Bifurcation modes in a nonlinear optical system with distributed field rotation

We consider a model of a nonlinear optical system with distributed field rotation described by a functional-differential diffusion equation. An existence theorem is proved for periodical spatially nonhomogeneous traveling-wave solutions, which are generated from a spatially homogeneous stationary solution by an Andronov-Hopf (cycle-generating) bifurcation. A series expansion of the solution in powers of a small parameter is obtained and a stability condition is given. Simulation results are used to discuss the properties of the model. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 89–99.     

Essentially nonlinear interaction Lagrangians and nonlocalized quantum field theory

Conclusions We have proposed a variant for the construction of a finite and unitary S-matrix through perturbation theory for almost any nonlinear interaction Lagrangian of scalar particles. We introduce into the conclusion, a scheme for constructing the S-matrix (see Fig. 2), in which once again we draw attention to the principal instants where supplementary postulates and assumptions are made, which it was essential to include for construction of the S-matrix of the theory.Joint Institute for Nuclear Research. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 2, No. 1, pp. 36–54, January, 1970.     

Atom-photon interactions with respect to quantum computation: A three-level atom in a two-mode field

In this paper, analysis of a quantum optical system—three-level atom in a quantum electromagnetic field is given. Evolution operators are constructed in closed form. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 44, Quantum Computing, 2007.     

Pair-interaction approximation in the equations of quantum field theory for a four-body system

It is shown that for the correct formulation of the pair-interaction approximation in the dynamical equations for a system of four and more particles in the various approaches of quantum field theory not only the sum of the pair-interaction potentials but also additional, two-pair kernels must be taken into account. Equations of two types with compact kernels that take into account these terms are obtained. The kernels of these equations are expressed in terms of the two-annd three-particle scattering amplitudes. The equations of the first type have a structure identical to their nonrelativistic analog, whereas the equations of the second type differ from the nonrelativistic equations even in the number of components. An advantage of these equations is that they can be generalized to the case of arbitrarily many particles.A. M. Razmadze Mathematics Institute, Georgian SSR Academy of Sciences, Tbilisi. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 95–112, January, 1992.     

One-Time Pad as a nonlinear dynamical system

The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, DNA cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, AES are not even proven to be computationally secure). In this work, we prove that the OTP encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the GLS that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that OTP encryption is related to Randomized Arithmetic Coding – a scheme for joint compression and encryption.     

Nonlocal quantum field theory,nonlinear interaction lagrangians,and the convergence of the perturbation-theory series

Conclusions Thus, for a definite class of significantly nonlinear interaction Lagrangians, we were able to construct, within the framework of nonlocal quantum field theory, the S-matrix of the theory in the form of a convergent perturbation-theory series in the Euclidean formulation of the theory. It was shown earlier that after a continuation into the physical domain, the S-matrix will be unitary in every order of perturbation theory. The next problem is the study of the behavior of the amplitudes of physical processes within the framework of the complete converging series which represents the total S-matrix of the theory.Joint Institute for Nuclear Research. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 2, No. 3, pp. 302–310, March, 1970.     

Some quantum optical states as realizations of Lie groups

We start with the Heisenberg–Weyl algebra and after the definitions of the Fock states we give the definition of the coherent state of this group. This is followed by the exposition of the SU(2) and SU(1, 1) algebras and their coherent states. From there we go on describing the binomial state and its extensions as realizations of the SU(2) group. This is followed by considering the negative binomial states, and some squeezed states as realizations of the SU(1, 1) group. Generation schemes based on physical systems are mentioned for some of these states.     

Matter-wave chaos with a cold atom in a standing-wave laser field

Coherent motion of cold atoms in a standing-wave field is interpreted as a propagation in two optical potentials. It is shown that the wave-packet dynamics can be either regular or chaotic with transitions between these potentials after passing field nodes. Manifestations of de Broglie-wave chaos are found in the behavior of the momentum and position probabilities and the Wigner function. The probability of those transitions depends on the ratio of the squared detuning to the Doppler shift and is large in that range of the parameters where the classical motion is shown to be chaotic.     

Relaxation of a quantum particle in a magnetic field

Theoretical and Mathematical Physics -