Minkowski-Fock states in accelerated frames

The vibrational structure of the Frenkel exciton states of a molecular crystal is investigated by a variational technique using a rigid-lattice-model Hamiltonian. The spirit of the weak coupling formalism is strictly adhered to by constructing crystal wavefunctions from products of isolated molecule wavefunctions so that the only parameters of the theory are Franck—Condon factors and vibrational frequency shifts. The basis set consists of all vibronic, i.e., single particle, states belonging to the same electronic state transforming according to a given wave vector, plus a set of two-particle states in which vibronic and ground vibrational excitation occupy different sites. Interactions between single-particle states are treated in detail, as are interactions between one- and two-particle states. However, part of the interaction between certain two-particle states is neglected and this makes the treatment progressively less accurate for higher vibrational states and stronger coupling. Electron exchange effects, coupling of excitons to photons, higher electronic states, and ion-pair states are not considered. It is shown how each element of the conventional weak coupling energy matrix is supplemented by terms which account for the interaction between one- and two-particle states as well as interactions among the two-particle states. For a given wave vector each single-particle state is accompanied by a family of two-particle bands which rapidly increases in size for higher vibrational states. In the weak coupling limit the families are widely separated, while intermediate coupling corresponds to two-particle bandwidths comparable with the vibrational spacing. The onset of strong coupling corresponds to overlapping of adjacent families.

The massive high-temperature phase of the chiral Potts quantum chain is studied using perturbative methods. For the ℤ3-chain we present high-temperature expansions for the ground-state energy and the dispersion relations of the two single-particle states as well as two-particle states at general values of the parameters. We also present a perturbative argument showing that a large class of massive ℤn-spin quantum chains have quasiparticle spectra withn-1 fundamental particles. It is known from earlier investigations that—at special values of the parameters—some of the fundamental particles exist only for limited ranges of the momentum. In these regimes our argument is not rigorous, as one can conclude from a discussion of the radius of convergence of the perturbation series. We also derive correlation functions from a perturbative evaluation of the ground-state for the ℤ3-chain. In addition to an exponential decay we observe an oscillating contribution. The oscillation length seems to be related to the asymmetry of the dispersion relations. We show that this relation is exact at special values of the parameters for general ℤn using a form factor expansion.

Within the Ultra-relativistic Quantum Molecular Dynamics model (UrQMD) coupled with nucleon coalescence model and Mini-Spanning-Tree model, the yields of light nuclei have been stimulated in Au + Au collisions over an energy range of sNN=2.0∼7.7GeV and the momentum correlation functions of light nuclei pairs have been calculated by both the Lednický-Lyuboshitz and the Correlation After Burner methods. We compare the yields of light nuclei and their momentum correlation functions at midrapidity in this energy region with experimental data. It is found that there are differences between the results of the two models, and the coalescence method seems less valid at low collision energy. Furthermore, both the peak values of proton-proton correlation functions and the transition point of elliptic flows from out-of-plane to in-plane emission show a turning point around 3-4 GeV, which suggests that there is a relation between momentum correlation function and collective flow of particles.

We have measure the correlation of microwave field and intensity versus polarization of the source and detector in a ensemble of randomly positioned alumina spheres. Unlike correlation functions in space, frequency, and time, for which the corresponding parameter may be unbounded and the field correlation function vanishes asymptotically with increasing parameter shift, the polarization variable is of finite range and the field correlation function vanishes when either the source or detector is rotated by 90 degrees. This facilitates an unambiguous experimental separation of the intensity correlation function into three components, with a form that is independent of the closeness to the localization threshold. The polarization correlation function depends upon the underlying field correlation function in a manner analogous to that found for the intensity correlation function with displacement [1]. The first component of the intensity correlation function is the product of the square of the field correlation function with shift of either source or detector and dominates intensity fluctuations. The field correlation function is simply the cosine of the angular shift of the polarization of the electromagnetic field. The second component is associated with long-range intensity correlation. It is proportional to the sum of the square of the field correlation function with respect to variation of the source and detector. The third component of the polarization correlation function gives rise to universal conductance fluctuations. It is the sum of a multiplicative and additive term involved in the short and long-range contributions to the correlation function and also includes a constant term, which is independent of polarization. Thus, the functional form of the intensity correlation function with polarization is remarkably simple. It is determined exclusively by the cosine of the angular shift of the polarization of the electric field at the source and detector.

