Journal articles: 'Free energy perturbation theory'

1

Mon, K. K. "Lower free energy bound for hard-sphere perturbation theory." Journal of Chemical Physics 116, no. 21 (June 2002): 9392–94. http://dx.doi.org/10.1063/1.1472507.

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Kalikmanov, V. I., R. Hagmeijer, and C. H. Venner. "Statistical Mechanical Perturbation Theory of Solid–Vapor Interfacial Free Energy." Journal of Physical Chemistry C 121, no. 12 (March 17, 2017): 6868–73. http://dx.doi.org/10.1021/acs.jpcc.7b01331.

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3

Vilseck, Jonah Z., Julian Tirado-Rives, and William L. Jorgensen. "Determination of partial molar volumes from free energy perturbation theory." Physical Chemistry Chemical Physics 17, no. 13 (2015): 8407–15. http://dx.doi.org/10.1039/c4cp05304d.

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Free Energy Perturbation calculations are employed to determine free energies of solvation (ΔG_solv) for benzene and benzene-derivatives at elevated pressures. Absolute and relative partial molar volumes are determined as the pressure derivative of ΔG_solv.

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4

Topor, Nadia. "Perturbation Method for Boundary S-Matrix in 2D Quantum Field Theory." Modern Physics Letters A 12, no. 38 (December 14, 1997): 2951–62. http://dx.doi.org/10.1142/s0217732397003071.

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We develop a perturbation theory for evaluating the boundary S-matrix in 2D quantum field theory. We apply this approach to calculate the one-loop boundary S-matrix for the elementary particle of the sine–Gordon model with a boundary interaction. Our perturbative result agrees with the exact expression of the S-matrix conjectured by Goshal; it also allows us to derive the perturbative relation between the parameter ϑ in the S-matrix and the free parameter M in the boundary action, in the particular case in which its other free parameter φ0 is zero.

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5

PERIWAL, VIPUL. "FREE ENERGY DECREASES ALONG WILSON RENORMALIZATION GROUP TRAJECTORIES." Modern Physics Letters A 10, no. 21 (July 10, 1995): 1543–48. http://dx.doi.org/10.1142/s0217732395001666.

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The free energy is shown to decrease along Wilson renormalization group trajectories, in a dimension-independent fashion, for d>2. The argument assumes the monotonicity of the cutoff function, and positivity of a spectral representation of the two-point function. The argument is valid for all orders in perturbation theory.

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Tobias, Douglas J., and Charles L. Brooks. "Calculation of free energy surfaces using the methods of thermodynamic perturbation theory." Chemical Physics Letters 142, no. 6 (December 1987): 472–76. http://dx.doi.org/10.1016/0009-2614(87)80646-2.

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7

Nieto, Agustin. "Perturbative QCD at High Temperature." International Journal of Modern Physics A 12, no. 08 (March 30, 1997): 1431–64. http://dx.doi.org/10.1142/s0217751x97001043.

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Recent developments of perturbation theory at finite temperature based on effective field theory methods are reviewed. These methods allow the contributions from the different scales to be separated and the perturbative series to be reorganized. The construction of the effective field theory is shown in detail for ϕ4 theory and QCD. It is applied to the evaluation of the free energy of QCD at order g5 and the calculation of the g6 term is outlined. Implications for the application of perturbative QCD to the quark–gluon plasma are also discussed.

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8

ABE, MITSUO, and NOBORU NAKANISHI. "NONRENORMALIZABILITY MAY BE SUPERFICIAL IN THE COVARIANT FORMALISM OF QUANTUM GRAVITY." Modern Physics Letters A 10, no. 21 (July 10, 1995): 1501–6. http://dx.doi.org/10.1142/s0217732395001629.

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It is pointed out that the nonrenormalizability of quantum Einstein gravity may be caused by the inadequacy of the conventional perturbative approach. It is more reasonable to reconsider the problem in the light of a newly proposed perturbative scheme, which is free of the ad hoc assumption on which the conventional perturbation theory is based. It is explicitly shown that there is a gravity-theory example which is nonrenormalizable in the usual sense but completely finite if the new perturbative scheme is applied.

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9

MA, BO-QIANG, and JI SUN. "NEW SCALING VARIABLE FROM LIGHT-CONE PERTURBATION THEORY." International Journal of Modern Physics A 06, no. 03 (January 30, 1991): 345–63. http://dx.doi.org/10.1142/s0217751x91000216.

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We argue from both the quark language and the free field light-cone expansion in light-cone perturbation theory that the constraint of overall “energy” conservation in deep inelastic lepton-nucleon scattering yields a similar new scaling variable xp, which reduces to the Weizmann variable, the Bloom-Gilman variable and the Bjorken variable at some approximations. The xp rescaling is expected to be a good scaling variable, and hence gives strong power-law type corrections to the deviations of Bjorken scaling. An understanding of this xp rescaling from both the free field operator product expansion (OPE) and the ordinary OPE is also given, indicating it is likely a higher order effect in the coefficient functions, i.e. it does not belong to the higher twist effect. Therefore this xp rescaling is likely a new effect contributing to the power-law type corrections.

