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We shed a new light on the longstanding problem of covariant charges in diffeomorphism invariant theories like General Relativity (GR) by noting the other important feature of the theory, the background independence. To this end, we develop covariant phase space formalism in which we allow for the boundaries of spacetime to have arbitrary fluctuations. Within this formalism we show non-covariance of charges appear in inevitable integration constants which also break background independence in the expression of charges. We then apply the same formalism to black hole thermodynamics. We generalize the seminal Iyer-Wald derivation the first law of bl1ack hole thermodynamics by relaxing the need for the assumptions at a bifurcation surface and asymptotic infinity, as well as addressing questions regarding the integrability of charges. We also present a first principles derivation of the Smarr relation within our framework., Comment: 5+3 pages, 3 figures, Wording and presentation improved, the version appearing in PRD

We reconsider formulating $D$ dimensional gauge theories, with the focus on the case of gravity theories, in spacetimes with boundaries. We extend covariant phase space formalism to the cases in which boundaries are allowed to fluctuate. We analyze the symplectic form, the freedoms (ambiguities), and its conservation for this case. We show that boundary fluctuations render all the surface charges integrable. We study the algebra of charges and its central extensions, charge conservation, and fluxes. We briefly comment on memory effects and questions regarding semiclassical aspects of black holes in the fluctuating boundary setup., Comment: 24 pages, 2 figures

We use quotients of span categories to introduce the language of a topos. We also study the logical relations and the quotients of span categories derived from them. As an application we show that the category of Boolean toposes is a reflective subcategory of the category of toposes, when the morphisms are logical functors.

Quantum detailed balance conditions and quantum fluctuation relations are two important concepts in the dynamics of open quantum systems: both concern how such systems behave when they thermalize because of interaction with an environment. We prove that for thermalizing quantum dynamics the quantum detailed balance conditions yield the validity of a quantum fluctuation relation (where only forward-time dynamics is considered). This implies that to have such a quantum fluctuation relation (which in turn enables a precise formulation of the second law of thermodynamics for quantum systems) it suffices to fulfill the quantum detailed balance conditions. We, however, show that the converse is not necessarily true; indeed, there are cases of thermalizing dynamics which feature the quantum fluctuation relation without satisfying detailed balance. We illustrate our results with three examples., Comment: 9 Pages

We analyze the impact of loss in lattices of coupled optical waveguides and find that in such case, the hopping between adjacent waveguides is necessarily complex. This results not only in a transition of the light spreading from ballistic to diffusive, but also in a new kind of diffraction that is caused by loss dispersion. We prove our theoretical results with experimental observations., Comment: Accepted for publication in PRL, 5+8 pages (Paper + Supplemental material), 4 figures

We propose an exactly solvable waveguide lattice incorporating inhomogeneous coupling coefficient. This structure provides a classical analogue to the squeezed number and squeezed coherent intensity distribution in quantum optics where the propagation length plays the role of squeezed amplitude. The intensity pattern is obtained in a closed form for an arbitrary distribution of the initial beam profile. We have also investigated the phase transition to the spatial Bloch-like oscillations by adding a linear gradient to the propagation constant of each waveguides ($ \alpha $). Our analytical results show that the Bloch-like oscillations appear above a critical value for the linear gradient of propagation constant ($ \alpha > \alpha_{c} $). The phase transition (in the propagation properties of the waveguide) is a result of competition between discrete and Bragg diffraction. Moreover, the light intensity decay algebraically along each waveguide at the critical point while it falls off exponentially below the critical point ($ \alpha < \alpha_{c} $)., Comment: 7 Pages, 7 Figure

We investigate numerically the effect of long-range interaction on the transverse localization of light. To this end, nonlinear zigzag optical waveguide lattices are applied, which allows precise tuning of the second-order coupling. We find that localization is hindered by coupling between next-nearest lattice sites. Additionally, (focusing) nonlinearity facilitates localization with increasing disorder, as long as the nonlinearity is sufficiently weak. However, for strong nonlinearities, increasing disorder results in weaker localization. The threshold nonlinearity, above which this anomalous result is observed grows with increasing second-order coupling., Comment: Accepted to PRA, 5 pages, 9 figures

This paper has been withdrawn by the author due to a crucial sign error in equation 1., Comment: This paper has been withdrawn

