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Jan Smit - One of the best experts on this subject based on the ideXlab platform.
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Classical Approximation to quantum cosmological correlations
2007Co-Authors: Meindert Van Der Meulen, Jan SmitAbstract:We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. As a toy model, we study $\phi^3$ theory on a de Sitter background for a massless minimally coupled scalar field $\phi$. We find that for tree level and one loop contributions in the quantum theory, a good Classical Approximation can be constructed, but for higher loop corrections this is in general not expected to be possible. The reason is that loop corrections get non-negligible contributions from loop momenta with magnitude up to the Hubble scale H, at which scale Classical physics is not expected to be a good Approximation to the quantum theory. An explicit calculation of the one loop correction to the two point function, supports the argument that contributions from loop momenta of scale $H$ are not negligible. Generalization of the arguments for the toy model to derivative interactions and the curvature perturbation leads to the conclusion that the leading orders of non-Gaussian effects generated after horizon exit, can be approximated quite well by Classical methods. Furthermore we compare with a theorem by Weinberg. We find that growing loop corrections after horizon exit are not excluded, even in single field inflation.
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tachyonic preheating using 2pi 1 n dynamics and the Classical Approximation
2004Co-Authors: Alejandro Arrizabalaga, Jan Smit, Anders TranbergAbstract:We study the process of tachyonic preheating using approximative quantum equations of motion derived from the 2PI effective action. The O(N) scalar (Higgs) field is assumed to experience a fast quench which is represented by an instantaneous flip of the sign of the mass parameter. The equations of motion are solved numerically on the lattice, and the Hartree and 1/N-NLO Approximations are compared to the Classical Approximation. Classical dynamics is expected to be valid, since the occupation numbers can rise to large values during tachyonic preheating. We find that the Classical Approximation performs excellently at short and intermediate times, even for couplings in the larger region currently allowed for the SM Higgs. This is reassuring, since all previous numerical studies of tachyonic preheating and baryogenesis during tachyonic preheating have used Classical dynamics. We also compare different initializations for the Classical simulations.
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initial conditions for simulated tachyonic preheating and the hartree ensemble Approximation
2002Co-Authors: M Salle, Jan Smit, Jeroen C VinkAbstract:In numerical simulations studying preheating in the Classical Approximation there is the problem how to derive the Classical initial conditions from the quantum vacuum fluctuations. In past treatments, the initial conditions often put an energy density into the Classical field of order of the cutoff, leading to a divergent temperature after thermalization. We suggest a solution to the problem which follows naturally from a Hartree ensemble Approximation, introduced recently as an improvement over the standard Hartree Approximation. We study the effects on particle numbers of the various treatments, within the context of `tachyonic preheating' in 1+1 dimensional $\phi^4$ theory.
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Classical Approximation for time dependent quantum field theory diagrammatic analysis for hot scalar fields
1998Co-Authors: Gert Aarts, Jan SmitAbstract:Abstract We study time-dependent correlation functions in hot quantum and Classical field theory for the λθ 4 case. We set up the Classical analogue of thermal field theory and make a direct comparison between the quantum and Classical diagrams. A restriction to time-independent correlation functions gives the connection with conventional dimensional reduction. If the parameters in the Classical theory are chosen according to the dimensional reduction matching relations, the Classical expressions are cutoff independent and they approximate the quantum expressions, provided that the external momenta and frequencies are small with respect to the temperature.
E K U Gross - One of the best experts on this subject based on the ideXlab platform.
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mixed quantum Classical dynamics from the exact decomposition of electron nuclear motion
2014Co-Authors: Ali Abedi, Federica Agostini, E K U GrossAbstract:We present a novel mixed quantum-Classical approach to the coupled electron-nuclear dynamics based on the exact factorisation of the electron-nuclear wave function, recently proposed in Abedi A., Maitra N. T. and Gross E. K. U., Phys. Rev. Lett., 105 (2010) 123002. In this framework, the correct Classical limit of the nuclear dynamics is worked out by taking the Classical limit of the exact time-dependent Schr?dinger equation satisfied by the nuclear wave function. The effect of the time-dependent scalar and vector potentials, representing the exact electronic back-reaction on the nuclear subsystem, is consistently derived within the Classical Approximation. We examine with an example the performance of the proposed mixed quantum-Classical scheme in comparison with exact calculations.
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mixed quantum Classical dynamics from the exact decomposition of electron nuclear motion
2014Co-Authors: Ali Abedi, Federica Agostini, E K U GrossAbstract:We present a novel mixed quantum-Classical approach to the coupled electron-nuclear dynamics based on the exact factorization of the electron-nuclear wave function, recently proposed in [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. In this framework, Classical nuclear dynamics is derived as the lowest order Approximation of the time dependent Schr\"odinger equation that describes the evolution of the nuclei. The effect of the time dependent scalar and vector potentials, representing the exact electronic back-reaction on the nuclear subsystem, is consistently derived within the Classical Approximation. We examine with an example the performance of the proposed mixed quantum-Classical scheme in comparison with exact calculations.
G Ortenzi - One of the best experts on this subject based on the ideXlab platform.
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quasi Classical Approximation in vortex filament dynamics integrable systems gradient catastrophe and flutter
2013Co-Authors: B G Konopelchenko, G OrtenziAbstract:Quasi-Classical Approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this Approximation, the governing equations are given by elliptic system of quasi-linear partial differential equations of the first order. Dispersionless Da Rios system and dispersionless Hirota equation are among them. They describe motion of vortex filament with slow-varying curvature and torsion without or with axial flow. Gradient catastrophe for governing equations is studied. It is shown that geometrically this catastrophe manifests as a fast oscillation of a filament curve around the rectifying plane which resembles the flutter of airfoils. Analytically, it is the elliptic umbilic singularity in the terminology of the catastrophe theory. It is demonstrated that its double scaling regularization is governed by the Painleve I equation.
