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Path Integral (path + integral)

Distribution by Scientific Domains
Physics and Astronomy75%

Selected Abstracts

Equation of State of Strongly Coupled Quark,Gluon Plasma , Path Integral Monte Carlo Results

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 7-8 2009
V.S. Filinov
Abstract A strongly coupled plasma of quark and gluon quasiparticles at temperatures from 1.1Tc to 3Tc is studied by path integral Monte Carlo simulations. This method extends previous classical nonrelativistic simulations based on a color Coulomb interaction to the quantum regime. We present the equation of state and find good agreement with lattice results. Further, pair distribution functions and color correlation functions are computed indicating strong correlations and liquid-like behavior (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Thermodynamics of Hydrogen and Hydrogen-Helium Plasmas: Path Integral Monte Carlo Calculations and Chemical Picture

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 3-4 2005
V. S. Filinov
Abstract In this paper we study thermodynamic properties of hydrogen and hydrogen-helium mixtures with the help of the direct path integral Monte Carlo simulations. The results are compared with available theoretical and experimental methods based, in particular, on chemical picture. We investigate the effects of temperature ionization in low-density hydrogen plasma. We also present a number of calculated isotherms for hydrogenhelium mixture with the mass concentration of helium Y = 0.234 in the range from 104 K to 2 · 105 K. In the density region where a sharp conductivity rise have been observed experimentally the simulations give indications for one or two plasma phase transitions, in accordance with earlier theoretical predictions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Thermodynamic Properties and Plasma Phase Transition in dense Hydrogen

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 5-6 2004
V. S. Filinov
Abstract The internal energy and equation of state of dense hydrogen are investigated by direct path integral Monte Carlo method simulations which are further improved in comparison to our previous results. Data for four isotherms , T = 10, 000K, 30, 000K, 50, 000K, and 100, 000K , are presented. For T = 10, 000K it is shown that the internal energy is lowered due to droplet formation for densities of the order 1023cm,3 giving direct support for the existence of a plasma phase transition in megabar hydrogen. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Coherent state path integral and super-symmetry for condensates composed of bosonic and fermionic atoms

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 9-10 2007
B. Mieck
Abstract A super-symmetric coherent state path integral on the Keldysh time contour is considered for bosonic and fermionic atoms which interact among each other with a common short-ranged two-body potential. We investigate the symmetries of Bose-Einstein condensation for the equivalent bosonic and fermionic constituents with the same interaction potential so that a super-symmetry results between the bosonic and fermionic components of super-fields. Apart from the super-unitary invariance U(L | S) of the density terms, we specialize on the examination of super-symmetries for pair condensate terms. Effective equations are derived for anomalous terms which are related to the molecular- and BCS- condensate pairs. A Hubbard-Stratonovich transformation from ,Nambu'-doubled super-fields leads to a generating function with super-matrices for the self-energy whose manifold is given by the orthosympletic super-group Osp(S,S | 2L). A nonlinear sigma model follows from the spontaneous breaking of the ortho-symplectic super-group Osp(S,S | 2L) to the coset decomposition Osp(S,S | 2L) \ U(L | S), U(L | S). The invariant subgroup U(L | S) for the vacuum or background fields is represented by the density terms in the self-energy whereas the super-matrices on the coset space Osp(S,S | 2L) \ U(L | S) describe the anomalous molecular and BCS- pair condensate terms. A change of integration measure is performed for the coset decomposition Osp(S,S | 2L) \ U(L | S) , U(L | S), including a separation of density and anomalous parts of the self-energy with a gradient expansion for the Goldstone modes. The independent anomalous fields in the actions can be transformed by the inverse square root of the metric tensor of Osp(S,S | 2L) \ U(L | S) so that the non-Euclidean integration measure with super-Jacobi-determinant can be removed from the coherent state path integral and Gaussian-like integrations remain. The variations of the independent coset fields in the effective actions result in classical field equations for a nonlinear sigma model with the anomalous terms. The dynamics of the eigenvalues of the coset matrices is determined by Sine-Gordon equations which have a similar meaning for the dynamics of the molecular- and BCS-pair condensates as the Gross-Pitaevskii equation for the coherent wave function in BEC phenomena. [source]

Semiclassical path integral theory of a double-well potential in an electric field

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2006
Theodosios G. Douvropoulos
Abstract A recently published methodology based on semiclassical path integral (SCPI) theory was implemented in the case of a model of a double-well potential perturbed by a static electric field, with application to the inversion frequency of NH3. This model was chosen as an idealized case for testing of the present approach, as well as for quantum mechanical models that might be applied in the future. The calculations were concerned with the variation of the frequency of inversion as a function of field strength, F, and of distance, xf (from the symmetric point xo = 0), where the field is "felt." It is found that this variation occurs sharply in very small regions of values of these parameters, and the system switches from internal oscillation to diffusion to the continuum. The fact that the theory is in analytic form allows the extraction of results and conclusions not only at the full SCPI level, but also at the Jeffreys,Wentzel,Kramers,Brillouin (JWKB) level. Comparison shows that the discrepancy sets in as the field strength increases, in accordance with the well-known limitations of the JWKB method regarding its dependence on the degree of variation of the potential as a function of position. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source]

Koopman-von Neumann formulation of classical Yang-Mills theories: I

ANNALEN DER PHYSIK, Issue 3 2006
P. Carta
Abstract In this paper we present the Koopman-von Neumann (KvN) formulation of classical non-Abelian gauge field theories. In particular we shall explore the functional (or classical path integral) counterpart of the KvN method. In the quantum path integral quantization of Yang-Mills theories concepts like gauge-fixing and Faddeev-Popov determinant appear in a quite natural way. We will prove that these same objects are needed also in this classical path integral formulation for Yang-Mills theories. We shall also explore the classical path integral counterpart of the BFV formalism and build all the associated universal and gauge charges. These last are quite different from the analog quantum ones and we shall show the relation between the two. This paper lays the foundation of this formalism which, due to the many auxiliary fields present, is rather heavy. Applications to specific topics outlined in the paper will appear in later publications. [source]

Recovering acoustic reflectivity using Dirichlet-to-Neumann maps and left- and right-operating adjoint propagators

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2005
M. W. P. Dillen
SUMMARY Constructing an image of the Earth subsurface from acoustic wave reflections has previously been described as a recursive downward redatuming of sources and receivers. Most of the methods that have been presented involve reflectivity and propagators associated with one-way wavefield components. In this paper, we consider the reflectivity relation between two-way wavefield components, each a solution of a Helmholtz equation. To construct forward and inverse propagators, and a reflection operator, the invariant-embedding technique is followed, using Dirichlet-to-Neumann maps. Employing bilinear and sesquilinear forms, the forward- and inverse-scattering problems, respectively, are treated analogously. Through these mathematical constructs, the relationship between a causality radiation condition and symmetry, with respect to a bilinear form, is associated with the requirement of an anticausality radiation condition with respect to a sesquilinear form. Using reciprocity, sources and receivers are redatumed recursively to the reflector, employing left- and right-operating adjoint propagators. The exposition of the proposed method is formal, that is numerical applications are not derived. The key to applications lies in the explicit representation, characterization and approximation of the relevant operators (symbols) and fundamental solutions (path integrals). Existing constructive work which could be applied to the proposed method are referred to in the text. [source]