We discuss Bohmian paths of the two-level atoms moving in a waveguide through an external resonance-producing field, perpendicular to the waveguide, and localized in a region of finite diameter. The time spent by a particle in a potential region is not well-defined in the standard quantum mechanics, but it is well-defined in the Bohmian mechanics. Bohm's theory is used for calculating the average time spent by a transmitted particle inside the field region and the arrival-time distributions at the edges of the field region. Using the Runge-Kutta method for the integration of the guidance law, some Bohmian trajectories were also calculated. Numerical results are presented for the special case of a Gaussian wave packet., Comment: 16 pages, 7 figures

It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin-1/2 particles. In the nonrelativistic domain this implies a guidance law for electrons which differs by an additional spin-dependent term from the one originally proposed by de Broglie and Bohm. Although the additional term in the guidance equation may not be detectable in the quantum measurements derived solely from the probability density $\rho$, it plays a role in the case of arrival-time measurements. In this paper we compute the arrival time distribution and the mean arrival time at a given location, with and without the spin contribution, for two problems: 1) a symmetrical Gaussian packet in a uniform field and 2) a symmetrical Gaussian packet passing through a 1D barrier. Using the Runge-Kutta method for integration of the guidance law, Bohmian paths of these problems are also computed.

In a Letter, Cabello proposed a quantum key distribution (QKD) Protocol which attended to Holevo limit. In this comment, we show that Eve could use a simple plan to distinguish among quantum keys, without being detected by Alice and Bob. In following, we show that our approach is not restricted to Cabello Protocol. With attention to our Eavesdropping approach, it seems that Mor's arguments for no-cloning principal for orthogonal states is not general enough to avoid eavesdropping., Comment: REVTeX4, 1 page, no figure, A. Cabello Reply, Physical Review Letters 100, 018902 (2008)

Entanglement and entanglement-assisted are useful resources to enhance the mutual information of the Pauli channels, when the noise on consecutive uses of the channel has some partial correlations. In this Paper, we study quantum-communication channels in $d$-dimensional systems and derive the mutual information of the quantum channels for maximally entangled states and product states coding with correlated noise. Then, we compare fidelity between these states. Our results show that there exists a certain fidelity memory threshold which depends on the dimension of the Hilbert space $(d)$ and the properties of noisy channels. We calculate the classical capacity of a particular correlated noisy channel and show that in order to achieve Holevo limit, we must use $d$ particles with $d$ degrees of freedom. Our results show that entanglement is a useful means to enhance the mutual information. We choose a special non-maximally entangled state and show that in the quasi-classical depolarizing and quantum depolarizing channels, maximum classical capacity in the higher memory channels is given by the maximally entangled state. Hence, our results show that for high error channels in every degree of memory, maximally entangled states have better mutual information., Comment: 15 pages, 5 figures, PHYSICAL REVIEW A 75, 042301 (2007)

In all local realistic theories worked out till now, locality is considered as a basic assumption. Most people in the field consider the inconsistency between local realistic theories and quantum mechanics to be a result of non-local nature of quantum mechanics. In this Paper, we derive the Greenberger-Horne-Zeilinger type theorem for particles with instantaneous (non-local) interactions at the hidden-variable level. Then, we show that the previous contradiction still exists between quantum mechanics and non-local hidden variable models., Comment: 9 pages, comments welcome

Considering the common cause principle, we construct a local-contextual hidden-variable model for the Bohm version of EPR experiment. Our proposed model can reproduce the predictions of quantum mechanics. It can be also extended to classical examples in which similar correlations may be revealed., Comment: 17 pages, 4 tables, 1 figure

We have presented a theoretical extended version of dense coding protocol using entangled position state of two particles shared between two parties. A representation of Bell states and the required unitary operators are shown utilizing symmetric normalized Hadamard matrices. In addition, some explicit and conceivable forms for the unitary operators are presented by using some introduced basic operators. It is shown that, the proposed version is logarithmically efficient than some other multi-qubit dense coding protocols., Comment: 4 pages, 1 figure, Revtex

