We introduce an exact mapping between the Dirac equation in (1+1)-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1+1)-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1+1)-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.

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Systems of particles in a confining potential exhibit a spatially dependent density which fundamentally alters the nature of phase transitions that occur. A specific instance of this situation, which is being extensively explored currently, concerns the properties of ultracold optically trapped atoms. Of interest are how the superfluid-insulator transition is modified by the inhomogeneity, and, indeed, the extent to which a sharp transition survives at all. This paper explores a classical analog of these systems, the Blume-Capel model with a spatially varying single-ion anisotropy and/or temperature gradient. We present results both for the nature of the critical properties and for the validity of the "local density approximation" which is often used to model the inhomogeneous case. We compare situations when the underlying uniform transition is first and second orders.

A one-dimensional quantum many-body system consisting of particles confined in a harmonic potential and subject to finite-range two-body and three-body inverse-square interactions is introduced. The range of the interactions is set by truncation beyond a number of neighbors and can be tuned to interpolate between the Calogero-Sutherland model and a system with nearest and next-nearest neighbors interactions discussed by Jain and Khare. The model also includes the Tonks-Girardeau gas describing impenetrable bosons as well as a novel extension with truncated interactions. While the ground state wavefunction takes a truncated Bijl-Jastrow form, collective modes of the system are found in terms of multivariable symmetric polynomials. We numerically compute the density profile, one-body reduced density matrix, and momentum distribution of the ground state as a function of the range r and the interaction strength.Quantum systems with inverse-square interactions play a prominent role across a wide variety of fields. They are ubiquitous in many-body physics where they have facilitated the understanding of fractional quantum Hall effect and generalized exclusion statistics 1-3 . Historically, their study played a key role in understanding the integrability of systems with long-range interactions and the development of asymptotic Bethe ansatz [4][5][6] . Following the pioneering works by Dyson 7 and Sutherland 4 , their connection to random matrix theory has remained a fruitful line of research 8,9 . They have also found applications in blackhole physics 10 and conformal field theory [11][12][13][14][15][16] . More recently, they have been explored in the context of quantum decay of many-particle unstable systems 17 and in the study of thermal machines in quantum thermodynamics 18,19 .In the one-dimensional continuum space, a many-body system with inverse-square interactions is generally known as the Calogero-Sutherland model (CSM) 4,20,21 . The CSM occupies a privileged status among exactly-solvable models as a source of inspiration [22][23][24] . In its original form, it describes one-dimensional bosons with inverse-square interactions of strength λ that exhibit a universal Luttinger liquid behavior 11 . Under harmonic confinement, this interacting Bose gas is equivalent to an ideal gas of particles with generalized exclusion statistics 3 . It is then referred to as the rational Calogero gas. Its connection with random matrix theory is manifested in the ground-state probability density distribution, which takes the form of the joint probability density for the eigenvalues of the Gaussian β -ensemble with Dyson index β = 2λ 4,9 . While the CSM has shed new light on interacting systems, it can be mapped to a set of noninteracting harmonic oscillators 25,26 . Further, the CSM can be extended to account for fermionic statistics, internal degrees of freedom, and additional interactions, e.g., of Coulomb type 25,26 . In particular, when the range of the interaction is truncated to nearest-neighbors, the system is quasi-exactl...

This paper attempts to resolve the issue of the nature of the 0.01-0.1 cm(-1) peak splittings observed in high-resolution IR spectra of polyatomic molecules. One hypothesis is that these splittings are caused by dynamical tunneling, a quantum-mechanical phenomenon whereby energy flows between two disconnected regions of phase-space across dynamical barriers. However, a competing classical mechanism for energy flow is Arnol'd diffusion, which connects different regions of phase-space by a resonance network known as the Arnol'd web. The speed of diffusion is bounded by the Nekhoroshev theorem, which guarantees stability on exponentially long time scales if the Hamiltonian is steep. Here we consider a non-convex Hamiltonian that contains the characteristics of a molecular Hamiltonian, but does not satisfy the Nekhoroshev theorem. The diffusion along the Arnol'd web is expected to be fast for a non-convex Hamiltonian. While fast diffusion is an unlikely competitor for longtime energy flow in molecules, we show how dynamical tunneling dominates compared to fast diffusion in the nearly integrable regime for a non-convex Hamiltonian, as well as present a new kind of dynamical tunneling.