Gaussian states as minimum uncertainty states

In bosonic fields, Gaussian states, which consist of a rather wide family of states including coherent states, squeezed states, thermal states, etc., have many classical-like features, and are usually defined from the mathematical perspective in terms of characteristic functions. It is well known that some special Gaussian states, such as coherent states, are minimum uncertainty states for the conventional Heisenberg uncertainty relation involving canonical pair of position and momentum observables. A natural question arises as whether all Gaussian states can be characterized as minimum uncertainty states. In this work, we show that indeed Gaussian states coincide with minimum uncertainty states for an information-theoretic refinement of the conventional uncertainty relation established in Luo (2005) [40]. This characterization puts Gaussian states on a novel basis of physical significance.     

On the effective potential minimum versus the tree level potential minimum

We analyze the effective potential minimum (true vacuum of the theory) versus the tree level potential minimum in order to decide under which conditions they coincide. A criterion is found. Applications are made to monomial potentials (Coleman-Weinberg type models) and to theN=1 Supergravity Minimal Model.     

On the fission width of isobaric analogue states

The experimental cross sections of the reactions ²⁰⁹Bi(p, f) and ²⁰⁶Pb(α, f) are analyzed to estimate the ratio Γ_f/Γ_tot for the IAS. From the comparison of the values Γ_f for the nuclear states with different isospins it follows that strong isospin effects exist in the nuclear fission process involving ²¹⁰Po.     

Transition fission states for heated nuclei

Induced fission reactions of fissioning compound nuclei that result from the capture of various incident particles (nucleons, γ rays, multiply charged ions) by target nuclei are investigated using the generalized nucleus model and the Wigner random matrix method. The effect produced on the fission widths of the compound nucleus by the competition between the excitation energies of its collective vibrational degrees of freedom that lead to its scission into fission fragments and its rotational and multi-quasiparticle states is analyzed. Bohr’s concept of transition fission states developed for near-barrier nuclear fission is generalized to the induced fission of nuclei with the excitation energies noticeably higher than the fission barriers. The temperature of the fissioning nucleus in the vicinity of the point of its scission into fission fragments is estimated.     

Note on the time evolution of minimum uncertainty states

General conditions for a Hamiltonian to keep a minimum uncertainty state stable are obtained.     

P-odd and P-even correlations for third particles in ternary fission

Within quantum-mechanical fission theory, P-odd and P-even correlations in angular distributions of products of the ternary fission of nuclei that is induced by polarized cold and thermal neutrons are investigated on the basis of a nonevaporative mechanism of third-particle emission and under the assumption that a two-humped fission barrier exists. It is shown that these correlations for third particles are induced by the analogous correlations for ternary-fission fragments, the latter being transferred to the third particle because of the kinematical conditions of third-particle emission that are associated with the charge and mass asymmetry of fragments. Optimum methods for observing the above correlations for third particles are discussed. The possibility of discovering the emission of prescission neutrons in the fission process against the background of evaporated neutrons by means of studying P-odd and P-even correlations is explored.     

Spontaneous fission of isomeric states of actinide nuclei

Spontaneous fission half-lives of K-isomeric states are calculated on the basis of microscopic- macroscopic method. The isomeric state is assumed to be a 2-quasiparticle excited state with high angular momentum.The calculations were performed for nuclei with 96 < Z < 110 and 144 < N < 158. It was shown that in the case of K-isomeric states (if they exist) the spontaneous fission half-life time may be comparable to the spontaneous fission half-life time of the ground state. Therefore it was suggested that in measurements of fission half-lives it may be very important to distinguish between both possible components (or more) of the fission decay.     

The double minimum potential in the spectrum of HCOF

Rotational analyses conducted together with theoretical calculations of the relative intensities for vibronic transitions involving an excited state with a double minimum potential have led to confirmation of the previously established vibrational analysis and to a full characterization of the double-minimum potential function. The origin band at 37 490 cm^?1 has been shown to consist of the two transitions 6₀⁰ (true origin) and 6₀¹ separated by only 0.5 cm^?1 and with rotational structures corresponding to type C, allowed, and hybrid type AB, Herzberg-Teller induced, bands respectively.     

Classical properties of quantum systems in minimum uncertainty states

We derive a necessary condition for the equivalence of the Schrödinger equation with the evolution equation for the marginal coordinate probability density of the Liouville equation and propose an analogon of the quantum Fourier transformation in classical statistical mechanisms. It is shown that this quantum-classical equivalence holds for simple systems in minimum uncertainty states.     

测不准关系和最小不确定态

利用力学量算符的厄密性和希尔伯特状态矢量模的非负性，重新给出了关于测不准关系的数 学证明.简单的证明过程不仅揭示了测不准关系某些经常被忽视的特征，而且还可以直接给 出最小不确定态的充要条件.在此基础上，我们提出了对易子为非零常数的任意一对力学量 的最小不确定态问题，并且采用玻色型产生和湮没算符给出了它们的压缩态的明显表达式. 关键词： 海森堡测不准原理 最小不确定态 压缩态     

Even and odd amplitudes of distributions of third particles in nuclear fission

The principal values for the even and odd components of the amplitudes of the angular distributions of α particles emitted as the third particles in true low-energy ternary fission of nuclei are calculated within the quantum theory of fission using natural approximations for the dependence of the potential scattering phases of the α particle on its orbital momenta and experimental angular distributions, unperturbed by the fissioning nucleus rotation, of these third α particles. Knowing the angular dependences of these components, we can estimate the angular dependences of the T-odd ROT and TRI asymmetry coefficients for the ternary fission of actinide nuclei induced by cold polarized neutrons.     