Two particle correlations are used to extract information about the characteristic size of the system for proton-proton collisions at =900 GeV measured by the ALICE (A Large Ion Collider Experiment) detector at CERN. The correlation functions obtained show the expected Bose-Einstein effect for identical particles, but there are also long range correlations present that shift the baseline from the expected flat behavior. A possible source of these correlations is the conservation of energy and momentum, especially for small systems, where the energy available for particle production is limited. A new technique, first introduced by the STAR collaboration, of quantifying these long range correlations using energy-momentum conservation considerations is presented here. It is shown that the baseline of the two particle correlation function can be described using this technique.

view Abstract Citations (30) References (25) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Cluster-cluster clustering Barnes, J. ; Dekel, A. ; Efstathiou, G. ; Frenk, C. S. Abstract The cluster correlation function xic(r) is compared with the particle correlation function, xi(r) in cosmological N-body simulations with a wide range of initial conditions. The experiments include scale-free initial conditions, pancake models with a coherence length in the initial density field, and hybrid models. Three N-body techniques and two cluster-finding algorithms are used. In scale-free models with white noise initial conditions, xic and xi are essentially identical. In scale-free models with more power on large scales, it is found that the amplitude of xic increases with cluster richness; in this case the clusters give a biased estimate of the particle correlations. In the pancake and hybrid models (with n = 0 or 1), xic is steeper than xi, but the cluster correlation length exceeds that of the points by less than a factor of 2, independent of cluster richness. Thus the high amplitude of xic found in studies of rich clusters of galaxies is inconsistent with white noise and pancake models and may indicate a primordial fluctuation spectrum with substantial power on large scales. Publication: The Astrophysical Journal Pub Date: August 1985 DOI: 10.1086/163381 Bibcode: 1985ApJ...295..368B Keywords: Astronomical Models; Correlation; Cosmology; Galactic Clusters; Algorithms; Many Body Problem; Mass Distribution; White Noise; Astrophysics full text sources ADS |

Main disadvantage of a multicarrier communication system is high peak to average power ratio (PAPR) of the transmitted signal. The high PAPR causes the performance degradation due to nonlinear distortion in the high power amplifier (HPA). PAPR value is closely depends on transmitted power and correlation properties of the user’s spreading code. High peak and low average value of the transmitted power increases the PAPR. On the other side high auto correlation function (ACF) value and low cross correlation function (CCF) value of the spreading code also increases the PAPR. But to eliminate the multiple access interference (MAI) in receiver end, ACF should be peak and CCF should be posses zero for all time shifts. So, there is a conflicting nature of PAPR and bit error rate (BER). That’s why an exhaustive effort has been made in this paper for proper distribution of transmitted power within an acceptable range of peak transmitted power and evaluates the new spreading codes using Genetic Algorithms (GA). In general, to obtain optimum PAPR reduction using GA, total searching time to find out the proper amplitude and phase parameters must be accomplished. Simulation results show that PAPR and BER performance using this proposed technique is better than conventional network.

