On non‐equilibrium photon distributions in the Casimir effect

The electromagnetic field in a typical geometry of the Casimir effect is described in the Schwinger–Keldysh formalism. The main result is the photon distribution function (Keldysh Green function) in any stationary state of the field. A two‐plate geometry with a sliding interface in local equilibrium is studied in detail, and full agreement with the results of Rytov fluctuation electrodynamics is found.     

Environment induced quantum Zeno effect in coupled microwave cavities

We model a feasible experiment involving two interacting microwave cavities with very different quality factors. An excitation is initially present in the high Q cavity. Modeling the environment as linearly coupled oscillators, we find a Zeno-like behavior which should occur when the dissipation constant is large enough as compared to the unitary coupling.     

Casimir效应的一个简明计算

电磁场的真空态具有无穷大的能量,这个无穷大能量不可直接观测,只在某些特殊情况下才表现出可观测的效应,其中之一便是Casimir效应,通常这个效应的计算是在量子场论中,按重正化的办法进行,这里给出一个更为简明的算法。     

The Casimir pressure regularization in two-dimensional field models

A method for Casimir pressure calculation with the help of the regular part of the Green surface function is considered in the two-dimensional case. Also, a method for the approximate calculation of the regular part of the Green surface function using a Born-type series is suggested. It is tested for a problem for which the exact solution is known.     

The effect of probe-Ohmic environment coupling type and probe information flow on quantum probing of the cutoff frequency

This work aims to compare results of dissipating and pure dephasing single-qubit probes in characterizing the cutoff frequency of a harmonic reservoir Ohmic spectral density. In particular, we proved that a dissipating single-qubit improves the estimation precision of the cutoff frequency estimator. The information backflow and outflow of the dissipating and the dephasing single-qubit are compared. The relation between the quantum Fisher information and the information outflow and backflow of the probe is obtained. The results show that difference between the values of information outflow and backflow of a dissipating single-qubit is larger than a dephasing single-qubit. So, a single-qubit probe extracts more information from an Ohmic reservoir by increasing the difference between the values of information outflow and backflow of the probe.     

Searching for robust quantum memories in many coupled oscillators

The relation between microscopic symmetries in the system-environment interaction and the emergence of robust states is studied for many linearly coupled harmonic oscillators. Different types of symmetry, which are introduced into the model as terms in the coupling constants between each system?s oscillator and a common reservoir, lead to distinct robust modes. Since these modes are partially or completely immune to the symmetric part of the environmental noise, they are good candidates for building quantum memories. A comparison of the model investigated here, with bilinear system-reservoir coupling, and a model where such coupling presents an exponential dependence on the variables of interest is performed.     

The correspondence between Casimir pressure and energy in one-dimensional field models

We propose a method of calculation of Casimir pressure using the Green function for one-dimensional case. This method yields the renormalized pressure if an external field is absent, otherwise it permits us to calculate the dependence of pressure at one boundary on the other boundary’s coordinate. The calculated pressure permits one to obtain the Casimir energy for the systems under consideration.     

A new approach to nonrenormalizable models

Nonrenormalizable quantum field theories require counter-terms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counter-terms suggested by renormalized perturbation theory are in fact inappropriate for this purpose. Guided by the potential underlying causes of triviality of such models, as obtained by alternative analyses, we focus attention on the ground-state distribution function, and suggest a formulation of such distributions that exhibits nontriviality from the start. Primary discussion is focused on self-interacting scalar fields. Conditions for bounds on general correlation functions are derived, and there is some discussion of the issues involved with the continuum limit.     

Causal signal transmission by quantum fields. VI: The Lorentz condition and Maxwell’s equations for fluctuations of the electromagnetic field

The general structure of electromagnetic interactions in the so-called response representation of quantum electrodynamics (QED) is analysed. A formal solution to the general quantum problem of the electromagnetic field interacting with matter is found. Independently, a formal solution to the corresponding problem in classical stochastic electrodynamics (CSED) is constructed. CSED and QED differ only in the replacement of stochastic averages of c-number fields and currents by time-normal averages of the corresponding Heisenberg operators. All relations of QED connecting quantum field to quantum current lack Planck’s constant, and thus coincide with their counterparts in CSED. In Feynman’s terms, one encounters complete disentanglement of the potential and current operators in response picture.     

Casimir interactions in strained graphene systems

We theoretically study the strain effect on the Casimir interactions in graphene based systems. We found that the interactions between two strained graphene sheets are strongly dependent on the direction of stretching. The influence of the strain on the dispersion interactions is still strong in the presence of dielectric substrates but is relatively weak when the substrate is metallic. Our studies would suggest new ways to design next generation devices.

