The Dynamics of Quantum Correlations Between Two Atoms in Two Coupled Cavities

The dynamics of the quantum correlation between two atoms in two single-mode cavities is studied. For the initial Bell state |Ψ ⁺〉, the quantum consonance is equal to the entanglement, and larger than quantum discord. For the initial Bell state |Φ ⁺〉, the quantum consonance is larger than entanglement, but not larger than quantum discord all the time. As the increase of the cavity-cavity coupling strength, the evolution period of quantum correlation becomes smaller. Consonance is not smooth at some points while cavities are coupled with each other.     

Quantum deformation of compactified Minkowski space

The quantum GrassmanianG(2|0; ? _q ^4|0 ) of “quantum 2-planes ? _q ^2|0 in the quantum 4-plane ? _q ^4|0 ”, which provides aq-deformation of compactified complexified Minkowski space, is proposed. A quantum analogue of classical Plücker embedding of the usual GrassmanianG(2; ?²) into a non-degenerate quadric in ??⁵ is found.     

On the ground state of Ising models with arbitrary spin quantum number

The ground state of a class of Ising models with site dependent arbitrary spin quantum number is shown to be restricted to ±S_i^MAX state where S_i^MAX is the spin quantum number at the site i.     

Laplace operator and hodge decomposition for quantum groups and quantum spaces

LetΓ=Γ _±,z be one of theN ²-dimensional bicovariant first order differential calculi for the quantum groups GL _q (N), SL _q (N), SO _q (N), or Sp _q (N), whereq is a transcendental complex number andz is a regular parameter. It is shown that the de Rham cohomology of Woronowicz’s external algebraΓ ^{^} coincides with the de Rham cohomologies of its leftinvariant, its right-invariant and its biinvariant subcomplexes. In the cases GL _q (N) and SL _q (N) the cohomology ring is isomorphic to the biinvariant external algebraΓ _inv ^{^} and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in these cases. The main technical tool is the spectral decomposition of the quantum Laplace-Beltrami operator. It is also applicable for quantum Euclidean spheres. The eigenvalues of the Laplace-Beltrami operator in cases of the general linear quantum group, the orthogonal quantum group, and the quantum Euclidean spheres are given.     

Classical and quantum statistical mechanics in a common Liouville space

It is shown that the extremal phase-space representations of quantum mechanics can be expressed in terms of wave-functions on L²-spaces which are embedded in L²(Γ). In L²(Γ) all these representations are restrictions of a globally defined representation of the canonical commutation relations. The master Liouville space $\text{B}$²(Γ) over L²(Γ) can accommodate representations of both classical and quantum statistical mechanics, and serves as a medium for their comparison. As a specific example, a Boltzmann-type equation on $\text{B}$²(Γ) is considered in the classical as well as quantum context.     

Energy spectrum of the A + + e complex in a quantum dot in the adiabatic approximation

The energy states of an A ⁺ + e complex in a quantum dot described within the hard-wall potential model are considered using the zero-range potential method in the adiabatic approximation. These complexes can be formed under nonequilibrium conditions (for example, under photoexcitation). A relationship describing the dependence of the binding energy of a hole located at a neutral acceptor on the parameters of the zero-range potential of the system and the quantum state of the electron is obtained analytically. It is demonstrated that, in quantum dots of small radius, the binding energy of a hole in the A ⁺ + e complex can be considerably higher than the ground-state energy of the A ⁺ stationary center.     

Quantum Hypothesis Testing for Gaussian States: Quantum Analogues of χ2, t-, and F-Tests

We consider quantum counterparts of testing problems for which the optimal tests are the χ², t-, and F-tests. These quantum counterparts are formulated as quantum hypothesis testing problems concerning Gaussian state families, and they contain nuisance parameters, which have group symmetry. The quantum Hunt-Stein theorem removes some of these nuisance parameters, but other difficulties remain. In order to remove them, we combine the quantum Hunt-Stein theorem and other reduction methods to establish a general reduction theorem that reduces a complicated quantum hypothesis testing problem to a fundamental quantum hypothesis testing problem. Using these methods, we derive quantum counterparts of the χ², t-, and F-tests as optimal tests in the respective settings.     