Potential for describing single nucleon states during fission

A potential is suggested for describing single nucleon states encountered during both symmetric and asymmetric nuclear fission. The equipotential surfaces for this potential will correspond to quite arbitrary nuclear shapes; intersecting spheres and ellipsoids of various shapes, Cassini ovaloids, and more general figures which are not symmetric about the z axis. Methods are considered for solving the Schrödinger equation for those parts of the potential which depend on z, and energy levels are found in this potential for some different deformations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 7, pp. 23–31, July 1971.     

A secondary minimum in the potential energy surface of Ca

Strutinsky type calculations are extended to lighter nuclei. Secondary minima in the potential energy surface generally considered to account for the existence of fission isomers occur also in the lighter mass region. Results for ⁴⁰Ca are compared with experimental evidences.     

High-spin states in the neutron rich fission fragments138Xe and139Xe

High-spin structures in the neutron-rich nuclei^138Xe and¹³⁹Xe have been investigated by observing prompt γ -rays from the spontaneous fission of²⁴⁸Cm with the Eurogam spectrometer. The partial level schemes were constructed on the basis of double-, triple- and quadruple-γ coincidences. The ground state band in¹³⁸Xe has been extended up to 5 MeV excitation energy. The structure of the newly observed medium-spin states in¹³⁹Xe is similar to the one of heavier N=85 isotones where vf ₇ ^2/3 , vh_9/2f ₇ ^2/2 and vf ₇ ^2/3 ? 3^? multiplets have been observed.     

Nonlinear coherent states of the Fokas-Lagerstrom potential

In this paper, we introduce an algebraic approach to construct Fokas-Lagerstrom coherent states. To do so, we define deformed creation and annihilation operators associated to this system and investigate their algebra. We show that these operators satisfy the f-deformed Weyl-Heisenberg algebra. Then, we propose a theoretical scheme to generate the aforementioned coherent states. The present contribution shows that the Fokas-Lagerstrom nonlinear coherent states possess some non-classical features.     

Coriolis interaction in the second well of deformation potential and low-energy fission

It is shown that, because of sufficiently large energy spacing between neutron resonance states (NRS-II) in the second well of the deformation potential for actinide nuclei, the Coriolis interaction, mixing the states of an axially symmetric deformed nuclei with different values of the projection K of the nuclear spin J onto the symmetry axis, is week, and the K value in the wave functions of NRS-II is a good quantum number. It is concluded that the K distribution for the states of fissile actinide nuclei in the vicinity of their scission point into fission fragments is determined by simultaneous influence of the internal and external fission barriers, which allows to coordinate the experimental data on subbarrier photofission with the P-odd and P-even correlations in the angular distributions of fission fragments.     

Application of the real Weinberg states in potential scattering

This work is the first step in a systematic application of a resonant scattering theory due to Huby in which the real Weinberg state is the crucial feature. The scattering cross sections ofl=0,1, 2 partial waves in a square well potential are calculated with the aid of the real Weinberg states. Perfect agreement with the exact calculation is obtained. Approximate cross sections resulting from a schematic approximation in the formalism which, apart from other desirable features, display the Breit-Wigner energy factor in the phase shifts, are also found to agree perfectly with the exact calculation. Some simple approximations of the complex and real Weinberg states are investigated, but none is found to be satisfactory forl>0 partial waves in complete contrast to works of previous authors on thel=0 partial wave.     

Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states

A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the Miller-Robert-Sommeria (MRS) entropy under these sole constraints. We assume that these constraints are selected by properties of forcing and dissipation. We find that the vorticity fluctuations are Gaussian while the mean flow is characterized by a linear [`(w)]-y\overline{\omega}-\psi relationship. Furthermore, we prove that the maximization of entropy at fixed energy, circulation and microscopic enstrophy is equivalent to the minimization of macroscopic enstrophy at fixed energy and circulation. This provides a justification of the minimum enstrophy principle from statistical mechanics when only the microscopic enstrophy is conserved among the infinite class of Casimir constraints. Relaxation equations towards the statistical equilibrium state are derived. These equations can serve as numerical algorithms to determine maximum entropy or minimum enstrophy states. We use these relaxation equations to study geometry induced phase transitions in rectangular domains. In particular, we illustrate with the relaxation equations the transition between monopoles and dipoles predicted by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)]. We take into account stable as well as metastable states and show that metastable states are robust and have negative specific heats. This is the first evidence of negative specific heats in that context. We also argue that saddle points of entropy can be long-lived and play a role in the dynamics because the system may not spontaneously generate the perturbations that destabilize them.