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10

Greeff, C. W. "Tests of Monte Carlo perturbation theory for the free energy of liquid copper." Journal of Chemical Physics 128, no. 18 (May 14, 2008): 184104. http://dx.doi.org/10.1063/1.2917355.

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11

Cinal, M., S. Olszewski, and T. Kwiatkowski. "Correlation energy of the free‐electron pair in the second‐order perturbation theory." Journal of Chemical Physics 98, no. 2 (January 15, 1993): 1262–70. http://dx.doi.org/10.1063/1.464294.

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12

Hamza, A., Á. Vibók, G. J. Halász, and I. Mayer. "Second-order energy components in basis-set-superposition-error-free intermolecular perturbation theory." Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) 107, no. 1 (December 1, 2001): 38–47. http://dx.doi.org/10.1007/s00214-001-0299-5.

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13

Romero-Téllez, Sonia, Alejandro Cruz, Laura Masgrau, Àngels González-Lafont, and José M. Lluch. "Accounting for the instantaneous disorder in the enzyme–substrate Michaelis complex to calculate the Gibbs free energy barrier of an enzyme reaction." Physical Chemistry Chemical Physics 23, no. 23 (2021): 13042–54. http://dx.doi.org/10.1039/d1cp01338f.

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A protocol based on the free energy perturbation theory justifies the suitable use of the exponential average and provides a practical way to determine the Gibbs free energy barrier of an enzyme reaction.

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14

ALDAYA, V., M. CALIXTO, and F. F. LÓPEZ-RUIZ. "NON-CANONICAL PERTURBATION THEORY OF NONLINEAR SIGMA MODELS." Modern Physics Letters A 26, no. 02 (January 20, 2011): 127–38. http://dx.doi.org/10.1142/s0217732311034670.

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We explore the O(N)-invariant Non-Linear Sigma Model (NLSM) in a different perturbative regime from the usual relativistic-free-field one, by using non-canonical basic commutation relations adapted to the underlying O(N) symmetry of the system, which also account for the nontrivial (nonflat) geometry and topology of the target manifold.

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15

SRIVASTAVA, Y. N., O. PANELLA, and A. WIDOM. "INSTABILITY OF THE PERTURBATION THEORETICAL CHROMODYNAMIC VACUUM." International Journal of Modern Physics A 24, no. 06 (March 10, 2009): 1097–103. http://dx.doi.org/10.1142/s0217751x09043080.

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The standard model of strong interactions invokes the quantum chromodynamics (QCD) of quarks and gluons interacting within a fluid. At sufficiently small length scales, the effective interactions between the color charged particles within the fluid are thought to be weak. Short distance asymptotic freedom provides the perturbation theory basis for comparisons between QCD theory and laboratory high energy scattering experiments. It is here shown that the asymptotically free vacuum has negative dissipation implicit in the color electrical conductivity. Negative dissipation implies an asymptotically free QCD negative temperature excited state amplifier unstable to decay. The qualitative experimental implications of this instability are explored.

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16

Heit, Yonaton N., and Gregory J. O. Beran. "How important is thermal expansion for predicting molecular crystal structures and thermochemistry at finite temperatures?" Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 72, no. 4 (July 16, 2016): 514–29. http://dx.doi.org/10.1107/s2052520616005382.

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Molecular crystals expand appreciably upon heating due to both zero-point and thermal vibrational motion, yet this expansion is often neglected in molecular crystal modeling studies. Here, a quasi-harmonic approximation is coupled with fragment-based hybrid many-body interaction calculations to predict thermal expansion and finite-temperature thermochemical properties in crystalline carbon dioxide, ice Ih, acetic acid and imidazole. Fragment-based second-order Möller–Plesset perturbation theory (MP2) and coupled cluster theory with singles, doubles and perturbative triples [CCSD(T)] predict the thermal expansion and the temperature dependence of the enthalpies, entropies and Gibbs free energies of sublimation in good agreement with experiment. The errors introduced by neglecting thermal expansion in the enthalpy and entropy cancel somewhat in the Gibbs free energy. The resulting ∼ 1–2 kJ mol−1errors in the free energy near room temperature are comparable to or smaller than the errors expected from the electronic structure treatment, but they may be sufficiently large to affect free-energy rankings among energetically close polymorphs.

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17

FERNÁNDEZ, FRANCISCO M. "HIGH-TEMPERATURE SERIES FOR THERMODYNAMIC FUNCTIONS." Journal of Theoretical and Computational Chemistry 02, no. 01 (March 2003): 1–5. http://dx.doi.org/10.1142/s0219633603000343.

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We propose a high-temperature expansion for thermodynamic functions. As an example we calculate the free energy for a restricted plane rigid rotor and compare present approach with perturbation theory.