Renormalization-group (RG) methods developed previously for the study of the growth of order in unstable systems are extended to treat the spinodal decomposition of the two-dimensional spin-exchange kinetic Ising model. The conservation of the order parameter and fixed-length sum rule are properly preserved in the theory. Various correlation functions in both coordinate and momentum space are calculated as functions of time. The scaling function for the structure factor is extracted. We compare our results with direct Monte Carlo (MC) simulations and find them in good agreement. The time rescaling parameter entering the RG analysis is temperature dependent, as was determined in previous work through a RG analysis of MC simulations. The results exhibit a long-time logarithmic growth law for the typical domain size, both analytically and numerically. In the time region where MC simulations have previously been performed, the logarithmic growth law can be fitted to a power law with an effective exponent. This exponent is found to be in excellent agreement with the result of MC simulations. The logarithmic growth law agrees with a physical model of interfacial motion which involves an interplay between the local curvature and an activated jump across the interface.

By employing the spin-boson model in a dense limit of environmental modes, quantum entanglement and correlation of sub-Ohmic and Ohmic baths for dissipative quantum phase transitions are numerically investigated based on the variational principle. With several measures borrowed from quantum information theory, three different types of singularities are found for the first-order, second-order, and Kosterlitz-Thouless phase transitions, respectively, and the values of transition points and critical exponents are accurately determined. Besides, the scaling form of the quantum discord in the Ohmic case is identified, quite different from that in the sub-Ohmic regime. In a two-spin model, two distinct behaviors of the quantum discord are uncovered: one is related to the quantum entanglement between two spins and the other is decided by the correlation function in the position space rather than the entanglement.

Temporal evolution characteristics and prediction methods of spatial correlation function shape of rough soil surfaces

We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

We perform a model-independent, non-perturbative investigation of two-point and three-point finite-volume correlation functions in the energy regime where two-particle states can go on-shell. We study three-point functions involving a single incoming particle and an outgoing two-particle state, relevant, for example, for studies of meson decays (e.g., B-to-pi Kll) or meson photo production (e.g., pi gamma-to-pi pi). We observe that, while the spectrum solely depends on the on-shell scattering amplitude, the correlation functions also depend on off-shell amplitudes. The main result of this work is a generalization of the Lellouch-Luscher formula relating matrix elements of currents in finite and infinite spatial volumes. We extend that work by considering a theory with multiple, strongly-coupled channels and by accommodating external currents which inject arbitrary four-momentum as well as arbitrary angular momentum. The result is exact up to exponentially suppressed corrections governed by the pion mass times the box size. We also apply our master equation to various examples, including the two processes mentioned above as well as examples where the final state is an admixture of two open channels.

We consider the non-equilibrium dynamics after a sudden quench of the magnetic field in the transverse field Ising chain starting from excited states of the pre-quench Hamiltonian. We prove that stationary values of local correlation functions can be described by the generalized Gibbs ensemble. Then we study the full time evolution of the transverse magnetization by means of stationary phase methods. The equal-time two-point longitudinal correlation function is analytically derived for a particular class of excited states for quenches within the ferromagnetic phase, and studied numerically in general. The full time dependence of the entanglement entropy of a block of spins is also obtained analytically for the same class of states and for arbitrary quenches.

We give new proofs of a global and a local property of the integrals which compute closed string theory amplitudes at genus zero. Both kinds of properties are related to the newborn theory of single-valued periods, and our proofs provide an intuitive understanding of this relation. The global property, known in physics as the KLT formula, is a factorisation of the closed string integrals into products of pairs of open string integrals. We deduce it by identifying closed string integrals with special values of single-valued correlation functions in two dimensional conformal field theory, and by obtaining their conformal block decomposition. The local property is of number theoretical nature. We write the asymptotic expansion coefficients as multiple integrals over the complex plane of special functions known as single-valued hyperlogarithms. We develop a theory of integration of single-valued hyperlogarithms, and we use it to demonstrate that the asymptotic expansion coefficients belong to the ring of single-valued multiple zeta values.

The typical method for obtaining a power spectrum from values of the correlation function is through the FFT (fast Fourier transform). A novel approach to improving the FFT spectrum when it is corrupted by noise is presented. The method minimises a relative entropy functional involving spectral densities and requires knowledge only of the variance of the noise that is corrupting the FFT spectrum.