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quasi Classical Approximation in vortex filament dynamics integrable systems gradient catastrophe and flutter
2012Co-Authors: B G Konopelchenko, G OrtenziAbstract:QuasiClassical Approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this Approximation the governing equations are given by elliptic system of quasi-linear PDEs of the first order. Dispersionless Da Rios system and dispersionless Hirota equation are among them. They describe motion of vortex filament with slow varying curvature and torsion without or with axial flow. Gradient catastrophe for governing equations is studied. It is shown that geometrically this catastrophe manifests as a fast oscillation of a filament curve around the rectifying plane which resembles the flutter of airfoils. Analytically it is the elliptic umbilic singularity in the terminology of the catastrophe theory. It is demonstrated that its double scaling regularization is governed by the Painleve' I equation.
Gert Aarts - One of the best experts on this subject based on the ideXlab platform.
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spectral function at high temperature in the Classical Approximation
2001Co-Authors: Gert AartsAbstract:At high temperature the infrared modes of a weakly coupled quantum field theory can be treated nonperturbatively in real time using the Classical field Approximation. We use this to introduce a nonperturbative approach to the calculation of finite-temperature spectral functions, employing the Classical KMS condition in real time. The method is illustrated for the one-particle spectral function in a scalar field theory in 2+1 dimensions. The result is compared with resummed two-loop perturbation theory and both the plasmon mass and width are found to agree with the analytical prediction.
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divergences in real time Classical field theories at nonzero temperature
2000Co-Authors: Gert Aarts, B J Nauta, Chris Van WeertAbstract:The Classical Approximation provides a non-perturbative approach to time-dependent problems in finite temperature field theory. We study the divergences in hot Classical field theory perturbatively. At one loop, we show that the linear divergences are completely determined by the Classical equivalent of the hard thermal loops in hot quantum field theories, and that logarithmic divergences are absent. To deal with higher-loop diagrams, we present a general argument that the superficial degree of divergence of Classical vertex functions decreases by one with each additional loop: one-loop contributions are superficially linearly divergent, twoloop contributions are superficially logarithmically divergent, and three- and higher-loop contributions are superficially finite. We verify this for two-loop SU( N) self-energy diagrams in Feynman and Coulomb gauges. We argue that hot, Classical scalar field theory may be completely renormalized by local ~mass! counterterms, and discuss renormalization of SU(N) gauge theories. The Classical Approximation @1# is a useful tool for the study of infrared properties of quantum fields at high temperature @2‐9#, which may be applied to calculate nonperturbative phenomena such as the Chern-Simons diffusion rate @10‐12 #~ relevant for theories of baryogenesis @13#! and the dynamics of the electroweak phase transition @14# ,a s well as real-time ~plasmon! properties of hot non-Abelian gauge theories @15#. The Classical theory is expected to be a good Approximation at low-energy because the Classical limit \!0 and the low-energy limit of the Bose-Einstein distribution function n yield the same result:
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Classical Approximation for time dependent quantum field theory diagrammatic analysis for hot scalar fields
1998Co-Authors: Gert Aarts, Jan SmitAbstract:Abstract We study time-dependent correlation functions in hot quantum and Classical field theory for the λθ 4 case. We set up the Classical analogue of thermal field theory and make a direct comparison between the quantum and Classical diagrams. A restriction to time-independent correlation functions gives the connection with conventional dimensional reduction. If the parameters in the Classical theory are chosen according to the dimensional reduction matching relations, the Classical expressions are cutoff independent and they approximate the quantum expressions, provided that the external momenta and frequencies are small with respect to the temperature.
Giuseppe Mussardo - One of the best experts on this subject based on the ideXlab platform.
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Bound States of Majorana Fermions in Semi-Classical Approximation
2015Co-Authors: Giuseppe MussardoAbstract:We derive a semi-Classical formula for computing the spectrum of bound states made of Majorana fermions in a generic non-integrable two-dimensional (2D) quantum field theory with a set of degenerate vacua. We illustrate the application of the formula in a series of cases, including an asymmetric well potential where the spectra of bosons and fermions may have some curious features. We also discuss the merging of fermionic and bosonic spectra in the presence of supersymmetry. Finally, we use the semi-Classical formula to analyse the evolution of the particle spectra in a class of non-integrable supersymmetry models.
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bound states of majorana fermions in semi Classical Approximation
2015Co-Authors: Giuseppe MussardoAbstract:We derive a semi-Classical formula for computing the spectrum of bound states made of Majorana fermions in a generic non-integrable 2d quantum field theory with a set of degenerate vacua. We illustrate the application of the formula in a series of cases, including an asymmetric well potential where the spectra of bosons and fermions may have some curious features. We also discuss the merging of fermionic and bosonic spectra in the presence of supersymmetry. Finally, we use the semi-Classical formula to analyse the evolution of the particle spectra in a class of non-integrable supersymmetry models.
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finite volume form factors in semi Classical Approximation
2003Co-Authors: Giuseppe Mussardo, Valentina Riva, G M SotkovAbstract:Abstract A semi-Classical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the spectral representation of correlation functions in a finite volume. Illustrative examples of the applicability of the method are provided by the sine-Gordon and the broken φ 4 theories in 1+1 dimensions.