Amplitude-squared squeezing in superposed coherent states

We study amplitude-squared squeezing of the Hermitian operator Z_θ=Z₁ cosθ+Z₂ sin θ, in the most general superposition state , of two coherent states and . Here operators Z_1,2 are defined by , a is annihilation operator, θ is angle, and complex numbers C_1,2 , α, β are arbitrary and only restriction on these is the normalization condition of the state . We define the condition for a state to be amplitude-squared squeezed for the operator Z_θ if squeezing parameter , where N=a⁺a and . We find maximum amplitude-squared squeezing of Z_θ in the superposed coherent state with minimum value 0.3268 of the parameter S for an infinite combinations with α- β= 2.16 exp [±i(π/4) + iθ/2], and with arbitrary values of (α+β) and θ. For this minimum value of squeezing parameter S, the expectation value of photon number can vary from the minimum value 1.0481 to infinity. Variations of the parameter S with different variables at maximum amplitude-squared squeezing are also discussed.     

Algebraic structure of nonassociative spinor field

An analysis of the algebra of octonions, the algebraic structure of nonassociative spinors, is presented, and a spinor field theory that is completely identical to Dirac theory is constructed in an associative basis. A spinor covariance transformation is introduced, and it is shown that it coincides with the Poincaré group of 4-dimensional space. The field equation is introduced through a spinor invariance transformation. Constraints imposed by the field equation on the eigenvalues of the transformation generators are considered. It is proved that the particles in a system at rest which are nonzero are , the unit; , the energysign of the particle; and s ₆, one of the spin components of the particle. Tbilisi University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 59–65, November, 1998.     

Renormalization of nonperturbative functional integral for independent value models

It is shown that one can consider the perturbatively nonrenormalizable independent value P () models as renormalizable in nonperturbative theory. Their generating functionals are explicitly calculated by lattice limit.     

Nonperturbative Green's function approach to quantum field theory and arbitrariness of solutions

Green's function equations are considered for interacting spinor and (pseudo) scalar fields with interactions . These equations do not determine higher many-point functions if two-point functions are given as “input.” If vertex parts are given as input, two-point functions are determined but higher many-point functions are not determined.     

Violation of chiral symmetry in curved spacetime with a magnetic field

The phase structure of a four-fermion (4F) model in curved spacetime with a magnetic field is investigated (in the framework of a 1/N expansion and an approximation linear in the curvature). The effective potential for the combined fields is calculated for the following situations: a) nonzero curvature and b) nonzero curvature and nonzero magnetic field. It is shown that the gravitational field may offset the magnetic-field effect, with restoration of chiral symmetry as the result. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 43–47, July, 1997.     

Yet another formulation of the Dirac equation

The 2-by-2 Pauli matrix algebra is used to write the 1-by-4 Dirac field in anequivalent 2-by-2 matrix . The current 4-vectors and *_µ are then compared and the latter is shown to not be easily interpretable as a probability density, and also tocontain .     

Regularity of weak solutions to a two-dimensional modified Dirac-Klein-Gordon system of equations

We show that solutions to the modified Dirac-Klein-Gordon system in standard notation

Remarks on the uncertainty relation in scattering theory

It is shown that in scattering theory, the Heisenberg relation has the form for a wide class of potentials.H is the Hamiltonian of scattered particles, is a scattering state, and _± are wave operators. We discuss the interpretation of the obtained inequality and its entropic formulation.     

A model field theory in which two Nambu-Goldstone symmetries are realised by one massless pseudoscalar boson

We consider a model field theory consisting of two Nambu-Jona-Lasinio spin 1/2 fields interacting via a coupling \(f(\bar \psi _1 \gamma ^\mu \gamma ^5 \psi _1 )(\bar \psi _2 \gamma _\mu \gamma ^5 \psi _2 )\) and which is therefore invariant under the two symmetries \(\psi _1 (x) \to e^{i\alpha _1 } \gamma ^5 \psi _1 (x)\) and \(\psi _2 (x) \to e^{i\alpha _2 } \gamma ^5 \psi _2 (x)\) . We look for solutions in which these symmetries are spontaneously broken by giving the fermions non-zero masses. Each of the two pairs of axial-vector vertex functions in the theory satisfy two coupled integral equations, which are solved in the ‘chain approximation’. We find that all four vertex functions have the same singularity structure, in particular a pole atq ²=0 corresponding to a massless pseudoscalar Nambu-Goldstone boson, and another pole corresponding to an axial-vector boson whose mass is cut-off dependent, but which for a certain range of values off ² is a stable particle. By considering the coupling of the strings of nucleon-antinucleon psuedoscalar ‘bubbles’ which generate the massless Nambu-Goldstone bosons associated with fermions 1 and 2, we show explicitly that there is only one massless Nambu-Goldstone boson in the theory.     

