Simons action suggested by this algebraic formulation. Some of these formulations are simpler than currently available alternatives. The paper treats both the functional integral and Hamiltonian approaches.

hep-lat↗

arXiv1996

Continuum limit of finite temperature $λϕ^4_3$ from lattice Monte Carlo

The $ϕ^4_3$ model at finite temperature is simulated on the lattice. For fixed $N_t$ we compute the transition line for $N_s \to \infty$ by means of Finite Size Scaling techniques. The crossings of a Renormalization Group trajectory with the transition lines of increasing $N_t$ give a well defined limit for the critical temperature in the continuum. By considering different RG trajectories, we compute $T^c/g$ as a function of the renormalized parameters.

hep-lat↗

arXiv1996

Symmetry Non Restoration and Inverse Symmetry Breaking on the lattice

We study the finite temperature symmetry behaviour of O(N_1) \times O(N_2) scalar models on the lattice and we prove that at sufficiently high temperatures and in arbitrary dimensions their full symmetry is always restored or, equivalently, that the phenomenon of Symmetry Non Restoration which, according to lowest order perturbation theory, takes place in the continuum version of these models, does not occur on the lattice.

hep-th↗

arXiv1996

$SU_q(2)$ Lattice Gauge Theory

We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, it then gets promoted to a quantum group gauge symmetry. The theory depends on two parameters - the deformation parameter $λ$ and the lattice spacing $a$. We show that the system of Kogut and Susskind is recovered when $λ\rightarrow 0$, while QCD is recovered in the continuum limit (for any $λ$). We thus have the possibility of having a two parameter regularization of QCD.

hep-th↗