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18

Ullmann, R. Thomas, and G. Matthias Ullmann. "A Generalized Free Energy Perturbation Theory Accounting for End States with Differing Configuration Space Volume." Journal of Physical Chemistry B 115, no. 3 (January 27, 2011): 507–21. http://dx.doi.org/10.1021/jp1093838.

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19

CRUCEAN, COSMIN, and RADU RACOCEANU. "REDUCTION FORMALISM FOR DIRAC FERMIONS ON DE SITTER SPACE–TIME." International Journal of Modern Physics A 23, no. 07 (March 20, 2008): 1075–87. http://dx.doi.org/10.1142/s0217751x08039475.

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The reduction formulas for Dirac fermions is derived using the exact solutions of free Dirac equation on de Sitter space–time. In the framework of the perturbation theory one studies the Green functions and derives the scattering amplitude in the first orders of perturbation theory.

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20

Lee, Seong-Chan, Zi-Hong Yoon, and Soon-Chul Kim. "Density profiles of fluids in some special symmetries." Canadian Journal of Physics 73, no. 7-8 (July 1, 1995): 432–39. http://dx.doi.org/10.1139/p95-062.

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A free-energy-functional approximation based on a semi-empirical method is proposed. The main advantage of the free-energy-functional approximation is its accuracy compared with other models and its relative simplicity compared with other well-known weighted-density approximations. The free-energy-functional approximation is applied to predict the density profiles of the hard-sphere fluids and the Lennard–Jones fluids in some special symmetries. For the density profiles near a hard flat wall, the results reproduced the hard-sphere oscillatory structures qualitatively and quantitatively. For the density profiles of hard-sphere fluids confined in a spherical cage, the results are also in a fair agreement with the computer simulations. For Lennard–Jones fluids, two kinds of density-functional perturbation theories, the density-functional mean-field theory (DFMFT) and the density-functional perturbation theory (DFPT), examined. The results show that at higher temperature the DFPT compares well with computer simulations. However, the agreement deteriorates slightly as the temperature of the Lennard–Jones fluids is reduced. These results demonstrate that both the free-energy-functional approximation and the DFPT succesfully describe the inhomogeneous properties of classical fluids.

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21

Jorgensen, William L., James F. Blake, and J. Kathleen Buckner. "Free energy of TIP4P water and the free energies of hydration of CH4 and Cl- from statistical perturbation theory." Chemical Physics 129, no. 2 (January 1989): 193–200. http://dx.doi.org/10.1016/0301-0104(89)80004-7.

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22

FRASCA, MARCO. "DUAL PERTURBATION EXPANSION FOR A CLASSICAL λϕ4 FIELD THEORY." International Journal of Modern Physics A 22, no. 07 (March 20, 2007): 1441–50. http://dx.doi.org/10.1142/s0217751x07036282.

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We prove the existence of a strong coupling expansion for a classical λϕ4 field theory in agreement with the duality principle in perturbation theory put forward in a paper: M. Frasca, Phys. Rev. A58, 3439 (1998). The leading order solution is a snoidal wave taking the place of plane waves of the free theory. We compute the first-order correction and show that higher-order terms do renormalize the leading order solution.

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23

GUPTA, V., D. V. SHIRKOV, and O. V. TARASOV. "NEW PERTURBATIVE APPROACH TO GENERAL RENORMALIZABLE QUANTUM FIELD THEORIES." International Journal of Modern Physics A 06, no. 19 (August 10, 1991): 3381–97. http://dx.doi.org/10.1142/s0217751x91001647.

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We develop further the new approach to perturbation theory for renormalizable quantum field theories (proposed some years ago) which gives renormalization-scheme-independent predictions for observable quantities. We call the resulting REnormalization-Scheme-Independent PErturba-tion theory RESIPE, for short. First, we formulate explicitly the relation of RESIPE to the renormalization group formalism for the massless one-coupling case. Then we extend this to the case where particle masses cannot be neglected. Further, we generalize the RESIPE formalism for the theory with two coupling constants. A new scheme-invariant perturbation expansion, without reference to renormalization group techniques, is given which is valid for the general case with masses, several kinematic variables and more than one coupling constant. In conclusion, we argue that the appropriately generalized RESIPE provides us with a picture of perturbative predictions, for renormalizable quantum field theories, that is free from regularization and renormalization scheme ambiguities.

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24

Choi, Hwanho, Hongsuk Kang, and Hwangseo Park. "Computational Prediction of Molecular Hydration Entropy with Hybrid Scaled Particle Theory and Free-Energy Perturbation Method." Journal of Chemical Theory and Computation 11, no. 10 (September 30, 2015): 4933–42. http://dx.doi.org/10.1021/acs.jctc.5b00325.

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25

Cataldo, Horacio M., and Carlos F. Tejero. "Perturbation theory for the free energy of classical two-dimensional solids with repulsive inverse-power interactions." Physical Review B 49, no. 22 (June 1, 1994): 16028–30. http://dx.doi.org/10.1103/physrevb.49.16028.

