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Register a new userBreakdown of separability due to confinement, submitted to Report on mathematical physics
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A simple system of two particles in a bidimensional configurational space $S$ is studied. The possibility of breaking in $S$ the time independent Schr{o}dinger equation of the system into two separated one-dimensional one-body Schr{o}dinger equations is assumed. In this paper, we focus on how the latter property is countered by imposing such boundary conditions as confinement in a limited region of $S$ and/or restrictions on the joint coordinate probability density stemming from the sign-invariance condition of the relative coordinate (an impenetrability condition). Our investigation demonstrates the reducibility of the problem under scrutiny into that of a single particle living in a limited domain of its bidimensional configurational space. These general ideas are illustrated introducing the coordinates $X_c$ and $x$ of the center of mass of two particles and of the associated relative motion, respectively. The effects of the confinement and the impenetrability are then analyzed by studying with the help of an appropriate Greens function and the time evolution of the covariance of $X_c$ and $x$. Moreover, to calculate the state of the single particle constrained within a square, a rhombus, a triangle and a rectangle the Greens function expression in terms of Jacobi $theta_3$-function is applied. All the results are illustrated by examples.
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We consider a surface code suffering decoherence due to coupling to a bath of bosonic modes at finite temperature and study the time available before the unavoidable breakdown of error correction occurs as a function of coupling and bath parameters. We derive an exact expression for the error rate on each individual qubit of the code, taking spatial and temporal correlations between the errors into account. We investigate numerically how different kinds of spatial correlations between errors in the surface code affect its threshold error rate. This allows us to derive the maximal duration of each quantum error correction period by studying when the single-qubit error rate reaches the corresponding threshold. At the time when error correction breaks down, the error rate in the code can be dominated by the direct coupling of each qubit to the bath, by mediated subluminal interactions, or by mediated superluminal interactions. For a 2D Ohmic bath, the time available per quantum error correction period vanishes in the thermodynamic limit of a large code size $L$ due to induced superluminal interactions, though it does so only like $1/sqrt{log L}$. For all other bath types considered, this time remains finite as $Lrightarrowinfty$.
The application of a high electrical field on metallic surfaces leads to the well described phenomena of breakdown. In the classical scenario, explosive electron emission (EEE), breakdown (BD) originates from an emitting site (surface protrusion). The conditioning process consists of burning the emitting sites one after another and numerous observations exhibit surfaces covered with molten craters that more or less overlap. When dealing with RF cavities for accelerators, where increasingly fields are now sought, one can legitimately wonder if other physical phenomena should also be taken into account. In particular, we believe that electromigration, especially at surfaces or grain boundaries cannot be neglected anymore at high field (i.e. 50-100 MV/m). Many publications in the domain of liquid metal emission sources show that very stable and strong emission sources, either ions or electrons, build up on metallic surfaces submitted to electrical fields through a mechanism that is slightly different from the usual localized breakdown evoked in accelerators. This mechanism involves the combination of electromigration and collective motion of surface atoms. The recent results obtained on 30 GHz CLIC (Compact Linear Collider) accelerating structures, altogether with the data exposed hereafter have led us to propose a complementary scenario (pre-plasma apparition), based on electromigration, which could explain early melting of large areas of the surface.
A model is described, in which electrical breakdown in high-voltage systems is caused by stochastic fluctuations of the mobile dislocation population in the cathode. In this model, the mobile dislocation density normally fluctuates, with a finite probability to undergo a critical transition due to the effects of the external field. It is suggested that once such a transition occurs, the mobile dislocation density will increase deterministically, leading to electrical breakdown. Model parametrization is achieved via microscopic analysis of OFHC Cu cathode samples from the CERN CLIC project, allowing the creation and depletion rates of mobile dislocations to be estimated as a function of the initial physical condition of the material and the applied electric field. We find analytical expressions for the mean breakdown time and quasistationary probability distribution of the mobile dislocation density, and verify these results by using a Gillespie algorithm. A least-squares algorithm is used to fit these results with available experimental data of the dependence of the breakdown rate on the applied strength of the electric field and on temperature. The effects of the variation of some of the assumptions of the physical model are considered, and a number of additional experiments to validate the model are proposed, which include examining the effects of the temperature and pulse length, as well as of a time-dependent electric field, on the breakdown rate. Finally, applications of the model are discussed, including the usage of the quasistatic probability distribution to predict breakdowns, and applying the predictions of the model to improve the conditioning process of the cathode material.
We show that the probability distribution of the stationary state of a dissipative ac-driven two-level system exhibits discontinuities, i.e. jumps, for parameters at which coherent destruction of tunneling takes place. These discontinuities can be observed as jumps in the emission of the Mollow triplet. The jumps are the consequence of discontinuities in the transition rates, which we calculate numerically and analytically based on the secular Floquet-Redfield formalism.
The microscopic nature of an insulating state in the vicinity of a superconducting state, in the presence of disorder, is a hotly debated question. While the simplest scenario proposes that Coulomb interactions destroy the Cooper pairs at the transition, leading to localization of single electrons, an alternate possibility supported by experimental observations suggests that Cooper pairs instead directly localize. The question of the homogeneity, granularity, or possibly glassiness of the material on the verge of this transition is intimately related to this fundamental issue. Here, by combining macroscopic and nano-scale studies of superconducting ultrathin NbN films, we reveal nanoscopic electronic inhomogeneities that emerge when the film thickness is reduced. In addition, while thicker films display a purely two-dimensional behaviour in the superconducting fluctuations, we demonstrate a zero-dimensional regime for the thinner samples precisely on the scale of the inhomogeneities. Such behavior is somehow intermediate between the Fermi and Bose insulator paradigms and calls for further investigation to understand the way Cooper pairs continuously evolve from a bound state of fermionic objects into localized bosonic entities.
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