Renormalization in quantum mechanics

Gupta, Kumar S.; Rajeev, S. G.

doi:10.1103/physrevd.48.5940

Cited by 148 publications

(195 citation statements)

References 8 publications

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“…For instance, the scale invariance in the dynamics of a harmonically trapped 2D Bose gas nullifies the interaction-induced shift of the frequency of monopole excitations for all excitation amplitudes; however, this scale invariance is broken by the quantum many-body Hamiltonian, leading to a small shift, albeit discernible on a zero background [18]. In this context, the symmetry breaking by the secondary quantization may be considered as a manifestation of a general phenomenon known as the quantum anomaly [19]. In this Letter we develop a similar strategy for predicting beyond-MF effects in the one-dimensional (1D) self-attractive Bose gas in a MF range of parameters.…”

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confidence: 99%

Dissociation of One-Dimensional Matter-Wave Breathers due to Quantum Many-Body Effects

et al. 2017

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We use the ab initio Bethe ansatz dynamics to predict the dissociation of one-dimensional cold-atom breathers that are created by a quench from a fundamental soliton. We find that the dissociation is a robust quantum many-body effect, while in the mean-field (MF) limit the dissociation is forbidden by the integrability of the underlying nonlinear Schrödinger equation. The analysis demonstrates the possibility to observe quantum many-body effects without leaving the MF range of experimental parameters. We find that the dissociation time is of the order of a few seconds for a typical atomic-soliton setting. DOI: 10.1103/PhysRevLett.119.220401 Under normal conditions, interacting quantum Bose gases do not readily exhibit signatures of their corpuscular nature, but rather follow the behavior predicted by meanfield (MF) theory. The observability of microscopic quantum effects involving a substantial fraction of the particles in a coherent macroscopic setting generally requires going beyond MF, for example, at low density in one dimension (1D) [1,2] or high density in three dimensions (3D). In 3D systems, the high-density Lee-Huang-Yang corrections, which are induced by quantum correlations, were realized experimentally using the Feshbach resonance [3] and in the spectacular form of "quantum droplets" in dipolar [4][5][6] and isotropic [7] bosonic gases, i.e., as self-trapped states stabilized against the collapse by the beyond-MF selfrepulsion. This stabilization was predicted in Refs. [8][9][10]. Quantum effects involving a macroscopic number of atoms in collapsing attractive 3D gases and colliding condensates were also observed [11][12][13][14][15] and analyzed [16,17] in the MF density range.A generic opportunity to observe beyond-MF effects arises when a particular symmetry of the MF dynamics, which prohibits a certain effect, is broken at the microscopic level, thus making observation of the effect possible. For instance, the scale invariance in the dynamics of a harmonically trapped 2D Bose gas nullifies the interaction-induced shift of the frequency of monopole excitations for all excitation amplitudes; however, this scale invariance is broken by the quantum many-body Hamiltonian, leading to a small shift, albeit discernible on a zero background [18]. In this context, the symmetry breaking by the secondary quantization may be considered as a manifestation of a general phenomenon known as the quantum anomaly [19]. In this Letter we develop a similar strategy for predicting beyond-MF effects in the one-dimensional (1D) self-attractive Bose gas in a MF range of parameters. The respective MF equation amounts to the nonlinear Schrödinger (NLS) equation, integrable by the inverse-scattering transform [20]. The NLS rigidly links the structure of a time-dependent solution to its initial form, with many features of the latter rendered identifiable in the former. In particular, a sudden increase of the strength of the attractive coupling constant by a factor of 4, i.e., an interaction quench, converts a fundamental s...

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confidence: 99%

Dissociation of One-Dimensional Matter-Wave Breathers due to Quantum Many-Body Effects

et al. 2017

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“…The solution to the equation (25), given in [5], is a modified Bessel function with imaginary index is 0…”

Section: The Inverse-squared Potentialmentioning

confidence: 99%

“…The geometric scaling of the spectrum then holds right up to the accumulation point at E = 0, and the effective potential is of inverse-square type for all distances R > r 0 . This limit itself has interesting properties and given rise to various theoretical research [5][6][7]. Our contribution to this research here is a semiclassical description of the unitary Efimov system.…”

Section: Introductionmentioning

confidence: 99%

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Semiclassical analysis of the Efimov energy spectrum in the unitary limit

2011

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We demonstrate that the (s-wave) geometric spectrum of the Efimov energy levels in the unitary limit is generated by the radial motion of a primitive periodic orbit (and its harmonics) of the corresponding classical system. The action of the primitive orbit depends logarithmically on the energy. It is shown to be consistent with an inverse-squared radial potential with a lower cut-off radius. The lowest-order WKB quantization, including the Langer correction, is shown to reproduce the geometric scaling of the energy spectrum. The (WKB) mean-squared radii of the Efimov states scale geometrically like the inverse of their energies. The WKB wavefunctions, regularized near the classical turning point by Langer's generalized connection formula, are practically indistinguishable from the exact wave functions even for the lowest (n = 0) state, apart from a tiny shift of its zeros that remains constant for large n.

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“…In Refs. [2], [3], [4] and [5] the ultraviolet divergences generated by certain short range singular potentials are treated in a manner which is similar to Quantum Field Theory. The goal of the present work is different.…”

Section: Introductionmentioning

confidence: 99%