Transition energy and dipole oscillator strength of 1s23d-1s2 nf transitions for Sc18+ ion

The transition energies of the 1s²3d-1s² nf (4?n?9) transitions and fine structure splittings of 1s² nf (n?9) states for Sc¹⁸⁺ ion are calculated with the full-core plus correlation method. The quantum defect of 1s² nf series is determined by the single-channel quantum defect theory. The energies of any highly excited states with n?10 for this series can be reliably predicted using the quantum defect as function of energy. Three alternative forms of the dipole oscillator strengths for the 1s²3d-1s² nf (n?9) transitions of Sc¹⁸⁺ ion are calculated with the transition energies and wave functions obtained above. Combining the quantum defect theory with the discrete oscillator strengths, the discrete oscillator strengths for 1s²3d-1s² nf (n > 9) transitions and the oscillator strengths densities corresponding to the bound-free transitions are obtained.     

Quantum entanglement and quantum phase transitions in frustrated Majumdar-Ghosh model

By using the density matrix renormalization group technique, the quantum phase transitions in the frustrated Majumdar-Ghosh model are investigated. The behaviors of the conventional order parameter and the quantum entanglement entropy are analyzed in detail. The order parameter is found to peak at J₂∼0.58, but not at the Majumdar-Ghosh point (J₂=0.5). Although, the quantum entanglements calculated with different subsystems display dissimilarly, the extremes of their first derivatives approach to the same critical point. By finite size scaling, this quantum critical point J^C₂ converges to around 0.301 in the thermodynamic limit, which is consistent with those predicted previously by some authors (Tonegawa and Harada, 1987 [6]; Kuboki and Fukuyama, 1987 [7]; Chitra et al., 1995 [9]). Across the J^C₂, the system undergoes a quantum phase transition from a gapless spin-fluid phase to a gapped dimerized phase.     

The classical limit for quantum mechanical correlation functions

For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the quantum mechanical Hamiltonian and taken in coherent states centered inx- andp-space around? ^?1/2 (coordinates of a point in classical phase space) are shown to become the exponentials of coordinate functions of the classical orbit in phase space. In the same sense,? ^?1/2 [(quantum operator) (t) — (classical function) (t)] converges to the solution of the linear quantum mechanical system, which is obtained by linearizing the non-linear Heisenberg equations of motion around the classical orbit.     

Quasi-K quantum number in Gd

Evidence is discussed for the persistence of the K quantum number in a transitional nucleus ¹⁵²Gd in the form of a quasi-K quantum number K_σ. It plays an important role for β-transitions in a similar way to the K quantum number in deformed nuclei.     

The vibration-rotation spectrum of 14CO in the spectral range 2.40–3 μm

The infrared emission spectrum of the Δv = 2 sequence of the ¹⁴C¹⁶O molecule has been recorded at high resolution by Fourier transform spectrometry. More than 750 spectral lines have been assigned for a wide range of rotational quantum numbers (J = 0–60) and vibrational quantum numbers (v = 0–13). Using a variational method, a fully quantum mechanical potential energy curve (IPA potential) is determined. A comparison of this potential with the semiclassical RKR potential, which is based on a first-order WKB method, is carried out.     

Ergodical time evolution of a Gaussian wave packet in quantum dots

The time evolution of a Gaussian wave packet (GWP) confined in a quantum dot is numerically studied. The quantum dots are modelled by a two-dimensional square box and by the potential x⁴ + y⁴. For the case of an incommensurate energy spectrum the time evolution of observables has no global period. As a result this leads to ergodic phase portraits with a finite phase volume. For the spatially wide GWP the distribution function of quantum observables may be approximated as a Gaussian one. For the case of commensurate transition frequencies in the quantum well the time evolution of observables is periodical and the phase portraits have a zero phase volume.     

Aspects of supersymmetric quantum mechanics

We review the properties of supersymmetric quantum mechanics for a class of models proposed by Witten. Using both Hamiltonian and path integral formulations, we give general conditions for which supersymmetry is broken (unbroken) by quantum fluctuations. The spectrum of states is discussed, and a virial theorem is derived for the energy. We also show that the euclidean path integral for supersymmetric quantum mechanics is equivalent to a classical stochastic process when the supersymmetry is unbroken (E₀ = 0). By solving a Fokker-Planck equation for the classical probability distribution, we find P_c(y) is identical to |Ψ₀(y)|² in the quantum theory.     

