Nonsecular expansion for the evolution operator in nonrelativistic quantum electrodynamics

A solution is obtained for the evolution operator which describes a resonance interaction of a multilevel system with quantized electromagnetic field. Its Taylor expansion in the interaction parameter contains no secular terms. As an example, the interaction of a two-level system with one-mode field is considered (with one-and two-photon resonance).     

Method of semiclassical representation in quantum electrodynamics

The operators of the classical amplitudes of an electromagnetic field are introduced and a method of transferring from quantum electrodynamics to the semiclassical approximation both in the case of a free field and in the case of the interaction of the field with a quantum system is given. The method considered enables one to set up solutions of quantum electrodynamics in the case of an intense field from the solutions of the semiclassical problem. An operator method of obtaining solutions of the equations of semiclassical electrodynamics is considered. The physical meaning of the quantum corrections to the semiclassical electrodynamics of an intense field is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 77–98, February, 1980.     

Parametric instability and Hamiltonian chaos in cavity semiclassical electrodynamics

We study the nonlinear dynamics of the interaction of two-level atoms and a selected mode of a high-Q cavity with frequency modulation analytically and numerically. In the absence of modulation, the corresponding semiclassical Heisenberg equations for the expectation values of the collective atomic observables and the field-mode amplitudes allow, in the rotating wave approximation and in the strong-coupling limit, an exact solution with arbitrary detuning. Using this solution, we detect the coherent effect of trapping of the population of atomic levels and of trapping of the number of photons in the cavity. The explanation for this effect lies in the destructive interference of the atomic dipoles and the field mode. The integrable version of the system of equations exhibits a separatrix near which a stochastic layer is formed when modulation is introduced. The width of the layer is found to gradually increase with degree of modulation, and finally it fills the entire energy-permissible volume of the phase space. We show that the rotating wave approximation does not hinder the formation of Hamiltonian chaos in cavity semiclassical electrodynamics. The calculation of the maximum Lyapunov indices of nonlinear (in this approximation) equations of motion as functions of the modulation frequency δ and the frequency of natural Rabi oscillations of the atom-field system, Ω, suggests that Hamiltonian chaos appears first in the area of the fundamental parametric resonance, δ/2Ω≃1. Parametric instability increases with increasing modulation and decreasing detuning from the atom-field resonance, generating at exact resonance new areas of chaos corresponding to multiple parametric resonances. The results of numerical experiments and estimates of the characteristic parameters show that Rydberg atoms placed in a high-Q microwave cavity are possible objects for observing parametric instability and dynamical chaos. Zh. éksp. Teor. Fiz. 115, 740–753 (February 1999)     

A remark concerning the charge operator in quantum electrodynamics

The convergence of the integral over the local charge density toward the global charge is investigated within the framework of quantum electrodynamics.     

Evolution operator and quark structure of states in two-dimensional massless electrodynamics

In the two-dimensional electrodynamics of massless fermions (quarks) the time evolution operator is constructed. Its diagonalization permits one to find the physical states of the model in the terms of quarks. The existence of charge and chiral states is discussed. It is shown that such states can be found only with vanishing momentum, i.e., as vacuum states. The quark structure of physical particles is obtained in the infinite momentum frame.     

Markovian evolution of Gaussian states in the semiclassical limit

We derive an approximate Gaussian solution of the Lindblad equation in the semiclassical limit, given a general Hamiltonian and linear coupling with the environment. The theory is carried out in the chord representation and describes the evolved quantum characteristic function, which gives direct access to the Wigner function and the position representation of the density operator by Fourier transforms. The propagation is based on a system of non-linear equations taking place in a double phase space, which coincides with Heller's theory of unitary evolution of Gaussian wave packets when the Lindbladian part is zero. The example of a double well is worked out.     

