TY - JOUR
AB - We prove the Lee-Huang-Yang formula for the ground state energy of the 3D Bose gas with repulsive interactions described by the exponential function, in a simultaneous limit of weak coupling and high density. In particular, we show that the Bogoliubov approximation is exact in an appropriate parameter regime, as far as the ground state energy is concerned.
AU - Giuliani, Alessandro
AU - Robert Seiringer
ID - 2384
IS - 5-6
JF - Journal of Statistical Physics
TI - The ground state energy of the weakly interacting Bose gas at high density
VL - 135
ER -
TY - JOUR
AB - We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity, so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii energy functional accurately describes the ground-state energy of the corresponding N -body Hamiltonian with contact interaction provided the total angular momentum L is much less than N2. While the Gross-Pitaevskii energy is always an obvious variational upper bound to the ground-state energy, a more refined analysis is needed to establish it as an exact lower bound. We also discuss the question of Bose-Einstein condensation in the parameter range considered. Coherent states together with inequalities in spaces of analytic functions are the main technical tools.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2385
IS - 6
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Yrast line of a rapidly rotating Bose gas: Gross-Pitaevskii regime
VL - 79
ER -
TY - JOUR
AB - We prove exponential decay of the off-diagonal correlation function in the two-dimensional homogeneous Bose gas when a2 ρ is small and the temperature T satisfies T> 4πρ ln | ln (a2 ρ) |. Here, a is the scattering length of the repulsive interaction potential and ρ is the density. To the leading order in a2 ρ, this bound agrees with the expected critical temperature for superfluidity. In the three-dimensional Bose gas, exponential decay is proved when T- Tc (0) Tc (0) >5 a ρ1/3, where Tc (0) is the critical temperature of the ideal gas. While this condition is not expected to be sharp, it gives a rigorous upper bound on the critical temperature for Bose-Einstein condensation.
AU - Robert Seiringer
AU - Ueltschi, Daniel
ID - 2386
IS - 1
JF - Physical Review B - Condensed Matter and Materials Physics
TI - Rigorous upper bound on the critical temperature of dilute Bose gases
VL - 80
ER -
TY - JOUR
AB - We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.
AU - Lewin, Mathieu
AU - Robert Seiringer
ID - 2387
IS - 5
JF - Journal of Statistical Physics
TI - Strongly correlated phases in rapidly rotating Bose gases
VL - 137
ER -
TY - JOUR
AB - This paper provides self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem recapitulates insights achieved by other investigators, and clarifies the connection of coherence and proper scoring rules to Bregman divergence.
AU - Predd, Joel B
AU - Robert Seiringer
AU - Lieb, Élliott H
AU - Osherson, Daniel N
AU - Poor, Harold V
AU - Kulkarni, Sanjeev R
ID - 2388
IS - 10
JF - IEEE Transactions on Information Theory
TI - Probabilistic coherence and proper scoring rules
VL - 55
ER -
TY - CONF
AB - Let EMBEDk→d be the following algorithmic problem: Given a finite simplicial complex K of dimension at most k, does there exist a (piecewise linear) embedding of K into ℝd? Known results easily imply polynomiality of EMBEDk→2 (k = 1, 2; the case k = 1, d = 2 is graph planarity) and of EMBEDk→2k for all k ≥ 3 (even if k is not considered fixed). We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that EMBED d→d and EMBED(d-1)→d are undecidable for each d ≥ 5. Our main result is NP-hardness of EMBED2→4 and, more generally, of EMBEDk→d for all k, d with d ≥ 4 and d ≥ k ≥ (2d - 2)/3.