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26

Uzunov, Dimo I. "Fluctuation effects in metastable states near first-order phase transitions." International Journal of Modern Physics B 30, no. 21 (August 18, 2016): 1650149. http://dx.doi.org/10.1142/s0217979216501496.

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Fluctuation effects at first-order phase transitions driven by changes of other-than-temperature factors like pressure, concentration or external fields are investigated by perturbation theory. The results for the fluctuation contributions to the order parameter, the internal energy and the free energy at pre-transitional states near spinodal points of first-order phase transitions are presented to the first-nonvanishing order of the expansion parameters of the theory.

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27

Haug, Eberhard. "On Energy and Angular Distributions of Electrons in Triplet Production." Zeitschrift für Naturforschung A 40, no. 12 (December 1, 1985): 1182–88. http://dx.doi.org/10.1515/zna-1985-1202.

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The differential cross section of electron pair production in the field of free electrons (triplet production) is derived from the cross section for electron-positron bremsstrahlung exact to lowest order of perturbation theory. It is used to compute energy and angular distributions of the outcoming electrons. The results are compared with previous calculations. In particular, the accuracy of the momentum distribution according to the Borsellino approximation is discussed.

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28

NANDY, MALAY K., and JAYANTA K. BHATTACHARJEE. "MODE-COUPLING THEORY, DYNAMIC SCALING, AND TWO-DIMENSIONAL TURBULENCE." International Journal of Modern Physics B 09, no. 09 (April 20, 1995): 1081–97. http://dx.doi.org/10.1142/s0217979295000446.

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A self-consistent mode-coupling scheme, along with dynamic scaling ideas, is used to obtain a renormalized perturbation theory in the Eulerian framework from Wyld’s perturbation theory of the forced Navier-Stokes equation. For the force-correlation behaving as k−(d−4+y), the Kolmogorov and Kraichnan-Batchelor scaling spectra of two-dimensional turbulence for the inverse energy cascade, [Formula: see text] and the direct entropy cascade, [Formula: see text], are obtained for y=4 and y=6 respectively, including the logarithmic correction for the latter. Unlike the usual Eulerian formulations (e.g. the direct-interaction approximation), the theory is finite in the energy regime, while it becomes marginal in the enstrophy regime, leading to the logarithmic correction. Calculations yield C=6.447 and C′=1.923 at one-loop order, which are in exact agreement with those of field-theoretic renormalization group calculations [P. Olla, Phys. Rev. Lett. 67, 2465 (1991)]. However, a self-consistent treatment of the logarithmic scalings in E(k) and the inverse response-time yields a different value: C′=2.201. The theory is free of any external parameter; the choice of y(=4 or 6) is dictated by the condition of conserved transfer of energy or enstrophy.

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BIETENHOLZ, W., and T. STRUCKMANN. "PERFECT LATTICE PERTURBATION THEORY: A STUDY OF THE ANHARMONIC OSCILLATOR." International Journal of Modern Physics C 10, no. 04 (June 1999): 531–53. http://dx.doi.org/10.1142/s0129183199000413.

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As an application of perfect lattice perturbation theory, we construct an O(λ) perfect lattice action for the anharmonic oscillator analytically in momentum space. In coordinate space, we obtain a set of 2-spin and 4-spin couplings ∝λ, which we evaluate for various masses. These couplings never involve variables separated by more than two lattice spacings. The O(λ) perfect action is simulated and compared to the standard action. We discuss the improvement for the first two energy gaps ΔE1, ΔE2 and for the scaling quantity ΔE2/ΔE1 in different regimes of the interaction parameter, and of the correlation length. For the quartic oscillator — which corresponds to an asymptotically free theory — we also discuss a classically perfect action. The single gaps perform very well, which corresponds to a clearly improved asymptotic scaling. On the other hand, it turns out to be difficult to demonstrate an improvement for the scaling ratio.

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30

Li, Dong Lin, Ping Chen, Jian Xiong Yi, Bi Yu Tang, Li Ming Peng, and Wen Jiang Ding. "Thermal Properties of the FCC Al₃Zr : First-Principles Study." Materials Science Forum 650 (May 2010): 313–19. http://dx.doi.org/10.4028/www.scientific.net/msf.650.313.

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Ab inito density functional theory (DFT) and density function perturbation theory (DFPT) have been applied to investigate the thermal properties of the face-center-cubic (fcc) Al3Zr alloy over a wide range of pressure and temperature. Phonon dispersions were obtained at equilibrium and strained configurations by density functional perturbation theory. Using the quasiharmonic approximation for the free energy, several interesting physical quantities such as thermal Grüneisen parameter, heat capacity at constant pressure and volume, thermal expansion coefficient and entropy, as well as adiabatic bulk modulus and isothermal bulk modulus, were calculated as a function of temperature and pressure, and the variation features of these quantities were discussed in details.

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SUZUKI, HIROSHI. "THERMAL PARTITION FUNCTION OF NON-CRITICAL BOSONIC STRINGS." Modern Physics Letters A 04, no. 21 (October 20, 1989): 2085–92. http://dx.doi.org/10.1142/s0217732389002343.

