A classical model of EPR experiment with quantum mechanical correlations and bell inequalities

A simple model of a classical break-up process is given in which the correlation E(a,b) of the components A and B of the spins of the two subsystems along directions a and b gives precisely the quantum mechanical result $\text{?cos(}\text{a·b}\text{)}$. The model is “local”, but the normalization procedure of correlation functions in terms of “hidden variables” is different from that used in deriving Bell's inequalities. A discretization procedure of the classical spins is then given which reproduces fully the dichotomous quantum mechanical results both for probabilities and for correlation functions. This procedure illustrates particularly clearly the difference between quantum and classical spins and provides a possible intuitive picture for the notion of the “reduction of the wave function”.     

A note on the Hilbert space formalism of quantum mechanics

In [5] M.J. Maczyński showed that the Hilbert space formalism of quantum mechanics (see [3]) can be derived from a set of seven axioms involving only the probability function p(A, α, E) and the complex field postulate. The purpose of this note is to give the next axiom that is equivalent to the analogous real field postulate.     

On procedures for the measurement of questions in quantum mechanics

It is shown that there exist observablesA and Borel setsE such that the procedure “measureA and give as output the number 1 (0) if theA measurement outcome is (is not) inE” does not correspond to a measurement of the proposition observable ?^A(E) usually assigned to such procedures. This result is discussed in terms of limitations on choice powers of observers.     

Euler elasticae in the plane and the Whitney-Graustein theorem

In this paper, we study normal forms of plane curves and knots. We investigate the Euler functional E (the integral of the square of the curvature along the given curve) for closed plane curves, and introduce a closely related functional A, defined for polygonal curves in the plane ?² and its modified version A _R , defined for polygonal knots in Euclidean space ?³. For closed plane curves, we find the critical points of E and, among them, distinguish the minima of E, which give us the normal forms of plane curves. The minimization of the functional A for plane curves, implemented in a computer animation, gives a very visual approximation of the process of gradient descent along the Euler functional E and, thereby, illustrates the homotopy in the proof of the classical Whitney-Graustein theorem. In ?³, the minimization of A _R (implemented in a 3D animation) shows how classical knots (or more precisely thin knotted solid tori, which model resilient closed wire curves in space) are isotoped to normal forms.     

Quantum and Classical Thermal Correlations in the XXZ Spin-1/2 Chain

We compute the quantum dissonance Q (non-entangled quantum correlation), entanglement E, quantum discord D (total quantum correlation) and classical correlation C in the eight-qubit XXZ spin-1/2 chain at finite temperatures. We find that not only D but also Q and C can clearly detect the critical points associated to quantum phase transitions for this model at finite temperatures. Moreover, Q can detect the special points of the system where the entanglement just appears or completely vanishes. Finally, we obtain two simple dominance relations: C≥E and D≥E+Q. Except these there are no other simple ordering relations in this model.     

Parrondo?s game using a discrete-time quantum walk

We present a new form of a Parrondo game using discrete-time quantum walk on a line. The two players A and B with different quantum coins operators, individually losing the game can develop a strategy to emerge as joint winners by using their coins alternatively, or in combination for each step of the quantum walk evolution. We also present a strategy for a player A (B) to have a winning probability more than player B (A). Significance of the game strategy in information theory and physical applications are also discussed.     

Simulation of coupon bond European and barrier options in quantum finance

Coupon bond European and barrier options are studied in the framework of quantum finance. The prices of European and barrier options are analyzed by generating sample values of the forward interest rates f(t,x) using a two-dimensional Gaussian quantum field A(t,x). The strong correlations of forward interest rates are described by the stiff propagator of the quantum field A(t,x). Using the Cholesky decomposition, A(t,x) is expressed in terms of white noise. The simulation results for European coupon bond and barrier options are compared with approximate formulas, which are obtained as power series in the volatility of the forward interest rates. The simulation shows that the simulated price deviates from the approximate value for large volatilities. The numerical algorithm is flexible and can be used for pricing any kind of option. It is shown that the three-factor HJM model can be derived from the quantum finance formulation.     

