On the possibility of quantization of the conductance in the microwave-induced resistive state of layered superconductors

It was observed that a microwave field induces constant differential resistance steps, close in magnitude to the reciprocal of the conductance quantum h/2e ², in the current-voltage characteristics (IVCs) of layered structures with an intrinsic Josephson effect under conditions of transport in a direction perpendicular to the layers. A qualitative explanation of this result is proposed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 68–71 (10 January 1998)     

关于有源RLC电路的量子化

提出一种将有源ＲＬＣ电路量子化的方法,修正了有关文献中的错误。     

On a dynamical quantization

A concept of a noncanonical quantization, called dynamical quantization, is defined in an axiomatic way. A dynamical quantization of a system of two nonrelativistic point particles interacting via a harmonic potential is considered in more details. The quantized system exhibits some new features. In particular, it has finite space dimensions. The distance between the particles is preserved in time and can have at most four different values. The position of any one of them cannot be localized, since the operators of the coordinates do not commute. The particles are smeared with a certain probability within a finite volume, which moves together with their centre of mass. The orbital momentum of the composite system is either one or zero.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

有限空间中Dirac场的正则量子化

研究当存在边界的情形下 Dirac场的正则量子化问题. 采用文献[1]的观点, 将边界条件当作Dirac初级约束.与已有研究不同的是, 本文从离散的角度研究此问题. 将Dirac场的拉氏量和内在约束进行离散化, 并且将离散的边界条件当作初级Dirac约束. 因此, 从约束的起源来看, 这个模型中存在两种不同的约束: 一种是由于模型的奇异性而带来的约束, 即内在约束; 另一种是边界条件. 在对此模型进行正则量子化过程中提出一种能够平等地处理内在约束和边界条件的方法. 为了证明该方法能够平等地对待这两种起源不同的约束, 在计算Dirac 括号时分别选取了两个不同的子集合来构造"中间Dirac括号", 最后得到了相同的结果. 关键词： 边界条件 Dirac约束 Dirac括号     

On the possibility of a thermal spectrum of particles produced by an electric field

The exponentially damped electric field is shown to produce particles with a thermal spectrum from vacuum if the residual action of the field on the particles produced may be neglected.     

On the possibility of an analytic solution of the three-body problem

Three-body Faddeev equations in the Noyes-Fiedeldey form are rewritten as a matrix analog of a one-dimensional nonrelativistic Schrödinger equation. Unlike the method of K-harmonics, where a similar equation was obtained by expansion of a three-body Schrödinger equation wavefunction into the orthogonal set of functions of two variables (K-harmonics), the use of the Noyes-Fiedeldey form of Faddeev equations allows us to limit ourselves to the expansion in functions of one variable only. The solutions of the above mentioned matrix equation are obtained. These solutions converge uniformly within every interval of continuity of the matrix, which corresponds to the potential of that equation. Their asymptotic behavior for large interparticle distances is discussed. The solutions for the harmonic oscillator, inverse-square, and Coulomb-Kepler potentials are found. It is shown that energy levels in the last case may be calculated from a simple formula which is very similar to the corresponding formula for the two-body Coulomb-Kepler problem. This formula can be easily generalized to the case of n particles interacting with inverse distance potentials.     

On the possibility of a three-temporal Lorentz transformation

It is suggested that, strictly speaking, light speed invariance would not seem to be fully consistent with ordinary space geometry unless proper time is allowed to undergo one independent dilatation for each degree of space freedom.     