AU - Matoušek, Jiří
AU - Martin Tancer
AU - Uli Wagner
ID - 2433
TI - Hardness of embedding simplicial complexes in ℝd
ER -
TY - JOUR
AB - G protein-coupled receptors (GPCRs) have critical functions in intercellular communication. Although a wide range of different receptors have been identified in the same cells, the mechanism by which signals are integrated remains elusive. The ability of GPCRs to form dimers or larger hetero-oligomers is thought to generate such signal integration. We examined the molecular mechanisms responsible for the GABAB receptor-mediated potentiation of the mGlu receptor signalling reported in Purkinje neurons. We showed that this effect does not require a physical interaction between both receptors. Instead, it is the result of a more general mechanism in which the βγ subunits produced by the Gi-coupled GABAB receptor enhance the mGlu-mediated Gq response. Most importantly, this mechanism could be generally applied to other pairs of Gi- and Gq-coupled receptors and the signal integration varied depending on the time delay between activation of each receptor. Such a mechanism helps explain specific properties of cells expressing two different Gi- and Gq-coupled receptors activated by a single transmitter, or properties of GPCRs naturally coupled to both types of the G protein.
AU - Rives, Marie L
AU - Vol, Claire
AU - Fukazawa, Yugo
AU - Tinel, Norbert
AU - Trinquet, Eric
AU - Ayoub, Mohammed A
AU - Ryuichi Shigemoto
AU - Pin, Jean-Philippe
AU - Prezèau, Laurent
ID - 2499
IS - 15
JF - EMBO Journal
TI - Crosstalk between GABAB and mGlu1a receptors reveals new insight into GPCR signal integration
VL - 28
ER -
TY - JOUR
AB - Recent theoretical work has provided a basic understanding of signal propagation in networks of spiking neurons, but mechanisms for gating and controlling these signals have not been investigated previously. Here we introduce an idea for the gating of multiple signals in cortical networks that combines principles of signal propagation with aspects of balanced networks. Specifically, we studied networks in which incoming excitatory signals are normally cancelled by locally evoked inhibition, leaving the targeted layer unresponsive. Transmission can be gated 'on' by modulating excitatory and inhibitory gains to upset this detailed balance. We illustrate gating through detailed balance in large networks of integrate-and-fire neurons. We show successful gating of multiple signals and study failure modes that produce effects reminiscent of clinically observed pathologies. Provided that the individual signals are detectable, detailed balance has a large capacity for gating multiple signals.
AU - Vogels, Tim P
AU - Abbott, L F
ID - 8026
IS - 4
JF - Nature Neuroscience
SN - 1097-6256
TI - Gating multiple signals through detailed balance of excitation and inhibition in spiking networks
VL - 12
ER -
TY - JOUR
AB - We have developed a tunable source of Mie scale microdroplet aerosols that can be used for the generation of energetic ions. To demonstrate this potential, a terawatt Ti: Al2 O3 laser focused to 2×10 19 W/cm2 was used to irradiate heavy water (D2 O) aerosols composed of micron-scale droplets. Energetic deuterium ions, which were generated in the laser-droplet interaction, produced deuterium-deuterium fusion with approximately 2×10^3 fusion neutrons measured per joule of incident laser energy.
AU - Higginbotham, Andrew P
AU - Semonin, Octavi
AU - Bruce, S
AU - Chan, C
AU - Maindi, M
AU - Donnelly, Tom
AU - Maurer, M
AU - Bang, Woosuk
AU - Churina, I.V
AU - Osterholz, Jens
AU - Kim, I
AU - Bernstein, Aaron
AU - Ditmire, Todd
ID - 88
IS - 6
JF - Review of Scientific Instruments
TI - Generation of Mie size microdroplet aerosols with applications in laser-driven fusion experiments
VL - 80
ER -
TY - JOUR
AB - We demonstrate the time-resolved driving of two-photon blue sideband transitions between superconducting qubits and a transmission line resonator. As an example of using these sideband transitions for a two-qubit operation, we implement a pulse sequence that first entangles one qubit with the resonator and subsequently distributes the entanglement between two qubits. We show the generation of 75% fidelity Bell states by this method. The full density matrix of the two-qubit system is extracted using joint measurement and quantum state tomography and shows close agreement with numerical simulation.
AU - Leek, Peter J
AU - Filipp, Stefan
AU - Maurer, Patrick
AU - Baur, Matthias P
AU - Bianchetti, R
AU - Johannes Fink
AU - Göppl, M
AU - Steffen, L. Kraig
AU - Wallraff, Andreas
ID - 1766
IS - 18
JF - Physical Review B - Condensed Matter and Materials Physics
TI - Using sideband transitions for two-qubit operations in superconducting circuits
VL - 79
ER -