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The thermal free energy of free non-critical bosonic strings in a D-dimensional spacetime is examined. By integrating (or summing) over the Weyl freedom, the free energy and the one-loop vacuum amplitude are modular invariant for any D<26. Thus the (background) Weyl invariance is realized. In the case of L→∞, where L is the compactification radius of the Weyl mode, the physical spectrum circulating in the loop becomes continuous. A connection between this continuous spectrum and the unitarity of string perturbation theory is briefly mentioned.

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HOLLANDS, STEFAN, and ROBERT M. WALD. "CONSERVATION OF THE STRESS TENSOR IN PERTURBATIVE INTERACTING QUANTUM FIELD THEORY IN CURVED SPACETIMES." Reviews in Mathematical Physics 17, no. 03 (April 2005): 227–311. http://dx.doi.org/10.1142/s0129055x05002340.

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We propose additional conditions (beyond those considered in our previous papers) that should be imposed on Wick products and time-ordered products of a free quantum scalar field in curved spacetime. These conditions arise from a simple "Principle of Perturbative Agreement": for interaction Lagrangians L1 that are such that the interacting field theory can be constructed exactly — as occurs when L1 is a "pure divergence" or when L1 is at most quadratic in the field and contains no more than two derivatives — then time-ordered products must be defined so that the perturbative solution for interacting fields obtained from the Bogoliubov formula agrees with the exact solution. The conditions derived from this principle include a version of the Leibniz rule (or "action Ward identity") and a condition on time-ordered products that contain a factor of the free field φ or the free stress-energy tensor Tab. The main results of our paper are (1) a proof that in spacetime dimensions greater than 2, our new conditions can be consistently imposed in addition to our previously considered conditions and (2) a proof that, if they are imposed, then for any polynomial interaction Lagrangian L1 (with no restriction on the number of derivatives appearing in L1), the stress-energy tensor Θab of the interacting theory will be conserved. Our work thereby establishes (in the context of perturbation theory) the conservation of stress-energy for an arbitrary interacting scalar field in curved spacetimes of dimension greater than 2. Our approach requires us to view time-ordered products as maps taking classical field expressions into the quantum field algebra rather than as maps taking Wick polynomials of the quantum field into the quantum field algebra.

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GAO, YI, YU ZHAO, and X. C. ZENG. "REEXAMINATION OF LOW ENERGY STRUCTURES OF ${\rm Au}_{4}^{-}$ AND Au4." Journal of Theoretical and Computational Chemistry 09, supp01 (January 2010): 1–7. http://dx.doi.org/10.1142/s0219633610005499.

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Low energy isomers of [Formula: see text] and Au4 were reexamined using the hybrid density functional B3LYP method and the couple-cluster method with the aug-cc-pVDZ-PP and aug-cc-pVTZ-PP basis sets. For [Formula: see text], the B3LYP method favors the zigzag isomer and the second order Moller–Plesset perturbation (MP2) total energy calculation favors the D2h rhombus isomer, whereas the couple-cluster singles and doubles with perturbative triples [CCSD(T)] level of theory favors the Y-shaped C2v isomer. The pyramid isomer is much higher in energy and could be easily excluded. The Gibbs free energy correction based on harmonic approximation suggests that the zigzag isomer is lower in free energy than the D2h rhombus isomer at 298.15 K. These results confirm that the Y-shaped C2v isomer is the global minimum at both 0 K and room temperature and is thus the major isomer to account for the experimental photoelectron spectrum. The zigzag isomer is suggested, as a minor isomer, to account for the weak second peak at 3.40 eV in the experimental photoelectron spectrum. For neutral Au4 , the zigzag isomer is more stable than D2h rhombus isomer at the B3LYP level and the D2h rhombus isomer is the global minimum on basis of all post Hartree–Fock levels of theory.

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HUANG, KERSON. "TRIVIALITY OF THE HIGGS FIELD." International Journal of Modern Physics A 04, no. 05 (March 1989): 1037–53. http://dx.doi.org/10.1142/s0217751x89000479.

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We give a critical review of the "triviality" of the λϕ4 theory, i.e., the vanishing of the renormalized self-coupling. Evidence from perturbation theory and Monte-Carlo simulations are cited. It is noted that (a) the theory is "trivial" but not entirely free, for there is spontaneous symmetry breaking; (b) perturbation theory is unreliable. Soluble examples with similar behavior are compared, in particular the Lee model and the 3D δ function potential. The latter case is especially important, for it shows that triviality is a symptom that the interaction is too singular, and suggests a cure. The import for the Higgs sector of the standard model is discussed. It is argued that, like the Fermi pseudopotential, the Higgs field is a long-wavelength approximation that should be used in lowest order perturbation theory only.

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Moffat, J. W. "Non-anticommutative quantum gravity." International Journal of Modern Physics A 30, no. 17 (June 20, 2015): 1550101. http://dx.doi.org/10.1142/s0217751x15501018.

