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Decoherence, einselection, and the quantum origins of the classical
 REVIEWS OF MODERN PHYSICS 75, 715. AVAILABLE ONLINE AT HTTP://ARXIV.ORG/ABS/QUANTPH/0105127
, 2003
"... The manner in which states of some quantum systems become effectively classical is of great significance for the foundations of quantum physics, as well as for problems of practical interest such as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) ..."
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Cited by 113 (1 self)
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The manner in which states of some quantum systems become effectively classical is of great significance for the foundations of quantum physics, as well as for problems of practical interest such as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environmentinduced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal "Schrödingercat states." The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information
Quantum chaotic dynamics and random polynomials
 J. Stat. Phys
, 1996
"... We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of ”quantum chaotic dynamics”. It is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plan ..."
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We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of ”quantum chaotic dynamics”. It is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane. In order to further increase this tendency, we study in detail the particular case of selfinversive random polynomials and show that for them a finite portion of all roots lies exactly on the unit circle. Correlation functions of these roots are also computed analytically, and compared to the correlations of eigenvalues of random matrices. The problem of ergodicity of chaotic wavefunctions is also considered. For that purpose we introduce a family of random polynomials whose roots spread uniformly over phase space. While these results are consistent with random matrix theory predictions, they provide a new and different insight into the problem of quantum ergodicity. Special attention is devoted all over the paper to the role of symmetries in the distribution of roots of random polynomials.
Universal Results for Correlations of Characteristic Polynomials
 RiemannHilbert Approach. Commun. Math. Phys
, 2003
"... Abstract We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal polynomials; b) constructed from Cauchy transforms of the same ..."
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Abstract We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal polynomials; b) constructed from Cauchy transforms of the same orthogonal polynomials and finally c) those constructed from both orthogonal polynomials and their Cauchy transforms. These kernels are related with the RiemannHilbert problem for orthogonal polynomials. For the correlation functions we obtain exact expressions in the form of determinants of these kernels. Derived representations enable us to study asymptotics of correlation functions of characteristic polynomials via DeiftZhou steepestdescent/stationary phase method for RiemannHilbert problems, and in particular to find negative moments of characteristic polynomials. This reveals the universal parts of the correlation functions and moments of characteristic polynomials for arbitrary invariant ensemble of β = 2 symmetry class. 1.
Limiting eigenvalue distribution of random matrices with correlated entries
 Markov Proc. Rel. Fields 2
, 1996
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On asymptotics of large Haar distributed unitary matrices
"... this paper random unitary matrices are studied whose entries must be correlated. A unitary matrix U = (U ij ) is a matrix with complex entries and UU # = U # U = I ..."
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Cited by 26 (1 self)
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this paper random unitary matrices are studied whose entries must be correlated. A unitary matrix U = (U ij ) is a matrix with complex entries and UU # = U # U = I
Semiclassical Form Factor for Chaotic Systems With Spin 1/2
, 1999
"... . We study the properties of the twopoint spectral form factor for classically chaotic systems with spin 1/2 in the semiclassical limit, with a suitable semiclassical trace formula as our principal tool. To this end we introduce a regularized form factor and discuss the limit in which the socalled ..."
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Cited by 22 (17 self)
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. We study the properties of the twopoint spectral form factor for classically chaotic systems with spin 1/2 in the semiclassical limit, with a suitable semiclassical trace formula as our principal tool. To this end we introduce a regularized form factor and discuss the limit in which the socalled diagonal approximation can be recovered. The incorporation of the spin contribution to the trace formula requires an appropriate variant of the equidistribution principle of long periodic orbits as well as the notion of a skew product of the classical translational and spin dynamics. Provided this skew product is mixing, we show that generically the diagonal approximation of the form factor coincides with the respective predictions from random matrix theory. PACS numbers: 03.65.Sq, 05.45.Mt k Email address: bol@physik.uniulm.de  Email address: kep@physik.uniulm.de + Address after 1 October 1999: Abteilung Theoretische Physik, Universitat Ulm, AlbertEinsteinAllee 11, D89069 Ulm, G...
Random matrices, magic squares and matching polynomials
, 2004
"... Characteristic polynomials of random unitary matrices have been intensively studied in recent years: by number theorists in connection with Riemann zetafunction, and by theoretical physicists in connection with Quantum Chaos. In particular, Haake and collaborators have computed the variance of the c ..."
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Characteristic polynomials of random unitary matrices have been intensively studied in recent years: by number theorists in connection with Riemann zetafunction, and by theoretical physicists in connection with Quantum Chaos. In particular, Haake and collaborators have computed the variance of the coefficients of these polynomials and raised the question of computing the higher moments. The answer turns out to be intimately related to counting integer stochastic matrices (magic squares). Similar results are obtained for the moments of secular coefficients of random matrices from orthogonal and symplectic groups. Combinatorial meaning of the moments of the secular coefficients of GUE matrices is also investigated and the connection with matching polynomials is discussed.
Spectral statistics for the Dirac operator on graphs
, 2002
"... We determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the BohigasGiannoniSchmit conjecture for such systems with timereversal symmetry the energy level statistics are expected, in the semiclassical limit, to correspon ..."
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Cited by 16 (5 self)
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We determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the BohigasGiannoniSchmit conjecture for such systems with timereversal symmetry the energy level statistics are expected, in the semiclassical limit, to correspond to those of random matrices from the Gaussian symplectic ensemble. This is confirmed by numerical investigation. The scattering matrix used to formulate the quantisation condition is found to be independent of the type of spinor. We derive an exact trace formula for the spectrum and use this to investigate the form factor in the diagonal approximation.
Quantum Chaos, Transport, and Decoherence in Atom Optics
, 2001
"... Experimental research is often a collaborative endeavor, and the work presented in this dissertation is certainly no exception. During the past six years I have had the pleasure of working with a number of bright and enthusiastic people that I would like to mention here. First of all, I would like t ..."
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Experimental research is often a collaborative endeavor, and the work presented in this dissertation is certainly no exception. During the past six years I have had the pleasure of working with a number of bright and enthusiastic people that I would like to mention here. First of all, I would like to thank my advisor, Mark Raizen. Mark is always brimming with intriguing new ideas, and he has an exceptional sense for interesting physics problems. Mark has provided an exciting and supportive research environment for his students. I have truly enjoyed and greatly benefited from spending the past few years under his guidance. I have collaborated with Windell Oskay on all of the research in this dissertation. I cannot imagine having done the experiments in this dissertation without Windell’s remarkable productivity and superior technical prowess. This is especially true of the chaosassisted tunneling experiments in Chapter 6, where the two of us managed an enormously complicated experiment and took enough data to literally choke our computer. Windell’s rocksolid and extensive LabVIEW code (which featured its own web