Functional Integral Method Research Articles

Straight-line path approximation for high energy elastic and inelastic scattering in quantum gravity

The asymptotic behavior of Planck energy elastic and inelastic amplitudes in quantum gravity is studied by means of the functional integration method. A straight-line path approximation is used to calculate the functional integrals which arise. Closed relativistically invariant expressions are obtained for the two "nucleons" elastic and inelastic amplitudes including the radiative corrections. Under the requirement of "softness" of the secondary gravitons a Poisson distribution for the number of particles emitted in the collision is found.

Quantum cavitation in liquid helium: dissipation effects

We have investigated the quantum-to-thermal cavitation crossover temperature T ∗ in liquid helium using a functional–integral method in conjunction with a density functional description of the liquid. Dissipation is taken into account introducing a semiphenomenological Rayleigh's dissipation function. We have found that a rather small dissipation decreases T ∗ sizeably, which is a possible explanation why recent experiments on 3He have not yet found clear evidence of quantum cavitation at temperatures below the T ∗ predicted by calculations which neglect it.

Normalized vacuum states in [formula omitted] supersymmetric Yang–Mills quantum mechanics with any gauge group

We study the question of existence and the number of normalized vacuum states in N=4 super-Yang–Mills quantum mechanics for any gauge group. The mass deformation method is the simplest and clearest one. It allowed us to calculate the number of normalized vacuum states for all gauge groups. For all unitary groups, # vac=1, but for the symplectic groups [starting from Sp(6) ], for the orthogonal groups [starting from SO(8)] and for all the exceptional groups, it is greater than one. We also discuss at length the functional integral method. We calculate the “deficit term” for some non-unitary groups and predict the value of the integral giving the “principal contribution”. The issues like the Born–Oppenheimer procedure to derive the effective theory and the manifestation of the localized vacua in the asymptotic effective wave functions are also discussed.

Statistical properties of speckle distributions in resonant secondary emission

Quantitative analysis of speckle distributions, i.e., intensity fluctuations, in resonant secondary emission is a powerful tool to study quantum coherence in a wide range of optically excited systems. Finite directional or temporal resolution and any instability in the setup will necessarily reduce the fluctuations which would be misinterpreted as loss of coherence. We discuss the consequences of this averaging and show how the amount of averaging can be extracted from histograms of the speckle intensity and how it can be corrected for. Using functional integration methods, analytic expressions for the intensity distribution in experiments with finite directional or temporal resolution are derived. These should help to make the quantitative speckle analysis a widely used technique for measuring quantum coherence optically.

A warning on proving gauge independence using the functional integral method

We show that the proof for gauge independence of Green functions by functional integral methods is not always reliable because using similar formalism we could show that the fermionic two-point function in U(1) gauge theory is gauge independent, which is an incorrect result. A two-dimensional integral with similar structure is analysed and a possible explanation for this flaw is given.

ON THE ENTROPY CHANGE FOR A FLUID CONTAINING SWIMMING MICRO-ORGANISMS

We consider the two-dimensional hydrodynamical theory of nearly circular biological objects (cilia) in the creeping approximation, focusing on the time rate of entropy production in the fluid as calculated by means of functional integration methods. It is pointed out that the formalism leads to an entropy change in the fluid which is always negative. This change has, for thermodynamic reasons, to be compensated for, by a change of entropy for the micro-organism itself which is positive, and which is large enough to outweigh the entropy change in the fluid. We consider also briefly the generalization to nonuniform closed objects.

Finite temperature magnetic properties of the PrCo 2 intermetallic compound

In this work we calculate in a quantitative way the temperature dependence of localized and itinerant magnetizations of the PrCo 2 intermetallic compound. In the model we start from a two-sublattice Hamiltonian which includes itinerant electrons, localized states and the crystal-field effects on the 4f levels of rare-earth ion. In the calculation we used the functional integral method to treat the electron–electron interaction and the molecular field approximation to deal with the indirect interaction between localized states.

ζ-function regularization, the multiplicative anomaly, and finite temperature quantum field theory

We discuss the role of the multiplicative anomaly for a complex scalar field at finite temperature and density. It is argued that physical considerations must be applied to determine which of the many possible expressions for the effective action obtained by the functional integral method is correct. This is done by first studying the non-relativistic field where the thermodynamic potential is well-known. The relativistic case is also considered. We emphasize that the role of the multiplicative anomaly is not to lead to new physics, but rather to preserve the equality among the various expressions for the effective action.