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A calculation of the one loop gravitational self-energy graph in non-anticommutative quantum gravity reveals that graviton loops are damped by internal momentum dependent factors in the modified propagator and the vertex functions. The non-anticommutative quantum gravity perturbation theory is finite for matter-free gravity and for matter interactions.

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BELLISSARD, JEAN, and HERMANN SCHULZ-BALDES. "SCATTERING THEORY FOR LATTICE OPERATORS IN DIMENSION d ≥ 3." Reviews in Mathematical Physics 24, no. 08 (September 2012): 1250020. http://dx.doi.org/10.1142/s0129055x12500201.

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This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed Hamiltonian. For dimension d ≥ 3, the wave operator is given by an explicit formula in terms of this dilation operator, the free resolvent and the perturbation. From this formula, the scattering and time delay operators can be read off. Using the index theorem approach, a Levinson theorem is proved which also holds in the presence of embedded eigenvalues and threshold singularities.

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37

SEKE, JOSIP. "AN ELEMENTARY UNAMBIGUOUS, COMPLETE RENORMALIZATION PROCEDURE IN NONRELATIVISTIC QUANTUM ELECTRODYNAMICS." Modern Physics Letters B 13, no. 01 (January 10, 1999): 27–32. http://dx.doi.org/10.1142/s0217984999000051.

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A new unambiguous, complete renormalization procedure is presented. Without introducing any energy (or mass) counter terms, by using the elementary time-dependent perturbation theory, it is shown that the renormalization procedure is equivalent to the identification and removement of those terms which stem from the experimentally unobservable free-electron–vacuum-field interaction.

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38

Farsoiya, Palas Kumar, Y. S. Mayya, and Ratul Dasgupta. "Axisymmetric viscous interfacial oscillations – theory and simulations." Journal of Fluid Mechanics 826 (August 15, 2017): 797–818. http://dx.doi.org/10.1017/jfm.2017.443.

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We study axisymmetric, free oscillations driven by gravity and surface tension at the interface of two viscous, immiscible, radially unbounded fluids, analytically and numerically. The interface is perturbed as a zeroth-order Bessel function (in space) and its evolution is obtained as a function of time. In the linearised approximation, we solve the initial value problem (IVP) to obtain an analytic expression for the time evolution of wave amplitude. It is shown that a linearised Bessel mode temporally evolves in exactly the same manner as a Fourier mode in planar geometry. We obtain novel analytical expressions for the time varying vorticity and pressure fields in both fluids. For small initial amplitudes, our analytical results show excellent agreement with those obtained from solving the axisymmetric Navier–Stokes equations numerically. We also compare our results with the normal mode approximation and find the latter to be an accurate representation at very early and late times. The deviation between the normal mode approximation and the IVP solution is found to increase as a function of viscosity ratio. The vorticity field has a jump discontinuity at the interface and we find that this jump depends on the viscosity and the density ratio of the two fluids. Upon increasing the initial perturbation amplitude in the simulations, nonlinearity produces qualitatively new features not present in the analytical IVP solution. Notably, a jet is found to emerge at the axis of symmetry rising to a height greater than the initial perturbation amplitude. Increasing the perturbation amplitude further causes the jet to undergo end pinch off, giving birth to a daughter droplet. This can happen either for an advancing or a receding jet, depending on the viscosity ratio. A relation is found between the maximum jet height and the perturbation amplitude. Hankel transform of the interface demonstrates that at large perturbation amplitudes higher wavenumbers emerge, sharing some of the energy of the lowest mode. When these additional higher modes are present, the interface has pointed crests and rounded troughs.

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Itoh, M. "Perturbation theory of the structure factor and the Helmholtz free energy of a classical fluid: II. Thermodynamic consistency." Journal of Physics C: Solid State Physics 21, no. 18 (June 30, 1988): 3387–96. http://dx.doi.org/10.1088/0022-3719/21/18/005.

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Moser, Roger. "Towards a variational theory of phase transitions involving curvature." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 4 (August 2012): 839–65. http://dx.doi.org/10.1017/s0308210510000995.

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An anisotropic area functional is often used as a model for the free energy of a crystal surface. For models of faceting, the anisotropy is typically such that the functional becomes non-convex, and then it may be appropriate to regularize it with an additional term involving curvature. When the weight of the curvature term tends to zero, this gives rise to a singular perturbation problem.The structure of this problem is comparable to the theory of phase transitions studied first by Modica and Mortola. Their ideas are also useful in this context, but they have to be combined with adequate geometric tools. In particular, a variant of the theory of curvature varifolds, introduced by Hutchinson, is used in this paper. This allows an analysis of the asymptotic behaviour of the energy functionals.

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ROUHANI, S., and M. V. TAKOOK. "ABELIAN GAUGE THEORY IN DE SITTER SPACE." Modern Physics Letters A 20, no. 31 (October 10, 2005): 2387–96. http://dx.doi.org/10.1142/s0217732305018347.