On the possibility of a two-bang supernova collapse

Summary The possibility of a two-bang stellar collapse originating SN 1987a, and having the characteristics of the events recorded in Mont Blanc and Kamiokande, is discussed here. According to the ?standard? collapse models of nonrotating stars, which predict the formation of a neutrinosphere with a nondegenerate neutrino gas inside the star, the Mont Blanc and Kamiokande data for the first burst give a too large stellar mass. On the contrary, a degenerate neutrino gas with low temperatureT≈0.5 MeV, and chemical potential μ≈(12÷15), predicts a relatively low total energy outflowW _ν≈(2÷6)·10⁵⁴ erg, and a small number of expected interactions in Kamiokande. A possible scenario is suggested: a massive (M≈20M _⊙) rotating star is fragmented into two pieces, one light and the other heavy, at the onset of the collapse. The massive component collapses to a black hole, and produces the first burst. Neutrinos are trapped inside the collapsing star because of elastic scattering in the outer core off heavy nuclei, withA≳300. It is shown that neutrinos fill up the quantum states, producing a degenerate neutrino gas. The second burst is explained by coalescence of the light fragment (M≈(1÷3)M _⊙) onto the massive black hole. The time delay between the two observed bursts (4.7 h) is mostly connected with gravitational braking, when the light fragment falls down onto the black hole, with an accompanying emission of gravitational waves for times of order of hours.

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Riassunto Si discute la possibilità che la supernova 1987a abbia avuto origine da un collasso a due stadi, avente le caratteristiche degli eventi registrati nell'Osservatorio Neutrinico del Monte Bianco e nell'esperimento di Kamioka. Secondo i modelli ?standard? di collasso di stelle senza rotazione, che prevedono la formazione di una neutrinosfera con un gas non degenere di neutrini al suo interno, i dati del Monte Bianco e di Kamioka per il primo burst comportano un valore troppo alto della massa stellare. Al contrario, un gas degenere di neutrini a bassa temperatureT∼0.5 MeV e con potenziale chimico μ∼(12÷15) comporta un'emissione totale in neutrini relativamente bassaW _ν∼(2÷6)·10⁵⁴ erg ed un piccolo numero di interazioni in Kamiokande. Si suggerisce un possibile scenario: una stella massiva (M∼20M _⊙) in rotazione si frammenta in due oggetti, uno leggero e l'altro pesante, all'inizio del collasso. L'oggetto massivo collassa in un buco nero e produce il primo burst. I neutrini vengono intrappolati entro la stella collassante a causa dello scattering elastico nel core esterno dovuto a nuclei pesanti, conA≳300. Si mostra che i neutrini riempiono gli stati quantici, producendo un gas degenere di neutrini. Il secondo burst è spiegato dalla caduta del frammento leggeroM∼(1÷3)M _⊙ sul black hole massivo.

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Резюме В работе обсуждается возможность коллапса сверхновой SN 1987a, характеризующегося двумя взрывами и имеющего особенности, зарегистрированные на Мон Блане и в Камиоканде. Согласно ?стандартным? моделям коллапса невращающихся звезд, которые предсказывают образование нейтринной сферы с невырожденными нейтринным газом внутри звезды, данные на Мон Блане и в Камиоканде для первой вспышки дают слишком большую массу звезды. Напротив, вырожденный нейтринный газ с низкой температуройT≈0.5 МэВ и химическим потенциалом μ≈12÷15 предсказывает выход относительно малой полной энергииW _ν≈(2÷6)·10⁵⁴ эрг и малое число ожидаемых взаимодействий в Камиоканде. Предлагается возможный сценарий: массивная (M≈20M _⊙) врашаюшаяся звезда разделяется на две части, одна легкая и другая тяжелая, в начале коллапса. Массивная компонента коллапсирует в черную дыру и производит первую вспышку. Нейтрино захватывются внутри коллапсируыщей звезэы вследствие упругого рассеяния во внешней оболочке на тяжелых ядрах сA≥300. Показывается, что нейтрино заполняют квантовые состояния, обраяуя вырожденный нейтринный газ. Вторая вспышка объясняется коалесцией легкого фрагмента (M∼(1÷3)M _⊙) с массивной черной дырой. Время запаздывания между двумя наблюденными вспышками (4.7 часа) в основном связывается с гравитационным торможением, колэа легкий фрагмент падает на черную дыру, что сопровождается излучением гравитационных вплн в течение времени, порядка несколъких часов.

     

Discreteness of the volume of space from Bohr-Sommerfeld quantization

A major challenge for any theory of quantum gravity is to quantize general relativity while retaining some part of its geometrical character. We present new evidence for the idea that this can be achieved by directly quantizing space itself. We compute the Bohr-Sommerfeld volume spectrum of a tetrahedron and show that it reproduces the quantization of a grain of space found in loop gravity.     