Quantum efficiency and responsivity of InSb photodiodes utilizing the Moss-Burstein effect

In this work a detailed analysis of the quantum efficiency of InSb n⁺-p photodetectors produced by liquid phase epitaxy is given, in the case when the n⁺ region is doped to such a level that the Moss-Burstein effect plays an important role. Our starting point was the theoretically determined coefficient of intrinsic absorption and derived expressions for the generated photocurrent in the n⁺ region, depletion layer and p-phase of the photodetector. The results are presented in the form of graphical dependence of the quantum efficiency on the wavelength, with the electron concentration in the n⁺ layer as a parameter.     

Quantum corrections to the classical reflection factor in a2(1) Toda field theory

The O(β²) quantum correction to the classical reflection factor is calculated for one of the integrable boundary conditions of a₂⁽¹⁾ affine Toda field theory. This is found to agree with the conjectured exact reflection factor of the quantum theory. We consider the existence of other exact reflection factors consistent with our perturbative answer and examine the question of how duality transformations might relate theories with different boundary conditions.     

On a generalization of Wick-powers for generalized free-fields in terms of Jacobi-fields

Within the frame of Jacobi-fields a generalization of Wick-powers of generalized free fields is proposed. The key notion is that of a (generalized) contraction map. Those contraction maps F which yield a relativistic quantum field A^F are characterized. Using some simplifying assumptions the general form of a contraction map F which yields a relativistic quantum field A^F is determined. Furthermore, those contraction maps F are characterized for which A^F is in the Borchers class of the generalized free field A we start with. The Wick-product of generalized free fields appears as a particular example of this construction.     

Quantum efficiency for degenerate p-type photoluminescence and electroluminescence in GaAs crystals2

The radiative lifetime and the internal quantum efficiency for the degenerate p-type photoluminescence and the electroluminescence in GaAs crystals have been investigated with a simplified model of degenerate semiconductors in which the recombination constant B is approximately proportional to the ?$\text{5}\text{8}$power of the hole concentration. It is suggested that the radiative lifetime reaches a minimum at some hole concentration, in good agreement with the prediction of Dumke. At 77 K, the internal quantum efficiency exhibits a maximum, found to be 100% at 5 × 10¹⁸ cm^?3 for p-type GaAs crystals, in perfect agreement with experiments of Cusano, and for p-n GaAs junction crystals η_int, _max = 60% at 3 × 10¹⁸cm^?3. Finally, it is noted that in degenerate p-type GaAs crystals, the internal quantum efficiency increases linearly with increasing temperatures.     

Influence of the coulomb blockade effect on heat transfer in a one-dimensional system of spinless electrons

An analysis is made of some characteristics of the low-temperature thermal conductivity of a ballistic quantum dot, attributed to the influence of long-range Coulomb interaction in the geometric capacitance approximation. It is shown that at fairly low temperatures the thermal conductivity K exhibits Coulomb oscillations as a function of the electrostatic potential of the quantum dot. At the maximum of the Coulomb peak we find K ∝ T whereas at the minimum K ∝ T ³. The dependence K(T) is essentially nonmonotonic at temperatures corresponding to the characteristic spacing between the size-quantization levels in the quantum dot.     

Background Independent Quantum Mechanics,Metric of Quantum States,and Gravity: A Comprehensive Perspective

This paper presents a comprehensive perspective of the metric of quantum states with a focus on the geometry in the background independent quantum mechanics. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the quantum state space and Kähler manifold. The metric of quantum states in the classical configuration space with the pseudo-Riemannian signature and its possible applications are explored. On contrary to the common perception that a metric for quantum state can yield a natural metric in the configuration space when the limit ?→0, we obtain the metric of quantum states in the configuration space without imposing the limiting condition ?→0. Here Planck’s constant ? is absorbed in the quantity like Bohr radii \(\frac{1}{2mZ\alpha}\sim a_{0}\). While exploring the metric structures associated with Hydrogen like atom, we witness another interesting finding that the invariant lengths appear in the multiple of Bohr’s radii as: ds ²=a ₀ ² (? Ψ)².