     

Zeno effect in quantum Newton's cradle

We describe a chain of quantum oscillators which behaves analogously to Newton's cradle. The energy swings between the ends of the chain with very low population in its interior. Moreover, the oscillators at the ends can entangle with each other with negligible entanglement with the intermediate oscillators that mediate the process. Up to a certain number of oscillators, the system evolves in a manner similar to two coupled oscillators. The conditions for such behavior and the characteristic periods are analyzed. When that number exceeds a threshold, the dynamical regime changes to virtually freezing. In the oscillatory regime, Zeno effect can be observed. The parallelism between the Zeno dynamics in quantum Newton's cradle and in two coupled oscillators is highlighted. Promising platforms to observe such phenomena in the laboratory are cavities in photonic-band-gap material and trapped ions.     

On the effective non-Hermitian eigenvalue problems for resonant levels

Summary A class of non-Hermitian eigenvalue equations, which are aimed to determine positions and widths of resonant (decaying) levels, is derived quite generally through a projection operator procedure whereby the effects of the continuum states responsible for the decay is represented in an effective manner. The boundary conditions appropriate to these eigenvalue problems are discussed and the wave function renormalization is evaluated. A connection is drawn with the effective eigenvalue problems occurring in the many-body Green's functions theory. Features like the energy dependence of the self-energy for the single-particle Green's function and of the screened Coulomb interaction for the electron-hole Green's function are accordingly interpreted in terms of elimination of continuum channels.

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Riassunto é noto da tempo, soprattutto dai lavori di Feshbach sul metodo delle hamiltoniane efficaci per reazioni nucleari, che tecniche di operatori di proiezione sono particolarmente adatte a costruire hamiltoniane efficaci allo scopo di determinare i parametri rilevanti delle risonanze nella teoria della diffusione. In questo articolo si pone in maggiore risalto l'aspetto quasi-legato degli stati risonanti e si considera un problema modello dove un insieme di stati discreti é accoppiato con un insieme di stati continui, i quali sono poi eliminati dalla trattazione esplicita mediante operatori di proiezione. In questo modo la sottomatrice dell'operatore risolvente nel sottospazio degli stati discreti risulta espressa in termini di un'hamiltoniana efficace che è non hermitiana e dipendente dall'energia. Tale procedimento è poi collegato con la risoluzione della equazione di Schr?dinger soggetta alle condizioni al contorno del tipo Kapur-Peierls che sono appropriate agli stati quasi stazionari. Questo collegamento fornisce, tra l'altro, una relazione tra la rinormalizzazione della funzione d'onda e la dipendenza dall'energia dell'hamiltoniana efficace. I risultati generali così ottenuti sono poi applicati alla teoria delle funzioni di Green a molti corpi. In particolare, si mostra come sia l'equazione di Dyson che determina i livelli a quasi particella sia l'equazione agli autovalori per gli eccitoni con schermaggio dielettrico possano essere interpretate nel senso delle hamiltoniane efficaci.

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Резюме В общем виде выводится класс незрмитовых уравнений для собственных значений, которые преднаэначемы для определения положений и ширин резонансных (распадающих) уровней, используя процедуру операторов проектирования. В таком подходе влияние непрерывных состояний, ответственных за распад, учитывается эффективным образом. Обсуждаются граничные условия, соответствующие этим проблемам собственных значений, и вычисляется перенормировка волновой функции. Отмечается связь с проблемами эффективных собственных значений, которые имеют место в теории многочастичных гриновских функций. Такие особенности, как энергетическая зависимость собственной энергии для одночастичной функции Грина и экранированное кулоновское взаимодействие для электрон-дырочной гриновской функции, интерпретируются соответственно на основе исключения непрерывных каналов.

     

The energy—momentum tensor, the trace identity and the Casimir effect

The trace identity associated with the scale transformation x^Μ → x′^Μ = e^-ρx^Μ on the Lagrangian density for the noninteracting electromagnetic field in the co-variant gauge is shown to be violated on a single plate on which the Dirichlet boundary conditionA ^Μ(t, x¹, x², x³ = -a) = 0 is imposed. It is however respected in free space, i.e. in the absence of the plate. These results reinforce our assertions in an earlier paper where the same exercise was carried out using the Lagrangian density for the free, massive, real scalar field in 2 + 1 dimensions.     

