The chaotic emergence of thermalization in highly excited string decays

We analyse the most general process of a generic highly excited string that decays into a less excited, yet generic, highly excited string emitting a tachyon. We provide a simple and compact analytic description of the decay process which discriminates between and within the structure of every single microstate of the initial and final highly excited string. Taking into account the random nature of the decay process we extract the energy spectrum of highly excited strings, microstate by microstate, finding a behavior which corresponds to the greybody emission spectrum. In addition, by exploiting the analytic control of the decay process, we identify the origin of thermal effects which are triggered by the chaotic nature of the highly excited string interactions modeled by the microstates structure.Comment: 28 pages, 15 figure

DDF operators, open string coherent states and their scattering amplitudes

We study interactions of string coherent states in the DDF (after Di Vecchia, Del Giudice, Fubini) formalism. For simplicity we focus on open bosonic strings. After reviewing basic properties of DDF operators and of excited open strings, we present some classical profiles and show how they become more and more compact as the number of harmonics increases at fixed mass. We then compute various three- and four-point amplitudes with insertions of coherent states, tachyons and vector bosons on the boundary of the disk relying on a convenient choice of reference null momenta. We find that the amplitudes exponentiate in a rather subtle and interesting way. We then study the high-energy fixed-angle limit, dominated by a saddle-point when coherent states are present, and the soft behaviour as the momentum of a vector boson is taken to zero. We briefly comment on generalisation of our analysis to multiple intersecting and magnetised D-branes and to closed strings.Comment: 39 pages, 6 figure

String Memories ... openly retold

We identify string corrections to the EM memory effect. Though largely negligible in the low-energy limit, the effect become relevant in high-energy collisions and in extreme events. We illustrate our findings in a simple unoriented bosonic string model. Thanks to the coherent effect of the infinite tower of open string resonances, the corrections are non-perturbative in $\alpha'$, modulated in retarded time and slowly decaying even at large distances from the source. Remarkably compact expressions obtain for special choices of the kinematics in tree-level 4-point amplitudes. We discuss further corrections occurring at higher-points and the exponential damping resulting from broadening and shifting of the massive poles due to loops. Finally we estimate the range of the parameters and masses for detectability in semi-realistic (Type I) contexts and propose a rationale for this string memory effect.Comment: 16 pages, 5 figure

A measure for chaotic scattering amplitudes

We propose a novel measure of chaotic scattering amplitudes. It takes the form of a log-normal distribution function for the ratios $r_n={\delta_n}/{\delta_{n+1}}$ of (consecutive) spacings $\delta_n$ between two (consecutive) maxima of the scattering amplitude. We show that the same measure applies to the quantum mechanical scattering on a leaky torus as well as to the decay of highly excited string states into two tachyons. Quite remarkably the $r_n$ obey the same distribution that governs the non-trivial zeros of Riemann zeta function.Comment: v2: small corrections, references adde

Non-perturbative determination of improvement b

We present our preliminary results of the non-perturbative determination of the valence mass dependent coefficients bA - bP and bm as well as the ratio ZPZm=ZA entering the flavour non-singlet PCAC relation in lattice QCD with Nf = 3 dynamical flavours. We apply the method proposed in the past for quenched approximation and Nf = 2 cases, employing a set of finite-volume ALPHA configurations with Schrödinger functional boundary conditions, generated with O(a) improved Wilson fermions and the tree-level Symanzik-improved gauge action for a range of couplings relevant for simulations at lattice spacings of about 0.09 fm and below

Photon emission from an excited string

We compute the amplitude for an excited string in any precisely specified state to decay into another excited string in any precisely specified state, via emission of a tachyon or photon. For generic and highly excited string states, the amplitude is a complicated function of the outgoing kinematic angle, sensitive to the precise state. We compute the square of this amplitude, averaged over polarizations of the ingoing string and summed over polarizations of the outgoing string. The seeming intractability of these calculations is made possible by extracting amplitudes involving excited strings from amplitudes involving tachyons and a large number of photons; the number of photons grows with the complexity of the excited string state. Our work is in the spirit of the broad range of recent studies of statistical mechanics and chaos for quantum many-body systems. The number of different excited string states at a given mass is exponentially large, and our calculation gives the emission amplitude of a single photon from each of the microstates -- which, through the Horowitz-Polchinski correspondence principle, are in correspondence with black hole microstates.Comment: 32 page