On the quantization of gravity

We analyse the construction of quantum states for the case of gravity and matter using the solution of the 2-submanifold boundary value problem and “sum over paths” quantisation. This leads to a specification of such states in terms of a complete commuting set of operators. The “sum over topologies” definition is obtained only by a very ad hoc assumption which is made precise. The problem of the arbitrariness of the background metric discussed and resolved by analogy with QED.     

Third quantization: The problem of the cosmic vacuum,spontaneous symmetry breaking,and the possibility of an eternal universe

The existence of a fundamental length in general relativity, the Planck length, may lead to a breakdown of Lorentz invariance of the vacuum. The third quantization introduces renormalization fields of negative energy which do not interact with matter however. This revision leads to a measurable modification of the Casimir effect and can, at least in principle, lead to an eternal universe.What is science is not certain; what is certain is not science.     

On the possibility of a smectic-A phase in paraffins

It is proposed that for paraffins (CH₂)_N and N not too large melting may not lead immediately to an isotropic fluid but first to a layered liquid state with smectic-A properties.     

有限空间中经典场的正则量子化

从离散的角度研究带边界的1+1维经典标量场和Dirac场的正则量子化问题. 与以往不同的是, 这里将时间和空间两个变量同时进行变步长的离散, 应用变步长离散的变分原理, 得到离散形式的运动方程、边界条件和能量守恒的表达式. 然后, 根据Dirac理论, 将边界条件当作初级约束, 将边界条件和内在约束统一处理. 研究表明, 采用此方法, 不仅在每个离散的时空格点上能够建立起Dirac括号, 从而可以完成该模型的正则量子化;而且, 该方法还保持了离散情况下的能量守恒.     

Realization of the Schwinger term in the Gauss law and the possibility of correct quantization of a theory with anomalies

The explicit regularization of the Weyl fermion current leading to the anomalous commutation relation of the Gauss law constraint is established. This requires the modification of the canonical quantization of the corresponding gauge model. The modified form of functional integral quantization for this model is proposed.     

On the quantization of membrane theories

In connection with the quantization of membrane theories, a three-dimensional analogue of the conformal gauge is formulated on the basis of a non-linear gauge condition. The resulting action consists of polynomials in the membrane variables and Faddeev-Popov ghosts up to quartic terms, and it preserved the BRS symmetry. Some of the applications of this formulation are briefly discussed.     

On the quantization of anomalous theories

The possible definition of the Gauss' law operator in an anomalous gauge theory is discussed. It is shown that the most natural choice does not lead to any anomaly in the commutation rules. The case of two-dimensional theories is considered.     

On the quantization of supersymmetric particle

The modified action of Siegel for a point superparticle is quantized by using the BRS transformation. We also present another action for a superparticle. We discuss the second-quantization of a superparticle and then point out some difficulties in the covariant second quantization of superstring.     

On the quantization of dissipative systems

A recent paper of Dekker on the quantization of dissipative systems is examined in some detail. It is argued that one can construct a large number of classical equivalent Hamiltonians for damped systems. These can be formally quantized according to Dirac's method, and the resulting equations are mathematically consistent, but yield different eigenfunctions for the same classical system. However, this procedure should be rejected on physical grounds. That is in quantum mechanics, unlike classical dynamics, the definition of the time derivative of a dynamical variable is unique, and is given by the commutator of the proper Hamiltonian (or the energy operator) and that variable. If the proper Hamiltonian is used for the quantization of a damped system, then the quantal equations are inconsistent for the cases where the rate of energy dissipation depends on the velocity of the particle. As an alternative approach to the quantal theory of dissipative phenomena, a generalization of the Hamilton-Jacobi formalism is considered, where the equation for the principle functionS, depends not only on the space and time derivatives ofS, but onS itself. This leads to a new class of damped systems in classical mechanics. The original Schrödinger method of quantization via the Hamilton-Jacobi equation has been applied to this class of dissipative systems, with the result that the wave equation in this case is a solution of a non-linear Schrödinger-Langevin equation. This formulation has no analogue in the Hamiltonian approach, since in the latter, the resulting wave equation is always linear.Supported in part by a grant from the National Research Council of Canada.