Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits

It is well known that R^N has subspaces of dimension proportional to N on which the \ell_1 norm is equivalent to the \ell_2 norm; however, no explicit constructions are known. Extending earlier work by Artstein--Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits.Comment: 16 pages; minor changes in the introduction to make it more accessible to both Math and CS reader

The Exact Wavefunction Factorization of a Vibronic Coupling System

We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally the nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization and the adiabatic approximation

Many-body effects in the excitation spectrum of weakly-interacting Bose-Einstein condensates in one-dimensional optical lattices

In this work, we study many-body excitations of Bose-Einstein condensates (BECs) trapped in periodic one-dimensional optical lattices. In particular, we investigate the impact of quantum depletion onto the structure of the low-energy spectrum and contrast the findings to the mean-field predictions of the Bogoliubov-de Gennes (BdG) equations. Accurate results for the many-body excited states are obtained by applying a linear-response theory atop the MCTDHB (multiconfigurational time-dependent Hartree method for bosons) equations of motion, termed LR-MCTDHB. We demonstrate for condensates in a triple well that even weak ground-state depletion of around $1\%$ leads to visible many-body effects in the low-energy spectrum which deviate substantially from the corresponding BdG spectrum. We further show that these effects also appear in larger systems with more lattice sites and particles, indicating the general necessity of a full many-body treatment

Many-body tunneling dynamics of Bose-Einstein condensates and vortex states in two spatial dimensions

In this work, we study the out-of-equilibrium many-body tunneling dynamics of a Bose-Einstein condensate in a two-dimensional radial double well. We investigate the impact of interparticle repulsion and compare the influence of angular momentum on the many-body tunneling dynamics. Accurate many-body dynamics are obtained by solving the full many-body Schr\"odinger equation. We demonstrate that macroscopic vortex states of definite total angular momentum indeed tunnel and that, even in the regime of weak repulsions, a many-body treatment is necessary to capture the correct tunneling dynamics. As a general rule, many-body effects set in at weaker interactions when the tunneling system carries angular momentum.Comment: 26 pages, 9 figure

The V3, V4 and V6 bands of formaldehyde: A spectral catalog from 900 cm(-1) to 1580 cm(-1)

The results of a complete high resolution study of the three vibration-rotation bands v sub 3, v sub 4, and V sub 6 using both TDLs and FT-IR spectroscopy are presented. The reults are given in terms of a table of over 8000 predicted transition frequencies and strengths. A plot of the predicted and calculated spectra is shown. Over 3000 transitions were assigned and used in the simultaneous analysis of the three bands. The simultaneous fit permitted a rigorous study of Coriolis and other type iterations among bands yielding improved molecular constants. Line intensities of 28 transitions measured by a TDL and 20 transitions from FTS data were used, along with the eigenvectors from the frequency fitting, in a least squares analysis to evaluate the band strengths

Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential barrier is investigated. We determine on an accurate many-body level the system's ground-state phase diagram as well as a time-dependent phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We demonstrate for the first time the dynamical fragmentation of a BEC despite its ground state being condensed. The results are analyzed by a mean-field model and suggest that a large manifold of low-lying fragmented excited states can significantly impact the dynamics of trapped two-dimensional BECs.Comment: 5+eps pages, 4 figure