Compact and Loosely Bound Structures in Light Nuclei

A role of different components in the wave function of the weakly bound light nuclei states was studied within the framework of the cluster model, taking into account of orbitals "polarization". It was shown that a limited number of structures associated with the different modes of nucleon motion can be of great importance for such systems. Examples of simple and quite flexible trial wave functions are given for the nuclei $^8$Be, $^6$He. Expressions for the microscopic wave functions of these nuclei were found and used for the calculation of basic nuclear characteristics, using well known central-exchange nucleon-nucleon potentials.Comment: 19 pages, 3 ps figure

Quantum Abacus for counting and factorizing numbers

We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. A 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base 2, base 3, or base d representation. In operating the algorithm, the number n < N = d^K is read into a K-qudit register through its interaction with a stream of n particles passing in a nearby wire; this step corresponds to a quantum Fourier transformation from the Hilbert space of particles to the Hilbert space of qudit states. An inverse quantum Fourier transformation provides the number n in the base d representation; the inverse transformation is fully quantum at the level of individual qudits, while a simpler semi-classical version can be used on the level of qudit registers. Combining registers of qubits, qutrits, and qudits, where d is a prime number, with a simpler single-shot measurement allows to find the powers of 2, 3, and other primes d in the number n. We show, that the counting task naturally leads to the shift operation and an algorithm based on the quantum Fourier transformation. We discuss possible implementations of the algorithm using quantum spin-d systems, d-well systems, and their emulation with spin-1/2 or double-well systems. We establish the analogy between our counting algorithm and the phase estimation algorithm and make use of the latter's performance analysis in stabilizing our scheme. Applications embrace a quantum metrological scheme to measure a voltage (analog to digital converter) and a simple procedure to entangle multi-particle states.Comment: 23 pages, 15 figure

New Perturbation Theory for Nonstationary Anharmonic Oscillator

The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency in external field is used. Based on some intrinsic properties of unperturbed wave function the variational-iterational method is proposed, that make it possible to correct both the amplitude and the phase of wave function. As an application the first order correction are proposed both for wave function and S-matrix elements for asymmetric perturbation potential of type $V(x,\tau)=\alpha (\tau)x^3+\beta (\tau)x^4.$ The transition amplitude ''ground state - ground state'' $W_{00}(\lambda ;\rho)$ is analyzed in detail depending on perturbation parameter $\lambda$ (including strong coupling region $$ $\sim 1$) and one-dimensional refraction coefficient $\rho$.Comment: LaTeX, 13 page

Influence of low energy scattering on loosely bound states

Compact algebraic equations are derived, which connect the binding energy and the asymptotic normalization constant (ANC) of a subthreshold bound state with the effective-range expansion of the corresponding partial wave. These relations are established for positively-charged and neutral particles, using the analytic continuation of the scattering (S) matrix in the complex wave-number plane. Their accuracy is checked on simple local potential models for the 16O+n, 16O+p and 12C+alpha nuclear systems, with exotic nuclei and nuclear astrophysics applications in mind

Spherical model of the Stark effect in external scalar and vector fields

The Bohr-Sommerfeld quantization rule and the Gamow formula for the width of quasistationary level are generalized by taking into account the relativistic effects, spin and Lorentz structure of interaction potentials. The relativistic quasi-classical theory of ionization of the Coulomb system (V_{Coul}=-\xi/r) by radial-constant long-range scalar (S_{l.r.}=(1-\lambda)(\sigma r+V_0)) and vector (V_{l.r.}=\lambda(\sigma r+V_0)) fields is constructed. In the limiting cases the approximated analytical expressions for the position E_r and width \Gamma of below-barrier resonances are obtained. The strong dependence of the width \Gamma of below-barrier resonances on both the bound level energy and the mixing constant \lambda is detected. The simple analytical formulae for asymptotic coefficients of the Dirac radial wave functions at zero and infinity are also obtained.Comment: 25 pages, 4 figures. Submitted to Int. J. Mod. Phys.

Quantum divisibility test and its application in mesoscopic physics

We present a quantum algorithm to transform the cardinality of a set of charged particles flowing along a quantum wire into a binary number. The setup performing this task (for at most N particles) involves log_2 N quantum bits serving as counters and a sequential read out. Applications include a divisibility check to experimentally test the size of a finite train of particles in a quantum wire with a one-shot measurement and a scheme allowing to entangle multi-particle wave functions and generating Bell states, Greenberger-Horne-Zeilinger states, or Dicke states in a Mach-Zehnder interferometer.Comment: 9 pages, 5 figure

Centrifugal quantum states of neutrons

We propose a method for observation of the quasi-stationary states of neutrons, localized near the curved mirror surface. The bounding effective well is formed by the centrifugal potential and the mirror Fermi-potential. This phenomenon is an example of an exactly solvable "quantum bouncer" problem that could be studied experimentally. It could provide a promising tool for studying fundamental neutron-matter interactions, as well as quantum neutron optics and surface physics effects. We develop formalism, which describes quantitatively the neutron motion near the mirror surface. The effects of mirror roughness are taken into account.Comment: 13 pages, 10 figure

The Faraday Quantum Clock and Non-local Photon Pair Correlations

We study the use of the Faraday effect as a quantum clock for measuring traversal times of evanescent photons through magneto-refractive structures. The Faraday effect acts both as a phase-shifter and as a filter for circular polarizations. Only measurements based on the Faraday phase-shift properties are relevant to the traversal time measurements. The Faraday polarization filtering may cause the loss of non-local (Einstein-Podolsky-Rosen) two-photon correlations, but this loss can be avoided without sacrificing the clock accuracy. We show that a mechanism of destructive interference between consecutive paths is responsible for superluminal traversal times measured by the clock.Comment: 6 figure

Limitations on the principle of stationary phase when it is applied to tunneling analysis

Using a recently developed procedure - multiple wave packet decomposition - here we study the phase time formulation for tunneling/reflecting particles colliding with a potential barrier. To partially overcome the analytical difficulties which frequently arise when the stationary phase method is employed for deriving phase (tunneling) time expressions, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and an one-dimensional rectangular potential barrier. Summing the amplitudes of the reflected and transmitted waves - using a method we call multiple peak decomposition - is shown to allow reconstruction of the scattered wave packets in a way which allows the stationary phase principle to be recovered.Comment: 17 pages, 2 figure

The quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the theory of heavy-light mesons

We construct a relativistic potential quark model of $D$, $D_s$, $B$, and $B_s$ mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy quark is considered a local source of the gluon field. The effective interquark interaction is described by a combination of the perturbative one-gluon exchange potential $V_{\mathrm{Coul}}(r)=-\xi/r$ and the long-range Lorentz-scalar and Lorentz-vector linear potentials $S_{\mathrm{l.r.}}(r)=(1-\lambda)(\sigma r+V_0)$ and $V_{\mathrm{l.r.}}(r)=\lambda(\sigma r+V_0)$, where $0\leqslant\lambda<1/2$. Within the quasiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of $D$, $D_s$, $B$, and $B_s$ mesons, which ensure a high accuracy of calculations even for states with the radial quantum number $n_r\sim 1$. We show that the fine structure of P-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters: the strong-coupling constant $\alpha_s$ and the coefficient $\lambda$ of mixing of the long-range scalar and vector potentials $S_{\mathrm{l.r.}}(r)$ and $V_{\mathrm{l.r.}}(r)$. The quasiclassical formulas for asymptotic coefficients of wave function at zero and infinity are obtained.Comment: 22 pages, 6 figure