Superconducting states of the cylinder with a single vortex in magnetic field according to the Ginzburg-Landau theory

Self-consistent solutions of the nonlinear Ginzburg-Landau (GL) equations are investigated numerically for a superconducting (SC) cylinder, placed in an axial magnetic field, with a single vortex on the axis (m=1). Two modes, which show the original state of the cylinder, SC or normal (s ₀ andn ₀), are studied. The field increase (FI) and the field decrease (FD) regimes are studied. The critical fields destroying the SC state withm=1 are found in both regimes. It is shown that in a cylinder of radiusR and GL-parameter ϰ, there exist a number of solutions depending only on the radial co-ordinater corresponding to different states such as M,e, d, p,i, n, ,n ^*, and the state diagram on the plane of the variables (ϰ,R) is described. The critical fields corresponding to intrastate transitions and the onset of hysteresis are obtained. The critical fieldH ₀(R) dividing the paramagnetic and diamagnetic states of the cylinder withm=1 is determined. The limiting fields of supercooling or superheating of the normal state at which the restoration of the SC state occurs are established. It is shown, that (in both casesm=1,0) there exist two critical parameters, and , which divide bulk SC into three groups (with and ), in accordance with the behavior in a magnetic field. The parameters and mark the boundary for the existence of a supercooled normal -state in FD-regime and a superheated SC M-state in FI-regime respectively. It is shown, that the value , which was claimed in a number of papers as related to type-I superconductors, is illusory. We regret to inform that Professor Gely Zharkov passed away on 9th July 2004.     

Positive Lyapunov exponents for a class of ergodic Schrödinger operators

We present a simple method to estimate the Lyapunov exponent (E) for the system

Asymptotic behavior of solutions to certain nonlinear Schrödinger-Hartree equations

The asymptotic behavior of solutions to the Cauchy problem for the equation $$i\psi _\imath = \frac{1}{2}\Delta \psi - \upsilon (\psi )\psi , \upsilon = r^{ - 1} *|\psi |^2 ,$$ and for systems of similar form, is studied. It is shown that the norms $$\parallel \psi (t)\parallel _{L_2 (|x| \leqq R)}^2 + \parallel \nabla \psi (t)\parallel _{L_2 (|x| \leqq R)}^2 $$ are integrable in time for any fixedR>0, from which it follows that $$\mathop {\lim }\limits_{t \to \infty } \parallel \psi (t)\parallel _{L_2 (|x| \leqq R)} = 0.$$ \] Nevertheless, it is established that anL ₂-scattering theory is impossible.     

Absolute Continuity of the Spectrum of Coupled Identical Systems on 1D Lattices

We prove that the spectrum of the discrete Schrödinger operator on ?²(?²)

$$\begin{array}{@{}rcl@{}} (\psi _{n,m})\mapsto -(\psi _{n + 1,m} +\psi _{n-1,m} + \psi _{n,m + 1} +\psi _{n,m-1})+V_{n}\psi _{n,m} \ , \\ \quad (n, m) \in \mathbb {Z}^{2},\ \left \{ V_{n}\right \}\in \ell ^{\infty }(\mathbb {Z}) \end{array} $$

(1)

is absolutely continuous.

     

Boson Stars as Solitary Waves

We study the nonlinear equation

Green's functions of spinor field in conformally plane space—time

A complete set of solutions of the Dirac equation is found in space-time with the metric ds² = ²(d ²- dx²- dy²- dz²). For the Green's functions in$$ " align="middle" border="0"> and in$$ " align="middle" border="0"> , representations are found in the form of contour integrals from the Schwinger-De Witt nucleus over various contours.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 35–40, April, 1985.It remains to thank Yu. Yu. Vol'fengaut for discussions in the course of the present work.     

\left\langle {:\bar \psi \psi :} \right\rangle and three-point functions in QCD

We calculate the coefficients of to leading order in _s in the operator product expansion of the fundamental three-point functions of QCD in the deep Euclidean region. We demonstrate that these coefficients satisfy the Ward identities.Supported by BMFT 0233 REB4     

Parity anomaly in a \mathcal{P}\mathcal{T}-symmetric quartic Hamiltonian

In this paper, two independent methods are used to show that the non-Hermitian -symmetric wrong-sign quartic Hamiltonian H = (1/2m)p ² − gx ⁴ is exactly equivalent to the conventional Hermitian Hamiltonian . First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated by using functional-integration methods. As the linear term in the Hermitian Hamiltonian is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly is a consequence of the broken parity symmetry of the original non-Hermitian -symmetric Hamiltonian. The anomaly term in remains unchanged if an x ² term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states.     

Dirac Equation in an Axial Coulomb Potential

We consider solutions to the Dirac equation in the presence of an external axial vector potential coupled to the spinor field psi through the interaction term . There turn out to be no bound-state energies in this system consistent with a normalizable wave function.     

Modular construction of special mixed quantum states

For a homogeneous quantum network of N subsystems with n levels each we consider separable generalized Werner states. A generalized Werner state is defined as a mixture of the totally mixed state and an arbitrary pure state : with a mixture coefficient . For this density operator to be separable, will have an upper bound . Below this bound one should alternatively be able to reproduce by a mixture of entirely separable input-states. For this purpose we introduce a set of modules, each contributing elementary coherence properties with respect to a generalized coherence vector. Based on these there exists a general step-by-step mixing process for any . For being a cat-state it is possible to define an optimal process, which produces states right up to the separability boundary ( ).Received: 3 December 2002, Published online: 29 July 2003PACS: 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bells inequalities, GHZ states, etc.) - 03.67.-a Quantum information - 03.65.-w Quantum mechanics