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Quantization of spinor and vector free fields in four-dimensional de Sitter spacetime, in the ambient space notation, has been studied in the previous works. Various two-point functions for the above fields are presented in this paper. The interaction between the spinor field and the vector field is then studied by the Abelian gauge theory. The U (1) gauge invariant spinor field equation is obtained in a coordinate independent way notation and their corresponding conserved currents are computed. The solution of the field equation is obtained by the use of the perturbation method in terms of the Green's function. The null curvature limit is discussed in the final stage.

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FORMANECK, MARK S., GUOHUI LI, XIAODONG ZHANG, and QIANG CUI. "CALCULATING ACCURATE REDOX POTENTIALS IN ENZYMES WITH A COMBINED QM/MM FREE ENERGY PERTURBATION APPROACH." Journal of Theoretical and Computational Chemistry 01, no. 01 (July 2002): 53–67. http://dx.doi.org/10.1142/s0219633602000075.

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An approach for computing accurate redox potentials in enzymes is developed based on the free energy perturbation technique in a QM/MM framework. With an appropriate choice of the QM level and QM/MM coupling scheme, the intermolecular interaction between the redox center and the protein environment can be adequately described; the speed of QM/MM methods also allows a sufficient configurational sampling for the convergence of free energy derivatives. Following the implementation into the simulation package CHARMM, the method was tested with an application to the first reduction potential of FAD in cholesterol oxidase (Chox). In addition to an accurate QM level and adequate conformational samplings, the effect of long-range electrostatic interactions due to the bulk solvent was also found to be essential. Using a semi-empirical density functional theory (SCC-DFTB) as the QM level, and a multi-stage charge-scaling scheme based on Poisson–Boltzmann calculations for the solvation effect, satisfactory agreements with experimental measurements were obtained. The study of Chox also indicates that large errors in the calculated redox potential might arise if changes in the conformational properties of the protein during the redox process are not taken into account, such as in energy minimization type of studies based on only the X-ray structure of the enzyme in one redox state.

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CABO, ALEJANDRO, SIANNAH PEÑARANDA, and RENE MARTINEZ. "ON THE POSSIBILITY OF CONSTRUCTING COVARIANT CHROMOMAGNETIC FIELD MODELS." Modern Physics Letters A 10, no. 32 (October 20, 1995): 2413–25. http://dx.doi.org/10.1142/s0217732395002568.

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Expressions for SO(4) invariant Euclidean QCD generating functionals are introduced which should produce nonvanishing gluon condensates. We consider first the loop expansion of the corresponding effectíve action searching for a description differing from the usual perturbation theory. At this level, we consider special free propagators which have off-diagonal long range order. The calculation of the polarization tensor leads to a gluon mass term which is proportional to the squared root of the finite value for <G2>. The summation of all the one-loop contributions to the energy having only mass insertions, indicates the spontaneous generation of the condensate from the perturbative ground state in a way resembling the similar effect in the case of chromomagnetic field models.

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Higuchi, Masahiko, and Hiroshi Yasuhara. "A Proposal of an Orbital-Dependent Correlation Energy Functional for Energy-Band Calculations." International Journal of Modern Physics B 17, no. 17 (July 10, 2003): 3075–134. http://dx.doi.org/10.1142/s0217979203020715.

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An explicitly orbital-dependent correlation energy functional is proposed, which is to be used in combination with the orbital-dependent exchange energy functional in energy-band calculations. It bears a close resemblance to the second-order direct and exchange perturbation terms calculated with Kohn–Sham orbitals and Kohn–Sham energies except that one of the two Coulomb interactions entering each term is replaced by an effective interaction which contains information about long-, intermediate-, and short-range correlations beyond second-order perturbation theory. Such an effective interaction can rigorously be defined for the correlation energy of the uniform electron liquid and is evaluated with high accuracy in order to apply to the orbital-dependent correlation energy functional. The coupling-constant-averaged spin-parallel and spin-antiparallel pair correlation functions are also evaluated with high accuracy for the electron liquid. The present orbital-dependent correlation energy functional with the effective interaction borrowed from the electron liquid is valid for tightly-binding electrons as well as for nearly-free electrons in marked contrast with the conventional local density approximation. There is a strong possibility that the present orbital-dependent correlation energy functional, if applied to the so-called strongly correlated electron systems, will produce the energy-band structure significantly different from that calculated only with the orbital-dependent exchange energy functional particularly in the neighborhood of the Fermi level or the energy gap. A detailed discussion, accompanied by an accurate calculation of the quasiparticle energy dispersion of the electron liquid, is given about the relationship between Kohn–Sham equations and Dyson equations in order to justify the application of Kohn–Sham equations to the band theory.

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DEMETERFI, KRESIMIR, ANTAL JEVICKI, and JOĀO P. RODRIGUES. "PERTURBATIVE RESULTS OF COLLECTIVE STRING FIELD THEORY." Modern Physics Letters A 06, no. 35 (November 20, 1991): 3199–212. http://dx.doi.org/10.1142/s0217732391003699.

