Bose-Einstein condensates with attractive interatomic interactions undergo collective collapse be... more Bose-Einstein condensates with attractive interatomic interactions undergo collective collapse beyond a critical number. We show theoretically that if the low-lying collective modes of the condensate are excited, the radial breathing mode further destabilizes the condensate. Remarkably, excitation of the quadrupolar surface mode causes the condensate to become more stable, imparting quasiangular momentum to it. A significantly larger number of atoms may then occupy the condensate. Efforts are under way for the experimental realization of these effects.
H = 1 2(ˆ p2x + ˆ p2y) +1 2 ˆ x2ˆ y2, which is strongly chaotic in the classical limit. We are ab... more H = 1 2(ˆ p2x + ˆ p2y) +1 2 ˆ x2ˆ y2, which is strongly chaotic in the classical limit. We are able to calculate, essentially analytically, low-lying eigenvalues for this system. These approximate eigenvalues agree within a few percent with the numerical results. We believe that this is the first example of the use of TDVP dynamics to compute individual eigenvalues in a non-trivial system and one of the few such computations in a chaotic system by any method.
Stochastic resonance occurs when a nonlinear dynamical system is periodically modulated in the pr... more Stochastic resonance occurs when a nonlinear dynamical system is periodically modulated in the presence of noise. We study in this paper the effect of including quantal corrections on the thermal transition rates of such a system, by using the Gaussian effective potential. We demonstrate that these corrections sharpen the peak of the signal-to-noise ratio and shift it toward a lower
This talk discusses the unusual nature of the transition from quantum to classical behavior in sy... more This talk discusses the unusual nature of the transition from quantum to classical behavior in systems which are chaotic in their classical limit. I will start by showing that chaos implies that fine-scale structure grows exponentially rapidly in classical probability dynamics. The behavior of the corresponding quantum system can be very different. However, this fine-scale structure is sensitive to the least external noise. I will show that for classically chaotic systems, the balance between chaos and noise leads to novel non-equilibrium constant-entropy-producing states, characterized by the ratio between generalized Lyapunov exponents and the strength of the noise. This behavior also occurs in quantum systems close to the classical limit and suppresses the quantum-classical difference. The precise limits of the quantum world are therefore determined not just by hbar but also by chaos and entropy-production.
The Gaussian effective potential (GEP) is an approximation to quantum mechanics that semiquantita... more The Gaussian effective potential (GEP) is an approximation to quantum mechanics that semiquantitatively estimates quantum effects such as zero-point fluctuations and tunneling. We show how to use the GEP to compute semiclassical eigenvalues. It is well known that the GEP provides very accurate variational approximations to the ground-state energy of simple quantum systems; our results show that it also provides accurate excited-state energies. We also show how this method is related to the first-order Bargmann-Voros coherent-state representation of quantum mechanics, and that our results improve upon those derived from the latter method.
Bose-Einstein condensates with attractive interatomic interactions undergo collective collapse be... more Bose-Einstein condensates with attractive interatomic interactions undergo collective collapse beyond a critical number. We show theoretically that if the low-lying collective modes of the condensate are excited, the radial breathing mode further destabilizes the condensate. Remarkably, excitation of the quadrupolar surface mode causes the condensate to become more stable, imparting quasiangular momentum to it. A significantly larger number of atoms may then occupy the condensate. Efforts are under way for the experimental realization of these effects.
H = 1 2(ˆ p2x + ˆ p2y) +1 2 ˆ x2ˆ y2, which is strongly chaotic in the classical limit. We are ab... more H = 1 2(ˆ p2x + ˆ p2y) +1 2 ˆ x2ˆ y2, which is strongly chaotic in the classical limit. We are able to calculate, essentially analytically, low-lying eigenvalues for this system. These approximate eigenvalues agree within a few percent with the numerical results. We believe that this is the first example of the use of TDVP dynamics to compute individual eigenvalues in a non-trivial system and one of the few such computations in a chaotic system by any method.
Stochastic resonance occurs when a nonlinear dynamical system is periodically modulated in the pr... more Stochastic resonance occurs when a nonlinear dynamical system is periodically modulated in the presence of noise. We study in this paper the effect of including quantal corrections on the thermal transition rates of such a system, by using the Gaussian effective potential. We demonstrate that these corrections sharpen the peak of the signal-to-noise ratio and shift it toward a lower
This talk discusses the unusual nature of the transition from quantum to classical behavior in sy... more This talk discusses the unusual nature of the transition from quantum to classical behavior in systems which are chaotic in their classical limit. I will start by showing that chaos implies that fine-scale structure grows exponentially rapidly in classical probability dynamics. The behavior of the corresponding quantum system can be very different. However, this fine-scale structure is sensitive to the least external noise. I will show that for classically chaotic systems, the balance between chaos and noise leads to novel non-equilibrium constant-entropy-producing states, characterized by the ratio between generalized Lyapunov exponents and the strength of the noise. This behavior also occurs in quantum systems close to the classical limit and suppresses the quantum-classical difference. The precise limits of the quantum world are therefore determined not just by hbar but also by chaos and entropy-production.
The Gaussian effective potential (GEP) is an approximation to quantum mechanics that semiquantita... more The Gaussian effective potential (GEP) is an approximation to quantum mechanics that semiquantitatively estimates quantum effects such as zero-point fluctuations and tunneling. We show how to use the GEP to compute semiclassical eigenvalues. It is well known that the GEP provides very accurate variational approximations to the ground-state energy of simple quantum systems; our results show that it also provides accurate excited-state energies. We also show how this method is related to the first-order Bargmann-Voros coherent-state representation of quantum mechanics, and that our results improve upon those derived from the latter method.
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