Superadiabatic transitions in quantum molecular dynamics

We study the dynamics of a molecule’s nuclear wave function near an avoided crossing of two electronic energy levels for one nuclear degree of freedom. We derive the general form of the Schrödinger equation in the nth superadiabatic representation for all n є N. Using these results, we obtain closed formulas for the time development of the component of the wave function in an initially unoccupied energy subspace when a wave packet travels through the transition region. In the optimal superadiabatic representation, which we define, this component builds up monotonically. Finally, we give an explicit formula for the transition wave function away from the avoided crossing, which is in excellent agreement with high-precision numerical calculations

Determination of Non-Adiabatic Scattering Wave Functions in a Born-Oppenheimer Model

We study non--adiabatic transitions in scattering theory for the time dependent molecular Schroedinger equation in the Born--Oppenheimer limit. We assume the electron Hamiltonian has finitely many levels and consider the propagation of coherent states with high enough total energy. When two of the electronic levels are isolated from the rest of the electron Hamiltonian's spectrum and display an avoided crossing, we compute the component of the nuclear wave function associated with the non--adiabatic transition that is generated by propagation through the avoided crossing. This component is shown to be exponentially small in the square of the Born--Oppenheimer parameter, due to the Landau-Zener mechanism. It propagates asymptotically as a free Gaussian in the nuclear variables, and its momentum is shifted. The total transition probability for this transition and the momentum shift are both larger than what one would expect from a naive approximation and energy conservation

Avoided crossings in mesoscopic systems: electron propagation on a non-uniform magnetic cylinder

We consider an electron constrained to move on a surface with revolution symmetry in the presence of a constant magnetic field $B$ parallel to the surface axis. Depending on $B$ and the surface geometry the transverse part of the spectrum typically exhibits many crossings which change to avoided crossings if a weak symmetry breaking interaction is introduced. We study the effect of such perturbations on the quantum propagation. This problem admits a natural reformulation to which tools from molecular dynamics can be applied. In turn, this leads to the study of a perturbation theory for the time dependent Born-Oppenheimer approximation

Large Nc Continuum Reduction and the Thermodynamics of QCD

It is noted that if large Nc continuum reduction applies to an observable, then that observable is independent of temperature for all temperatures below some critical value. This fact, plus the fact that mesons and glueballs are weakly interacting at large Nc is used as the basis for a derivation of large Nc continuum reduction for the chiral condensate. The structure of this derivation is quite general and can be extended to a wide class of observables

The Hagedorn temperature Revisited

The Hagedorn temperature, T_H is determined from the number of hadronic resonances including all mesons and baryons. This leads to a stable result T_H = 174 MeV consistent with the critical and the chemical freeze-out temperatures at zero chemical potential. We use this result to calculate the speed of sound and other thermodynamic quantities in the resonance hadron gas model for a wide range of baryon chemical potentials following the chemical freeze-out curve. We compare some of our results to those obtained previously in other papers.Comment: 13 pages, 4 figure

Kappa-deformed Statistics and the Formation of a Quark-Gluon Plasma

The effect of the non-extensive form of statistical mechanics proposed by Tsallis on the formation of a quark-gluon plasma (QGP) has been recently investigated in ref. \cite{1}. The results show that for small deviations ($\approx 10$) from Boltzmann-Gibbs (BG) statistics in the QGP phase, the critical temperature for the formation of a QGP does not change substantially for a large variation of the chemical potential. In the present effort we use the extensive $\kappa$-deformed statistical mechanics constructed by Kaniadakis to represent the constituents of the QGP and compare the results with ref. [1].Comment: 2 Figure

N=(1,1) super Yang--Mills theory in 1+1 dimensions at finite temperature

We present a formulation of N=(1,1) super Yang-Mills theory in 1+1 dimensions at finite temperature. The partition function is constructed by finding a numerical approximation to the entire spectrum. We solve numerically for the spectrum using Supersymmetric Discrete Light-Cone Quantization (SDLCQ) in the large-N_c approximation and calculate the density of states. We find that the density of states grows exponentially and the theory has a Hagedorn temperature, which we extract. We find that the Hagedorn temperature at infinite resolution is slightly less than one in units of (g^(2) N_c/pi)^(1/2). We use the density of states to also calculate a standard set of thermodynamic functions below the Hagedorn temperature. In this temperature range, we find that the thermodynamics is dominated by the massless states of the theory.Comment: 16 pages, 8 eps figures, LaTe

Strangeness, Equilibration, Hadronization

In these remarks I explain the motivation which leads us to consider chemical nonequilibrium processes in flavor equilibration and in statistical hadroniziation of quark--gluon plasma (QGP). Statistical hadronization allowing for chemical non-equilibrium is introduced. The reesults of fits to RHIC-130 results, including multistrange hadrons, are shown to agree only with the model of an exploding QGP fireball.Comment: 8 pages including one figure, discussion contribution at Strange Quark Matter 2001, Frankfurt, submitted to J. Phys.

Semiclassical (Quantum Field Theory) and Quantum (String) de Sitter Regimes: New Results

We compute the quantum string entropy S_s(m, H) from the microscopic string density of states rho_s (m,H) of mass m in de Sitter space-time. We find for high m, a {\bf new} phase transition at the critical string temperature T_s= (1/2 pi k_B)L c^2/alpha', higher than the flat space (Hagedorn) temperature t_s. (L = c/H, the Hubble constant H acts at the transition as producing a smaller string constant alpha' and thus, a higher tension). T_s is the precise quantum dual of the semiclassical (QFT Hawking-Gibbons) de Sitter temperature T_sem = hbar c /(2\pi k_B L). We find a new formula for the full de Sitter entropy S_sem (H), as a function of the usual Bekenstein-Hawking entropy S_sem^(0)(H). For L << l_{Planck}, ie. for low H << c/l_Planck, S_{sem}^{(0)}(H) is the leading term, but for high H near c/l_Planck, a new phase transition operates and the whole entropy S_sem (H) is drastically different from the Bekenstein-Hawking entropy S_sem^(0)(H). We compute the string quantum emission cross section by a black hole in de Sitter (or asymptotically de Sitter) space-time (bhdS). For T_sem ~ bhdS << T_s, (early evaporation stage), it shows the QFT Hawking emission with temperature T_sem ~ bhdS, (semiclassical regime). For T_sem ~ bhdS near T_{s}, it exhibits a phase transition into a string de Sitter state of size L_s = l_s^2/L}, l_s= \sqrt{\hbar alpha'/c), and string de Sitter temperature T_s. Instead of featuring a single pole singularity in the temperature (Carlitz transition), it features a square root branch point (de Vega-Sanchez transition). New bounds on the black hole radius r_g emerge in the bhdS string regime: it can become r_g = L_s/2, or it can reach a more quantum value, r_g = 0.365 l_s.Comment: New original materia

A Nonlinear Adiabatic Theorem for Coherent States

We consider the propagation of wave packets for a one-dimensional nonlinear Schrodinger equation with a matrix-valued potential, in the semi-classical limit. For an initial coherent state polarized along some eigenvector, we prove that the nonlinear evolution preserves the separation of modes, in a scaling such that nonlinear effects are critical (the envelope equation is nonlinear). The proof relies on a fine geometric analysis of the role of spectral projectors, which is compatible with the treatment of nonlinearities. We also prove a nonlinear superposition principle for these adiabatic wave packets.Comment: 21 pages, no figur