Quantum spring from the Casimir effect

The Casimir effect arises not only in the presence of material boundaries but also in space with nontrivial topology. In this Letter, we choose a topology of the flat (D+1)$(D+1)$-dimensional spacetime, which causes the helix boundary condition for a Hermitian massless scalar field. Especially, Casimir effect for a massless scalar field on the helix boundary condition is investigated in two and three dimensions by using the zeta function techniques. The Casimir force parallel to the axis of the helix behaves very much like the force on a spring that obeys the Hooke's law when the ratio r of the pitch to the circumference of the helix is small, but in this case, the force comes from a quantum effect, so we would like to call it quantum spring. When r is large, this force behaves like the Newton's law of universal gravitation in the leading order. On the other hand, the force perpendicular to the axis decreases monotonously with the increasing of the ratio r. Both forces are attractive and their behaviors are the same in two and three dimensions.     

On the cutoff law of laser induced high harmonic spectra

The currently well accepted cutoff law for laser induced high harmonic spectra predicts the cutoff energy as a linear combination of two interaction energies, the ponderomotive energy U_p and the atomic biding energy I_p, with coefficients 3.17 and 1.32, respectively. Even though, this law has been there for twenty years or so, the background information for these two constants, such as how they relate to fundamental physics and mathematics constants, is still unknown. This simple fact, keeps this cutoff law remaining as an empirical one. Based on the cutoff property of Bessel functions and the Einstein photoelectric law in the multiphoton case, we show these two coefficients are algebraic constants, 9 - 42≈ 3.34 and 22- 1 ≈ 1.83, respectively. A recent spectra calculation and an experimental measurement support the new cutoff law.     

One-loop-dimensional reduction of the linear σ model

We perform the dimensional reduction of the linear σ model at one-loop level. The effective potential of the reduced theory obtained from the integration over the nonzero Matsubara frequencies is exhibited. Thermal mass and coupling constant renormalization constants are given, as well as the thermal renormalization group equation which controls the dependence of the counterterms on the temperature. We also recover, for the reduced theory, the vacuum unstability of the model for large N.     

Spin-2 Quantum Gauge Theories and Perturbative Gauge Invariance

In the framework of causal perturbation theory we analyze the gauge structure of a massless self-interacting quantum tensor field. We look at this theory from a pure field theoretical point of view without assuming any geometrical aspect from general relativity. To first order in the perturbation expansion of the S-matrix we derive necessary and sufficient conditions for such a theory to be gauge invariant, by which we mean that the gauge variation of the self-coupling with respect to the gauge charge operator Q is a divergence in the sense of vector analysis. The most general trilinear self-coupling of the graviton field turns out to be the one derived from the Einstein–Hilbert action plus divergences and coboundaries.     

Entanglement and teleportation via a chaotic system

The dynamics of an entangled state interacting with a single cavity mode is investigated in the presence of a random parameter. We show that the degree of entanglement decays with time and that the rate of decay is defined by features of a random parameter. Quantum teleportation through a dissipative channel and teleportation fidelity as a function of damping rates have been studied. The sensitivity of the fidelity with respect to the random parameter is discussed. We have evaluated the time interval during which one can perform quantum teleportation and send the information with reasonable fidelity for given values of the correlation length of the random parameter.     

The Vacuum Electromagnetic Fields and the Schrödinger Equation

We consider the simple case of a nonrelativistic charged harmonic oscillator in one dimension, to investigate how to take into account the radiation reaction and vacuum fluctuation forces within the Schrödinger equation. The effects of both zero-point and thermal classical electromagnetic vacuum fields, characteristic of stochastic electrodynamics, are separately considered. Our study confirms that the zero-point electromagnetic fluctuations are dynamically related to the momentum operator p=?i ? ?/? x used in the Schrödinger equation.     

On Quantum Spacetime and the horizon problem

In the special case of a spherically symmetric solution of Einstein equations coupled to a scalar massless field, we examine the consequences on the exact solution imposed by a semiclassical treatment of gravitational interaction when the scalar field is quantized. In agreement with Doplicher et al. (1995)  [2], imposing the principle of gravitational stability against localization of events, we find that the region where an event is localized, or where initial conditions can be assigned, has a minimal extension, of the order of the Planck length. This conclusion, though limited to the case of spherical symmetry, is more general than that of  [2] since it does not require the use of the notion of energy through the Heisenberg Principle, nor of any approximation as the linearized Einstein equations.We shall then describe the influence of this minimal length scale in a cosmological model, namely a simple universe filled with radiation, which is effectively described by a conformally coupled scalar field in a conformal KMS state. Solving the backreaction, a power law inflation scenario appears close to the initial singularity. Furthermore, the initial singularity becomes light like and thus the standard horizon problem is avoided in this simple model. This indication goes in the same direction as those drawn at a heuristic level from a full use of the principle of gravitational stability against localization of events, which point to a background dependence of the effective Planck length, through which a-causal effects may be transmitted.