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We present a summary of perturbative results obtained in the framework of collective string field theory. We discuss computations of tree-level scattering amplitudes, loop corrections to tachyon self-energy, ground state energy and finite temperature free energy. A comparison with results obtained in different approaches is given. We also discuss the physical implications of our results.

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KIM, SOON-CHUL. "LOCAL DENSITY DISTRIBUTION OF NONUNIFORM POLYMER MELTS AT SOLID-FLUID INTERFACES." International Journal of Modern Physics B 20, no. 17 (July 10, 2006): 2381–94. http://dx.doi.org/10.1142/s0217979206034790.

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We have developed the density functional theory (DFT) and density functional perturbation theory (DFPT) which are based both on the hybrid weighted-density approximation and on the higher-order weighted-density approximation, respectively, to study the structural and thermodynamic properties of polymer melts at interfaces. They were applied to predict the local density distributions, adsorption isotherms, surface excesses, and solvation forces of a freely jointed tangent hard-sphere chain in hard slit pores. The Wertheim's first-order perturbation theory extended by Yu and Wu [J. Chem. Phys.117, 2368 (2002)] was used to calculate the excess free energy and second-order direct correlation function due to the chain connectivity. The weight functions were calculated from the second-order direct correlation functions. The calculated results show that the DFT is in excellent agreement with the computer simulations and slightly better than the DFPT.

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FUCITO, F., and M. MARTELLINI. "RENORMALIZATION GROUP FLOWS IN NONPERTURBATIVE 2D QUANTUM GRAVITY." International Journal of Modern Physics A 07, no. 07 (March 20, 1992): 1361–74. http://dx.doi.org/10.1142/s0217751x92000594.

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We study the existence of solutions of the string equations which are pole-free on the positive real axis and exhibit such a solution following the work of Boutroux. We further study, using perturbation theory, the flows among different models and we find that there is no flow between the k=2 and k=3 theories. Moreover, we develop a nonperturbative renormalization-group scheme to extract the scaling behavior of the partition function of the k=2 model under perturbations. The key idea is to reinterpret the recent formulation, as Virasoro constraints, of the string-loop equations as generalized Callan-Symanzik renormalization-group equations.

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HOYER, PAUL. "PERTURBATIVE QED: THE SCHRÖDINGER PICTURE." International Journal of Modern Physics A 04, no. 04 (February 1989): 963–79. http://dx.doi.org/10.1142/s0217751x89000443.

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A derivation of ordinary QED perturbation theory is given in the Schrödinger picture. The path integral is restricted to fields in a finite time interval, ti ≤ t ≤ tf, with explicit boundary conditions given by vacuum state functionals at the initial and final times. The free photon vacuum functional is uniquely specified by the requirement of stationarity in time. For the free electron vacuum further conditions need to be imposed, e.g., the occupation of all negative energy states. The calculations are carried out using a discretized time interval of finite spacing dt, and exact results (to all orders in dt) are obtained for the free generating functionals in Coulomb gauge. Hence Feynman diagrams may be evaluated before the limits of continuous and infinite time are taken, with 1/dt and 1/(tf − ti) providing, respectively, an ultraviolet and an infrared cut-off on the energy integrals. The method may also be used for studying the time evolution of interacting states, in particular of bound states.

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Herbst, Ulrich, and Ralf Hofmann. "Emergent Inert Adjoint Scalar Field in SU(2) Yang-Mills Thermodynamics due to Coarse-Grained Topological Fluctuations." ISRN High Energy Physics 2012 (March 5, 2012): 1–20. http://dx.doi.org/10.5402/2012/373121.

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We compute the phase and the modulus of an energy- and pressure-free, composite, adjoint, and inert field in an SU(2) Yang-Mills theory at large temperatures. This field is physically relevant in describing part of the ground-state structure and the quasiparticle masses of excitations. The field possesses nontrivial -winding on the group manifold . Even at asymptotically high temperatures, where the theory reaches its Stefan-Boltzmann limit, the field , though strongly power suppressed, is conceptually relevant: its presence resolves the infrared problem of thermal perturbation theory.

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EFIMOV, G. V., and G. GANBOLD. "STRONG-COUPLING REGIME IN $g\phi^4_2$ THEORY." International Journal of Modern Physics A 18, no. 09 (April 10, 2003): 1637–56. http://dx.doi.org/10.1142/s0217751x03013727.

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The problem of the strong-coupling regime is considered in the scalar superrenormalizable field theory [Formula: see text]. By using the Gaussian transform, we have found an optimal representation within which the exact strong-coupling behavior of the free energy is already obtained in the leading-order approximation. Within this representation, the interaction becomes slower as the bare coupling constant grows, so the higher-order corrections can be systematically estimated by using a modified perturbation scheme. The next-to-leading terms give rise in insignificant corrections for finite coupling. The regularization procedure regroups the initial counterterms so that the divergencies are exactly removed in final expressions. The main idea is demonstrated in the simplest examples of a plain quartic integral and the anharmonic oscillator.

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Journal articles on the topic 'Free energy perturbation theory'

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