Molecular dynamics study of the tautomeric equilibrium in the Mannich base

The density functional theory ab initio quantum mechanical and molecular dynamics thermodynamic integration methods have been used to study the intramolecular proton transfer equilibrium in 2-[N,N-dimethylaminomethyl]-3,4,6-trichlorophenol. The model of slow proton transfer reaction was applied, where the geometry and charge data were linearly interpolated between two states calculated at the Becke3LYP 6-31G(d,p) level. This avoids the difficulties connected with the different time scales of proton transfer reaction and solvent relaxation processes. The calculated free energy differences obtained from ab initio calculations including the Tomasi model of the solvent reaction field (1.16 kcal mol−1) and from ab initio plus molecular dynamic thermodynamic integration calculations (1.7 ± 1.8 kcal mol−1) are in agreement with the experimental value 0.12 ± 0.02 kcal mol−1.

On the nature of the magnetic phase transition of the HoCo2 intermetallic

In this work we calculate the itinerant and localized magnetization curves of the Laves phase intermetallic compound HoCo2 and discuss the nature of its magnetic phase transition. The numerical results were calculated from the self-consistent solution of magnetic coupled equations obtained through the combination of functional integral methods with molecular field approximation.

Molecular-dynamics approach to itinerant magnetism with complex magnetic structures

A molecular-dynamics (MD) theory of itinerant magnetism which describes the complex magnetic systems with a large number of atoms in a unit cell is proposed on the basis of the isothermal molecular-dynamics method and the functional integral method. The MD approach allows us to predict automatically the complex magnetic structure with a few hundred atoms in a unit cell at finite temperatures. It is demonstrated by the numerical calculations for bcc Fe that the MD approach describes the second-order phase transition as a function of temperature because of a self-consistent effective medium in the theory. The application of the theory to the fcc transition metals with the use of 108 atoms and 256 atoms shows the existence of various complex magnetic structures for the d-electron numbers between 6.0 and 7.0 and the existence of strong spin frustrations in $\ensuremath{\gamma}$-Fe because of the competing magnetic interactions.

Order parameter quantum fluctuations in a two-dimensional system of mesoscopic Josephson junctions

The boson lattice Hubbard model is used to study the role of quantum fluctuations of the phase and local density of the superfluid component in establishing a global superconducting state for a system of mesoscopic Josephson junctions or grains. The quantum Monte Carlo method is used to calculate the density of the superfluid component and fluctuations in the number of particles at sites of the two-dimensional lattice for various average site occupation numbers n0 (i.e., number of Cooper pairs per grain). For a system of strongly interacting bosons, the phase boundary of the ordered superconducting state lies above the corresponding boundary for its quasiclassical limit—the quantum XY-model—and approaches the latter as n0 increases. When the boson interaction is weak in the boson Hubbard model (i.e., the quantum fluctuations of the phase are small), the relative fluctuations of the order parameter modulus are significant when n0<10, while quantum fluctuations in the phase are significant when n0<8; this determines the region of mesoscopic behavior of the system. Comparison of the results of numerical modeling with theoretical calculations show that mean-field theory yields a qualitatively correct estimate of the difference between the phase diagrams of the quantum XY-model and the Hubbard model. For a quantitative estimate of this difference the free energy and thermodynamic averages of the Hubbard model are expanded in powers of 1/n0 using the method of functional integration.

Dynamical theory of thermal spin fluctuations in metallic ferromagnets

A self-consistent dynamical theory of thermal spin fluctuations is developed which describes their spatial correlation. It is based on the functional integral method and utilizes the quadratic representation for the electron free energy in a fluctuating exchange field with renormalized susceptibilities allowing for the interaction of various spin fluctuation modes. Interpolation between the single-site and homogeneous susceptibilities is used, where these susceptibilities are found self-consistently. The average over fluctuations takes account of both long-wavelength and local excitations. A closed system of equations is formed for both unknown quantities: the magnetization and the mean-square exchange field at a site. The basic characteristics of a specific magnet are the density of electron states and the atomic magnetic moment at T=0. A method is proposed for separating the relatively slow thermal-spin fluctuations from the rapid zero-spin fluctuations forming the ground state of the magnets. At T=0 we have a system of equations of mean field theory. The temperature excites thermal spin fluctuations, which are described by taking account of correlation in time and space. The magnetization, susceptibility, magnitude of the spin fluctuations and their distribution over momenta, and the degree of magnetic short-range order in iron are calculated as functions of the temperature in the ferromagnetic and paramagnetic phases, and also at the transition between them, the Curie temperature.