In a recent paper, Struyve et al. [Struyve W, De Baere W, De Neve J and De Weirdt S 2003 J. Phys. A 36 1525] attempted to show that the thought experiment proposed in [Golshani M and Akhavan O 2001 J. Phys. A 34 5259, quant-ph/0103101] cannot distinguish between standard and Bohmian quantum mechanics. Here, we want to show that, in spite of their objection, our conclusion still holds out., Comment: 4 pages, no figures, Latex

Recently, three experiments have been proposed in order to show that the standard and Bohmian quantum mechanics can have different predictions at the individual level of particles. However, these thought experiments have encountered some objections. In this work, it is our purpose to show that our basic conclusions about those experiments are still intact., Comment: 8 pages, no figures, Revtex

In this investigation, we have considered two thought experiments to make a comparison between predictions of the standard and the Bohmian quantum mechanics. Concerning this, a two-particle system has been studied at two various situations of the entangled and the unentangled states. In the first experiment, the two theories can predict different results at the individual level, while their statistical results are the same. In the other experiment, not only they are in disagreement at the individual level, but their equivalence at the statistical level also breaks down, if one uses selective detection. Furthermore, we discuss about some objections that can be raised against the results of the two suggested experiments., Comment: 11 pages, 3 figure, Latex

The significance of proposals that can predict different results for standard and Bohmian quantum mechanics have been the subject of many discussions over the years. Here, we suggest a particular experiment (a two double-slit experiment) and a special detection process, that we call selective detection, to distinguish between the two theories. Using our suggested experiment, it is shown that the two theories predict different observable results at the individual level for a geometrically symmetric arrangement. However, their predictions are the same at the ensemble level. On the other hand, we have shown that at the statistical level, if we use our selective detection, then either the predictions of the two theories differ or where standard quantum mechanics is silent or vague, Bohmian quantum mechanics makes explicit predictions., Comment: 9 pages, 1 figure

In this investigation, we have suggested a special two-slit experiment which can distinguish between the standard and the Bohmian quantum mechanics. At the first step, we have shown that observable individual predictions obtained from these two theories are inconsistent for a special case. But, at the ensemble level, they are consistent as was expected. Then, as another special case and using selective detection, it is shown that an observable disagreement between the two theories can exist at the ensemble level of particles. This can encourage new efforts for finding other inconsistencies between the two theories, theoretically and experimentally., Comment: 5 pages, RevTex, no figures

It is generally believed that Bell's inequality holds for the case of entangled states, including two correlated particles or special states of a single particle. Here, we derive a single-particle Bell's inequality for two correlated spin states at two successive times, appealing to the statistical independence condition in an ideal experiment, for a locally causal hidden variables theory. We show that regardless of the locality assumption, the inequality can be violated by some quantum predictions., Comment: 14 pages, 1 figure, Latex file, To appear in Annales de la Fondation Louis de Broglie

Recently, people have caculated tunneling's characteristic times within Bohmian mechanics. Contrary to some characteristic times defined within the framework of the standard interpretation of quantum mechanics, these have reasonable values. Here, we introduce one of available definitions for tunnelling's characteristic times within the standard interpretation as the best definition that can be accepted for the tunneling times. We show that, due to experimental limitations, Bohmian mechanics leads to same tunneling times., Comment: 16 pages, 5 figures

Without imposing the locality condition,it is shown that quantum mechanics cannot reproduce all the predictions of a special stochastic realistic model used in certain spin-correlation experiments.This shows that the so-called locality condition is an unnecessary assumption of Bell's theorem., Comment: 5 pages LaTeX

We try to obtain Born's principle as a result of a subquantum heat death, using classical ${\cal H}$-theorem and the definition of a proper quantum ${\cal H}$-theorem, within the framwork of Bohm's theory. We shall show the possibility of solving the problem of action-reaction asymmetry present in Bohm's theory and the arrow of time problem in our procedure., Comment: 7 pages, Latex file, to appear in Foundations of Physics Letters

In a recent paper, A.Valentini tried to obtain Born's principle as a result of a subquantum heat death, using classical H-theorem and the definition of a proper quantum H-theorem within the framwork of Bohm's theory. In this paper, we shall show the possibility of solving the problem of action-reaction asymmetry present in Bohm's theory by modifying Valentini's procedure. However, we get his main result too., Comment: Latex file, 9 pages, some extra explanation have been omitted