A study of the giant dipole resonance of vibrational nuclei in the 103 ≦ A ≦ 133 mass region

This paper presents a set of experimental data concerning the giant dipole resonance of nuclei (GDR) in the 103 ≦ A ≦ 133 mass region. The cross sections σ(γ,n) and σ(γ, 2n) were obtained in the energy region 8–30 MeV by means of a monochromatic photon beam produced by annihilation in flight of positons. This paper attempts also to give an interpretation of the experimental behaviour of the GDR for vibrational nuclei in the 103 ≦ A ≦ 133 mass region in terms of the simple dynamic collective model. In particular it is shown that the width of the GDR increases as β increases and as E₂₊ decreases and that the theoretically predicted spreading of the dipole strength is confirmed by our experimental results. As to the characteristic behaviour of the GDR above its peak value at E₀, we come to the conclusion that the actual state of the art in (γ, xn) research does not allow one to make an unambiguous choice between isospin splitting or electric quadrupole absorption. Finally the numerical evaluations of the different sum rules are given and some empirical results concerning the average energy of the GDR as a function of A are also presented.     

Chiral symmetry breaking in nonequilibrium chemical systems: Time scales for chiral selection

The process through which an extremely weak parity violating interaction, of energy ΔE, can become the selector of molecular chirality over a sufficiently long time is discussed. For a model system it is shown that ΔE ≈ 5 × 10^-15kT can give a 90% selectivity in about 300 h - smaller ΔE being relevant to prebiotic evolution.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

Dynamical structure of peptide molecules: Fourier transform microwave spectroscopy of N-methylpropionamide

In order to clarify the dynamical aspects of the peptide structure, N-methylpropionamide (NMPA) was investigated as an example of peptide molecules: XCONHY (X=CH₃CH₂ and Y=CH₃ for NMPA), paying special attention to the internal rotation of the two methyl groups. NMPA was found to have an almost planar skeleton with an extended syn/trans conformation, as indicated by the observed value of I_aa+I_bb−I_cc, and its rotational spectra were interpreted in terms of group G₁₈ consisting of six symmetry species: A₁, A₂, E₁, E₂, E₃, and E₄. The A₁ and E₂ spectra were observed split in most of b-type transitions, yielding the internal-rotation potential barrier V₃ of 796 (21) cm⁻¹ for CH₃ in the ethyl group referred to as C-CH₃. The spectra of the three E species: E₁, E₃, and E₄ appeared several tens to thousands MHz apart from the corresponding A₁ spectra, suggesting the internal-rotation potential barrier of CH₃ bonded to the nitrogen, called N-CH₃, to be quite low. In sharp contrast with the A₁ spectra, which were well fitted to the ordinary asymmetric-rotor spectral pattern, a few higher-order terms were required to reproduce the E₁ spectra, presumably because of the low N-CH₃ barrier. The spectral analysis thus performed, in fact, led to the V₃ of 80.06487 (14) cm⁻¹, an order of magnitude lower than that of C-CH₃. The E₃ and E₄ spectra were found to form triplets with the corresponding E₁ lines at the center, and the E₃-E₁ and E₄-E₁ splittings were explained essentially by the contributions of the C-CH₃ internal rotation combined with the kinetic-energy coupling between the two methyl groups. The torsion around the C-C bond between the ethyl and carbonyl groups was suggested by an ab initio calculation to be of double minimum nature, but the observed A₁ spectra did not show any indication of such a double-minimum potential for the C-C torsion, although the possibility of a small hump being present at a planar conformation could not be entirely eliminated. The present results on NMPA along with those obtained on other peptide molecules will be of some significance in clarifying important problems of structural biology such as protein folding and signal transfer through biological systems.     

New insights into quantum and classical correlations in XY spin models

We compute quantum dissonance Q (non-entangled quantum correlation), entanglement E, quantum discord D (total quantum correlation) and classical correlation C for spin pairs at any distance in the infinite XY spin-1/2 chains, i.e., the anisotropic XY model and the isotropic XY model with three-spin interactions. We obtain two simple dominance relations: C ≥ E and D ≥ E + Q Except this, there are no other simple ordering relations between them. We also show that Q can detect the special points of the system where the entanglement just appears or completely disappears. In addition, it is worthwhile to mention that dissonance and classical correlation can also clearly spotlight the critical points of quantum phase transitions in XY spin-1/2 chains.     