Effective action and collective bose-excitations in the T-J-model

The two-dimensional (2D) t-T-model is investigated using the functional integration method. The effective action is obtained, and the spectrum of collective Bose-excitations in the superconductive phase of the system is calculated both in the phase-transition vicinity (Ginsburg-Landau region |T−Tc| ≪ Tc) and in the low-temperature region T ≪ Tc. Bibliography: 26 titles.

Magnetic Exchange Coupling in Ferromagnet/Superconductor/Ferromagnet Multilayers

The possibility of magnetic exchange coupling between two ferromagnets (F) separated by a superconductor (S) spacer is analyzed using the functional integral method. For this coupling to happen three basic conditions need to be satisfied. First, an indirect exchange coupling between the ferromagnets must exist when the superconductor is in its normal state. Second, superconductivity must not be destroyed due to the proximity to ferromagnetic boundaries. Third, roughness of the $F/S$ interfaces must be small. The appearance of the superconducting gap causes a reduction of the indirect exchange coupling existent in the normal state. This reduction is temperature dependent, being weaker near the critical temperature and stronger at zero temperature.

Finite-temperature theory of amorphous metallic magnetism with vector spins

A finite temperature theory of amorphous metallic magnetism which takes into account vector spins is developed to study noncollinear magnetism in amorphous Fe. This theory is based on the functional integral method for thermal spin fluctuations and the distribution function method for local magnetic moments with structural disorder. The numerical results at 35 K show up the existence of an isotropic spin-glass in amorphous Fe. When the d electron number n d is increased, the spin-glass changes toa noncollinear ferromagnet at n d = 7.40 and finally to a collinear ferromagnet beyond n d = 7.47.

Temperature dependence of random local moments and giant magnetoresistance of Fe/Cr multilayers

Finite-temperature properties of (Fe) 3/(Cr) 4 multilayers have been discussed by taking into account the effects of spin fluctuations with the use of the static functional integral method. The calculated temperature dependence of local moments of Fe and Cr, which are assumed to be randomly distributed at interfaces, deviates significantly from the Brillouin function. This unusual behavior of local moments is shown to reflect on the temperature dependence of the giant magnetoresistance.

Molecular dynamics approach to itinerant magnetism with complex magnetic structure

Molecular dynamics method which automatically determines complex magnetic structures of itinerant electron systems as well as their electronic structures is presented on the basis of the functional integral method. The method is tested for BCC Fe, and is applied to the FCC transition metals. The results for FCC transition metals with use of 108 atoms in a cell show a complex antiferromagnetic (AF) structure for the d electron number n d = 6.0, the first-kind AF for n d = 6.2, the helical structure with Q = (0, 1 3 , 1)2π/a for n d = 6.4 , the helical structure with the same Q but with modulated amplitudes of local moments for n d = 6.6 at 50 K.

Slave-Boson Functional-Integral Approach to the Hubbard Model with Orbital Degeneracy

A slave-boson functional-integral method has been developed for the Hubbard model with arbitrary, orbital degeneracy $D$. Its saddle-point mean-field theory is equivalent to the Gutzwiller approximation, as in the case of single-band Hubbard model. Our theory is applied to the doubly degenerate ($D = 2$) model, and numerical calculations have been performed for this model in the paramagnetic states. The effect of the exchange interaction on the metal-insulator (MI) transition is discussed. The critical interaction for the MI transition is analytically calculated as functions of orbital degeneracy and electron occupancy.

Molecular dynamics method to itinerant magnets with complex magnetic structure

A molecular dynamics method which allows us to determine the magnetic structures of itinerant magnets with a few hundred atoms in a unit cell has been developed on the basis of the functional integral method. The method yields the generalized Hartree–Fock approximation at the ground state, and describes the finite temperature magnetism accompanied by the second order phase transition. The results for fcc transition metals with the use of 108 atoms in a unit cell show a complex antiferromagnetic (AF) structure for the d electron number nd=6.0, the first-kind AF for nd=6.2, the helical structure with Q=(0,1/3,1)2π/a for nd=6.4, the helical structure with the same Q but with modulated amplitudes of local moments for nd=6.6. A helical structure with Q=(0,1/3,2/3)2π/a is obtained for γ-Fe.