The aim of this study is to analyze attempts to observe the so called Dynamical Casimir effect in cavities, changing their optical lengths by means of fast time variations of material properties ...(dielectric permeability or conductivity) of thin slabs attached to the cavity walls. The emphasis is made on the case of semiconductor slabs excited by short laser pulses. Considering the evolution of the classical electromagnetic field in this case, an approximate analytical solution for an infinite set of coupled ordinary differential equations for the mode amplitudes is derived under certain simplifying assumptions. According to this solution, an amplification of the initial field can be made, provided the induced dielectric permeability can become negative with a large absolute value. Evaluations of the feasibility of such a scenario are given.
Analytical solutions to the problem of mode splitting caused by a thin plain magnetized slab placed in a rectangular electromagnetic cavity are found in two special cases: an infinite slab between ...two ideal infinite plain mirrors (1D model) and a 2D model of a cavity confined in the direction of permanent magnetization. Under the resonance conditions, the time-dependent magnetization vectors inside the slab are strongly enhanced, with opposite directions in the split modes. For realistic parameters, the frequency splitting does not depend on the dielectric constant of the slab and the Landau-Lifshitz-Gilbert damping coefficient, whereas the loaded cavity quality factor is not sensitive to the slab position.
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Here, we present a critical review of recent developments in Casimir physics motivated by discoveries of novel materials. Specifically, topologically nontrivial properties of the graphene family, ...Chern and topological insulators, and Weyl semimetals have diverse manifestations in the distance dependence, presence of fundamental constants, magnitude, and sign of the Casimir interaction. Limited studies of the role of nonlinear optical properties in the interaction are also reviewed. We show that, since many new materials have greatly enhanced the nonlinear optical response, new efficient pathways for investigation of the characteristic regimes of the Casimir force need to be explored, which are expected to lead to new discoveries. Recent progress in the dynamical Casimir effect is also reviewed and we argue that nonlinear media can open up new directions in this field as well.
In this paper, we numerically study the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying particular attention to their differences from the standard ...(Klauder–Glauber–Sudarshan) coherent states, especially in the case of the high mean values of the number operator. In this case, the CPS can possess a strong coordinate (or momentum) squeezing, which is roughly twice weaker than for the vacuum squeezed states. The Robertson–Schrödinger invariant uncertainty product in the CPS logarithmically increases with the mean value of the number operator (whereas it is constant for the standard coherent states). Some measures of the (non)Gaussianity of CPS are considered.
The complex (dpp-bian)
−
Ga(σ-allyl)Cl (
1
), which was prepared by the oxidative addition of two equivalents of allyl chloride to digallane (dpp-bian)
2−
Ga—Ga(dpp-bian)
2−
, reacts with one ...equivalent of sodium in tetrahydrofuran (THF) at 40 °C to afford the complex (dpp-bian)
2−
(THF)Ga
2
(µ
2
-1,3-C
3
H
6
) (
2
), in which two gallium atoms are connected by the bridging propane-1,3-diyl moiety. Under more harsh conditions (80 °C), this reaction gives asymmetric anionic digallane (dpp-bian)Ga—Ga(dpp-bian)(σ-C
9
H
13
)
−
(
3
) with the Na(Et
2
O)
3
(THF)
+
cation as the counterion. The σ-H
13
moiety in digallane
3
resulted from the cyclotrimerization of three allyl radicals. Compounds
2
and
3
were characterized by IR spectroscopy, multinuclear NMR spectroscopy, and elemental analysis. Their molecular structures were determined by single-crystal X-ray diffraction. Compounds
2
and
3
are unique because they contain the previously unknown metal fragments M—CH
2
CH
2
CH
2
—M and σ-C
9
H
13
—M, respectively. It is suggested that these complexes are produced
via
cascade β-elimination, carbo- and hydrogallation reactions.
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Abstract
The paper is based on the talk with the same name given at the International scientific conference on mechanics “The Ninth Polyakhov’s Reading” dedicated to the 200th anniversary of the ...birth of the prominent Russian scientist Pafnuty Lvovich Chebyshev. The generalized Chebyshev problem is formulated, in which the motion of a system in the presence of given generalized forces should satisfy an additional system of linear differential equations in which the order of each equation exceeds three. These problems constitute a new class of control problems in which the motion program is given in the form of the above additional system of differential equations. These equations can be considered as linear nonholonomic constraints of high order, whose reactions are the desired control forces. To solve such problems, two theories were developed at the Department of Theoretical and Applied Mechanics of St. Petersburg University. In the first theory, we construct a consistent system of differential equations for the generalized coordinates and the Lagrange multipliers, which are considered as equitable unknown functions of time. The second theory is based on the generalized Gauss principle. The application of the theory is illustrated by the solution of a real space mechanics problem about the motion of an Earth satellite after fixing the value of its acceleration at some point in time. Especially efficient is the application of the second theory to the determination of the optimal control force for transferring a mechanical system with a finite number of degrees of freedom from an existing phase state to a new specified state within a specified period of time. The new method is used to solve the model problem of controlled horizontal motion of a cart bearing the axes of several mathematical pendulums. It is shown that the use of the generalized Gauss principle for solving this problem is undoubtedly superior to that of the classical Pontryagin maximum principle.
This is a brief description of some recent achievements in the theory of dynamical Casimir effect, mainly in connection with the experiment which is under preparation in the University of Padua. The ...first part of this paper is devoted to the theory of quantum damped oscillator with arbitrary time dependence of the frequency and damping coefficient. New results for the mean number of created photons, its variance and photon distribution function are given. The second part is devoted to calculations of the time-dependent shift of resonance frequency of an electromagnetic cavity due to strong variations of dielectric properties in a thin layer near an ideally conducting wall. A simple analytical formula for this shift is derived. It generalizes the known Schwinger-Bethe-Casimir result. The influence of different parameters on the photon generation rate is discussed. A brief review of recent publications on the subject is also included.
It was predicted some time ago that the cavity dynamical Casimir effect (generation of photons from the initial vacuum state in a cavity with moving walls) might be observed if a boundary vibrates at ...the double frequency of some selected cavity mode. However, to register the created photons one has to couple the cavity mode with some detector. Considering the harmonic oscillator model of a detector, we analyze how different coupling regimes can affect the statistics of the created quanta.
We propose a scheme for the generation of photons from a vacuum via time-modulation of a quantum system indirectly coupled to the cavity field through some ancilla quantum subsystem. We consider the ...simplest case when the modulation is applied to an artificial two-level atom (we call 't-qubit', that can be located even outside the cavity), while the ancilla is a stationary qubit coupled via the dipole interaction both to the cavity and t-qubit. We find that tripartite entangled states with a small number of photons can be generated from the system ground state under resonant modulations, even when the t-qubit is far detuned from both the ancilla and the cavity, provided its bare and modulation frequencies are properly adjusted. We attest our approximate analytic results by numeric simulations and show that photon generation from vacuum persists in the presence of common dissipation mechanisms.
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