Entropy increase for a class of dynamical maps

The dynamical evolution of a quantum system is described by a one parameter family of linear transformations of the space of self-adjoint trace class operators (on the Hilbert space of the system) into itself, which map statistical operators to statistical operators. We call such transformations dynamical maps. We give a sufficient condition for a dynamical map A not to decrease the entropy of a statistical operator. In the special case of an N-level system, this condition is also necessary and it is equivalent to the property that A preserves the central state.     

Discrimination of measurement contexts in quantum mechanics

We demonstrate that it is possible to discern the way that has been followed to measure a quantum observable that can be expressed in terms of different products of observables, whereas no such discrimination is possible by assigning predetermined values. Specifically we show how to distinguish different routes (contexts) to measure C=AB=A^′B^′, when C,A,B and C,A^′,B^′ commute with each other, but A and B do not commute with A^′ and B^′.     

Microwave spectrum of Trioxane in four excited degenerate vibrational states,especially in the 2ν20 (E) state and the combination state ν7 (A1) + ν20 (E)

The microwave spectra of the Trioxane molecule in the doubly excited degenerate vibrational state 2ν₂₀(E) and in the combination state ν₇(A₁) + ν₂₀(E) are reported for several J values. Molecular constants of these states have been determined. The excited states ν₂₀(E) = 1 and ν₁₉(E) = 1 previously studied by a perturbation formula have been analyzed by a direct diagonalization method of the energy matrix. Parameters which give the variation of the rotational constant B_V as a function of the quantum number v have been obtained.     

Second- and third-order elastic moduli of Co I

Elastic moduli of Co with A ₁-type structure are calculated using models in which the total energy is presented in the form of the energy of clusters consisting of pairs, triplets, and quadruplets of identical atoms. The irreducible energies of the clusters are assumed to contain two terms: E ∝ ?τ^?6, corresponding to the mutual attraction of the particles, and E ∝ ?τ^?6, corresponding to their mutual repulsion. Here, τ stands for the half-edge of an elementary cell. All 27 types of models expected in accordance with symmetry theory are analyzed. Of these, the 13 that yielded elastic modulus values satisfying the structural stability criteria are selected. The potentials of the selected models are used to predict the rigidity moduli of Co films with an A2-type structure.     

Effect of the second order spin orbit and spin-spin interactions on the E (G) level of Mn in ZnS

An interpretation of the structure of the ⁶A₁ → {₁A₁, ⁴E} zero phonon and phonon assisted transitions is given. Covalency effects show that the ⁶A₁ → ⁴A₁ and ⁶A₁ → ⁴E transitions are well separated; consequently none of the experimentally observed lines can be due to the ⁶A₁ → ⁴A₁ transition. The fine structure for the ⁴E level is interpreted in terms of the spin-spin and spin-orbit interactions. The results obtained are consistent with experiments.     

Correlation functions and the uniqueness of the state in classical statistical mechanics

A general criterion is derived which assures the uniqueness of the state of a classical statistical mechanical system in terms of a given system of correlation functions. The criterion is \(\sum\limits_k {(m_{k + j}^A )} ^{ - 1/k} = \infty\) for allj and all bounded setsA, where $$m_k^A = (k!)^{ - 1} \int\limits_A \cdots \int\limits_A {\varrho _k } (x_1 , \ldots ,x_k )dx_1 \ldots dx_1 .$$      

Remote entanglement for quantum networks

Quantum networks are distributed many-body quantum systems with tailored topology and controlled information exchange. We present two schemes to generate remote entanglement, in atomic external degrees of freedom and between cavities. In the first scheme, we entangle two atoms with their cavities in momentum space through Bragg diffraction. Thereafter, in order to trace out the cavities, we let resonantly interact an auxiliary atom with each cavity. In the last, we perform quantum measurement on two auxiliary atoms and get remote entangled state in atomic external degrees of freedom. In the second scheme, we have a three cavities system. The other two cavities, A and B, are entangled with indistinguishable modes of cavity, C. Performing quantum measurement on third cavity, C, we disentangle it from the system and the cavities, A and B, become entangled.