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684
Introduction to Representations of the Canonical Commutation and Anticommutation Relations
, 2005
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Electronic structure calculations with dynamical meanfield theory
 Rev. Mod. Phys
, 2006
"... A review of the basic ideas and techniques of the spectral densityfunctional theory is presented. This method is currently used for electronic structure calculations of strongly correlated materials where the oneelectron description breaks down. The method is illustrated with several examples wher ..."
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Cited by 30 (6 self)
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A review of the basic ideas and techniques of the spectral densityfunctional theory is presented. This method is currently used for electronic structure calculations of strongly correlated materials where the oneelectron description breaks down. The method is illustrated with several examples where interactions play a dominant role: systems near metalinsulator transitions, systems near volume collapse transitions, and systems with local moments. DOI: 10.1103/RevModPhys.78.865 PACS numbers: 71.20.b, 71.27.a, 75.30.m CONTENTS
The BCS functional for general pair interactions
 Commun. Math. Phys
"... Abstract. The BardeenCooperSchrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and posi ..."
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Cited by 26 (12 self)
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Abstract. The BardeenCooperSchrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a nontrivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is nonzero and exponentially small in the strength of the potential. 1.
Rapidly rotating atomic gases
 Advances in Physics, 57:539–616
, 2008
"... This article reviews developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single component atomic Bose gas, which (at least at rest) forms a BoseEinstein condensate. Rotation leads to the formation of quantized vortices which o ..."
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Cited by 24 (0 self)
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This article reviews developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single component atomic Bose gas, which (at least at rest) forms a BoseEinstein condensate. Rotation leads to the formation of quantized vortices which order into a vortex array, in close analogy with the behaviour of superfluid helium. Under conditions of rapid rotation, when the vortex density becomes large, atomic Bose gases offer the possibility to explore the physics of quantized vortices in novel parameter regimes. First, there is an interesting regime in which the vortices become sufficiently dense that their cores – as set by the healing length – start to overlap. In this regime, the theoretical description simplifies, allowing a reduction to single particle states in the lowest Landau level. Second, one can envisage entering a regime of very high vortex density, when the number of vortices becomes comparable to the number of particles in the gas. In this regime, theory predicts the appearance of a series of strongly correlated phases, which can be viewed as bosonic versions of fractional quantum Hall states. This article describes the
Lectures on hydrodynamic fluctuations in relativistic theories, J.Phys. A45
, 2012
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The statistical theory of quantum dots
 Rev. Mod. Phys
, 2000
"... A quantum dot is a submicronscale conducting device containing up to several thousand electrons. Transport through a quantum dot at low temperatures is a quantumcoherent process. This review focuses on dots in which the electron’s dynamics are chaotic or diffusive, giving rise to statistical prop ..."
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Cited by 20 (0 self)
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A quantum dot is a submicronscale conducting device containing up to several thousand electrons. Transport through a quantum dot at low temperatures is a quantumcoherent process. This review focuses on dots in which the electron’s dynamics are chaotic or diffusive, giving rise to statistical properties that reflect the interplay between onebody chaos, quantum interference, and electronelectron
Nonlinear waves in BoseEinstein condensates: physical relevance and mathematical techniques, preprint available at: http://wwwrohan.sdsu.edu/∼rcarrete
"... This Article is brought to you for free and open access by the Mathematics and Statistics at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Mathematics and Statistics Department Faculty Publication Series by an authorized administrator of ScholarWorks@UMass Amherst. For more infor ..."
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Cited by 18 (6 self)
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This Article is brought to you for free and open access by the Mathematics and Statistics at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Mathematics and Statistics Department Faculty Publication Series by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact
A Quantum LatticeGas Model for Computational Fluid Dynamics
, 1999
"... Quantumcomputing ideas are applied to the practical and ubiquitous problem of fluid dynamics simulation. Hence, this paper addresses two separate areas of physics: quantum mechanics and fluid dynamics (or specially, the computational simulation of fluid dynamics). The quantum algorithm is called a ..."
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Cited by 16 (4 self)
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Quantumcomputing ideas are applied to the practical and ubiquitous problem of fluid dynamics simulation. Hence, this paper addresses two separate areas of physics: quantum mechanics and fluid dynamics (or specially, the computational simulation of fluid dynamics). The quantum algorithm is called a quantum lattice gas. An analytical treatment of the microscopic quantum latticegas system is carried out to predict its behavior at the mesoscopic and macroscopic scales. At the mesoscopic scale, a lattice Boltzmann equation, with a nonlocal collision term that depends on the entire system wavefunction, governs the dynamical system. Numerical results obtained from an exact simulation of a onedimensional quantum latticemodel are included to illustrate the formalism. A symbolic mathematical method is used to implement the quantum mechanical model on a conventional workstation. The numerical simulation indicates that classical viscous damping is not present in the onedimensional quantum la...
A latticegas with longrange interactions coupled to a heat bath
 in [52
"... Introduced is a latticegas with longrange 2body interactions. An effective interparticle force is mediated by momentum exchanges. There exists the possibility of having both attractive and repulsive interactions using finite impact parameter collisions. There also exists an interesting possibili ..."
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Cited by 15 (8 self)
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Introduced is a latticegas with longrange 2body interactions. An effective interparticle force is mediated by momentum exchanges. There exists the possibility of having both attractive and repulsive interactions using finite impact parameter collisions. There also exists an interesting possibility of coupling these longrange interactions to a heat bath. A fixed temperature heat bath induces a permanent net attractive interparticle potential, but at the expense of reversibility. Thus the longrange dynamics is a kind of a Monte Carlo Kawasaki updating scheme. The model has a PρT equation of state. Presented are analytical and numerical results for a latticegas fluid governed by a nonideal equation of state. The model’s complexity is not much beyond that of the FHP latticegas. It is suitable for massively parallel processing and may be used to study critical phenomena in large systems. 1
Clifford geometric parameterization of inequivalent vacua
, 2001
"... We propose a geometric method to parameterize inequivalent vacua by dynamical data. Introducing quantum Clifford algebras with arbitrary bilinear forms we distinguish isomorphic algebras –as Clifford algebras – by different filtrations resp. induced gradings. The idea of a vacuum is introduced as th ..."
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Cited by 14 (13 self)
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We propose a geometric method to parameterize inequivalent vacua by dynamical data. Introducing quantum Clifford algebras with arbitrary bilinear forms we distinguish isomorphic algebras –as Clifford algebras – by different filtrations resp. induced gradings. The idea of a vacuum is introduced as the unique algebraic projection on the base field embedded in the Clifford algebra, which is however equivalent to the term vacuum in axiomatic quantum field theory and the GNS construction in C ∗algebras. This approach is shown to be equivalent to the usual picture which fixes one product but employs a variety of GNS states. The most striking novelty of the geometric approach is the fact that dynamical data fix uniquely the vacuum and that positivity is not required. The usual concept of a statistical quantum state can be generalized to geometric meaningful but nonstatistical, nondefinite, situations. Furthermore, an algebraization of states takes place. An application to physics is provided by an U(2)symmetry producing a gapequation which governs a phase transition. The parameterization of all vacua is explicitly calculated from propagator matrix elements. A discussion of the relation to BCS theory and BogoliubovValatin transformations is given.