Time operator and quantum projection evolution

In this paper, we consider time as a dynamical variable. In particular, we present the explicit realization of the time operator within four-dimensional nonrelativistic spacetime. The approach assumes including events as a part of the evolution. The evolution is not driven by the physical time, but it is based on the causally related physical events. The usual Schrödinger unitary evolution can be easily derived as a special case of the three-dimensional projection onto the space of simultaneous events. Also the time—energy uncertainty relation makes clear and mathematically rigorous interpretation.     

An approach to introducing fractional integro-differentiation in classical electrodynamics

Analogs for Maxwell’s equations with fractional derivatives are obtained using the concepts of an effective current and the velocity of a charged particle in a medium. The calibration invariance is considered and a diffusion-wave equation is found and analyzed for scalar and vector potentials. It is shown that the stochastic nature of charged particle motion in a medium influences the dynamics of an electromagnetic field.     

Renormalization group evolution of the non-unitary operator

Integrating out a heavy field gives rise to effective Lagrangian containing higher-dimensional operators. In the context of Type-I seesaw mechanism, integrating out the heavy right-handed neutrino field leads to unique dimension-five operator which gives the tree level neutrino mass term. Apart from these there are dimension-six operators that can have important implications. A linear combination of two such operators gives rise to the non-unitarity in the lepton mixing matrix, _UPMNS$U_{\mathrm{PMNS}}$. In this paper, we discuss the origin of non-unitarity at the high scale and its evolution through renormalization group running.     

量子扩散通道中Wigner算符的演化规律

众所周知,量子态的演化可用与其相应的Wigner函数演化来代替.因为量子态的Wigner函数和量子态的密度矩阵一样,都包含了概率分布和相位等信息,因此对量子态的Wigner函数进行研究,可以更加快速有效地获取量子态在演化过程的重要信息.本文从经典扩散方程出发,利用密度算符的P表示,导出了量子态密度算符的扩散方程.进一步通过引入量子算符的Weyl编序记号,给出了其对应的Weyl量子化方案.另外,借助于密度算符的另一相空间表示-Wigner函数,建立了Wigner算符在扩散通道中演化方程,并给出了其Wigner算符解的形式.本文推导出了Wigner算符在量子扩散通道中的演化规律,即演化过程中任意时刻Wigner算符的形式.在此结论的基础上,讨论了相干态经过量子扩散通道的演化情况.     

An exact relation for the Gell-Mann-Low function in supersymmetric electrodynamics

We get an exact relation for the β-function in SQED.     

On an evolution operator connecting Lagrangian and Hamiltonian formalisms

The unambiguous evolution operator K was recently introduced in the theory of constrained systems. By viewing K as a vector field over the Legendre transformation, we give an intrinsic characterization of it through simple and intuitive properties. Some immediate consequences are explored.     

Exact solutions to Landau-Zener problems by evolution operator method

Various analytic approaches have been developed to solve the famous Landau-Zener (LZ) problem. Here, we introduce a time-evolution operator method to investigate such a problem by numerically solving the induced algebraic equations (by Runge-Kutta method). Based on these calculations, transitions between two levels driven by various time-dependent external fields can be simulated in detail, typically near the so-called avoided crossing points. Far from these points, our results reduce to the original Landau-Zener transition (LZT).     

p-Form electrodynamics

A generalization of gauge theory in which the gauge potential1-form is replaced by a p-form is studied. Charged particles are then replaced by elementary extended objects of dimension p–1. It is shown that this extension is compatible with space-time locality only if the gauge group is U(1). A source which is a closed p–1 surface has zero total charge and corresponds to a particle-antiparticle pair. Its quantum rate of production in an external uniform field is evaluated semiclassically. The analog of the Dirac magnetic pole is constructed. It is another extended object, of dimension n–p–3, where n is the dimension of space-time. The electric and magnetic charges obey the Dirac quantization condition. This condition is derived in two different ways. One method makes use of local gauge patches and the other brings in singular gauge transformations. A topological mass term is introduced and it is shown that it can coexist with a magnetic pole when n=2p+1, provided the topological mass is quantized.