Analytic solution of the general anharmonic-oscillator problem

The regular and irregular solution of the differential three-dimensional Schrödinger equation with the confining potential , is presented. In full analogy with the recentq=1 conjecture of Singhet al. [1], the corresponding Green's function is constructed in terms of the extended continued fraction. For the simplest example withV(r)=r ²+² r ⁴, its convergence is proved and the resulting energy spectrum is numerically tested.     

Single fermion Green's function in the quantum ordered Fermi-system: Analytic solution

An exact self-consistent solution for a finite temperature quantum-ordered state of correlated electron system found previously (8 and 1) is used to derive the fermionic single-particle Green's function. The quantum order parameter (QOP) found in the form of a periodic (elliptic Jacoby) function of the Matsubara's imaginary time (Mukhin, 2009), plays the role of effective scattering potential seen by electrons. The analytic solution for the Green's function demonstrates the following new features: (1) the pseudo-gap behavior of the single-electron density of states (DOS) near the (shifted) Fermi-level;(2) the side-bands of decreasing intensity away from the Fermi-level; (3) scaling of the quasi-particle energies with the QOP amplitude; (4) fermionic quasi-particles in the QOP state are combined from two confined “odd” and “even” fermions that separately would be unstable. The false-color plot of single-fermion DOS in the limit of a periodic kink-like Matsubara time-dependence of QOP is presented and could be used as prediction for the ARPES experiments. The plot of the DOS transfer between different energies at the “fermi-surface” momentum for a given kink-like QOP is also presented. Some possibly observable consequences of the found finger-prints are discussed.     

The algebra of the quantum nondegenerate three-dimensional Kepler-Coulomb potential

The classical generalized Kepler-Coulomb potential, introduced by Verrier and Evans, corresponds to a quantum superintegrable system, with quadratic and quartic integrals of motion. In this paper we show that the algebra of the integrals is a quadratic ternary algebra, i.e a quadratic extension of a Lie triple system.     

Quantum logical solution to the measurement problem of quantum mechanics

In this paper I propose a reformulation and solution of the measurement problem of quantum mechanics. The reformulation depends on a quantum logical interpretation of quantum mechanics, broadly construed. The solution depends on a theorem about partial Boolean algebras which is proved here.     

Analytic solution to the problem of the gaussian beam propagation through nonuniform gas

The analytic solution to the problem of the Gaussian beam propagation through the non-uniform atmosphere has been derived.     

Bound states and equation of state for nondegenerate quantum systems with short-range interactions

The influence of bound states on the second virial coefficient for systems with short-range interactions is investigated, and the equation of state is determined by different methods. The dissociation equilibrium between bound and free particles is discussed.     

Hypothetical solution of the problem of measurement through the notion of quantum backward causality

The notion of thecoexistence in the quantum framework of causality forward or backward in time is proposed as a possible way for solving the problem of measurement.     

Widely tunable, nondegenerate three-wave mixing microwave device operating near the quantum limit

We present the first experimental realization of a widely frequency tunable, nondegenerate three-wave mixing device for quantum signals at gigahertz frequency. It is based on a new superconducting building block consisting of a ring of four Josephson junctions shunted by a cross of four linear inductances. The phase configuration of the ring remains unique over a wide range of magnetic fluxes threading the loop. It is thus possible to vary the inductance of the ring with flux while retaining a strong, dissipation-free, and noiseless nonlinearity. The device has been operated in amplifier mode, and its noise performance has been evaluated by using the noise spectrum emitted by a voltage-biased tunnel junction at finite frequency as a test signal. The unprecedented accuracy with which the crossover between zero-point fluctuations and shot noise has been measured provides an upper bound for the noise and dissipation intrinsic to the device.     

The exact solution of an equation for the Killing spinor on a nondegenerate deformed conifold

An explicit form of the Killing spinor (generator of N = 1 sypersymmetry) is found for a nondegenerate deformed conifold [3].     

On a solution to the problem of ensuring the security of quantum cryptography for an infinite communication channel

Quantum cryptography involves the fundamental question of the existence of secure protocols of quantum key distribution at any length of a communication channel (at any losses in it). A remarkable feature and novelty of the proposed protocol is that it ensures dual control; first, the intensity of a reference (intense) quantum state is controlled classically before the comparison (measurement) of coherent states from different time windows, and, second, the loss of coherence of a state is detected by interference measurements of an information quantum state and the reference quantum state tested against the conservation of the intensity. Thus, this is the only existing protocol stable to any losses in the communication channel. The length of the communication channel is limited only by dark noise in detectors.     

The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem

A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a general solution to the measurement problem, inasmuch it allows to derive the Born rule as an average over hidden-variables, describing not the state of the quantum entity, but its interaction with the measuring system. According to this modelization, a quantum measurement is to be understood, in general, as a tripartite process, formed by an initial deterministic decoherence-like process, a subsequent indeterministic collapse-like process, and a final deterministic purification-like process. We also show that quantum probabilities can be generally interpreted as the probabilities of a first-order non-classical theory, describing situations of maximal lack of knowledge regarding the process of actualization of potential interactions, during a measurement.     

Analytical solution for the one-dimensional scattering problem

We introduce the scattering problem in the case of one-dimensional space. The transmission factor is calculated for the whole domain of the potential energy. Connection with a field in interaction with a two-level quantum system is established for which the coupling parameter is considered to be explicitly time-dependent.     

Analytic solution of the multiloop Baxter equation

The asymptotic spectrum of anomalous dimensions of gauge-invariant operators in maximally supersymmetric Yang–Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its sl(2)$sl(2)$ subsector spanned by the twist-two single-trace Wilson operators, which are shared by all gauge theories, supersymmetric or not. We develop a formalism for the solution of the perturbative multiloop Baxter equation encoding their asymptotic anomalous dimensions, using Wilson polynomials as basis functions and Mellin transform technique. These considerations yield compact results which allow analytical calculations of multiloop anomalous dimensions bypassing the use of the principle of maximal transcendentality. As an application of our method we analytically confirm the known four-loop result. We also determine the dressing part of the five-loop anomalous dimensions.     

Biexcitonic fingerprint in the nondegenerate four-wave-mixing signal of weakly confined cadmium sulfur quantum dots

Nondegenerate four-wave mixing is analyzed with respect to biexcitonic contributions in the third-order nonlinear susceptibility x((3)) . The presence of biexcitons causes a distinct asymmetry in the frequency dependence of self-diffraction. By measurement of the dependence of the intensity of the self-diffracted signal on detuning between the two incident laser beams, the biexciton binding energy is determined to be E(XX)=7.8 meV for cadmium sulfur quantum dots of R=7.5 nm embedded in glass. Thus, even for weakly confined II-VI quantum dots with R~2.7a(B) , a confinement-induced enhancement of E(XX) was found.