Black Hole Emission in String Theory and the String Phase of Black Holes

String theory properly describes black-hole evaporation. The quantum string emission by Black Holes is computed. The black-hole temperature is the Hawking temperature in the semiclassical quantum field theory (QFT) regime and becomes the intrinsic string temperature, T_s, in the quantum (last stage) string regime. The QFT-Hawking temperature T_H is upper bounded by the string temperature T_S. The black hole emission spectrum is an incomplete gamma function of (T_H - T_S). For T_H << T_S, it yields the QFT-Hawking emission. For T_H \to T_S, it shows highly massive string states dominate the emission and undergo a typical string phase transition to a microscopic `minimal' black hole of mass M_{\min} or radius r_{\min} (inversely proportional to T_S) and string temperature T_S. The string back reaction effect (selfconsistent black hole solution of the semiclassical Einstein equations) is computed. Both, the QFT and string black hole regimes are well defined and bounded.The string `minimal' black hole has a life time tau_{min} simeq (k_B c)/(G hbar [T_S]^3). The semiclassical QFT black hole (of mass M and temperature T_H) and the string black hole (of mass M_{min} and temperature T_S) are mapped one into another by a `Dual' transform which links classical/QFT and quantum string regimes.Comment: LaTex, 22 pages, Lectures delivered at the Chalonge School, Nato ASI: Phase Transitions in the Early Universe: Theory and Observations. To appear in the Proceedings, Editors H. J. de Vega, I. Khalatnikov, N. Sanchez. (Kluwer Pub

Knots and Particles

Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil configurations, and our results suggest that all torus knots appear as solitons. Our observations open new theoretical possibilities in scenarios where stringlike structures appear, including physics of fundamental interactions and early universe cosmology. In nematic liquid crystals and 3He superfluids such knotted solitons might actually be observed.Comment: 9 pages, 4 color eps figures and one b/w because of size limit (color version available from authors

Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow

We report the observation of vortex formation upon the absorption of a thermal neutron in a rotating container of superfluid $^3$He-B. The nuclear reaction n + $^3$He = p + $^3$H + 0.76MeV heats a cigar shaped region of the superfluid into the normal phase. The subsequent cooling of this region back through the superfluid transition results in the nucleation of quantized vortices. Depending on the superflow velocity, sufficiently large vortex rings grow under the influence of the Magnus force and escape into the container volume where they are detected individually with nuclear magnetic resonance. The larger the superflow velocity the smaller the rings which can expand. Thus it is possible to obtain information about the morphology of the initial defect network. We suggest that the nucleation of vortices during the rapid cool-down into the superfluid phase is similar to the formation of defects during cosmological phase transitions in the early universe.Comment: 4 pages, LaTeX file, 4 figures are available at ftp://boojum.hut.fi/pub/publications/lowtemp/LTL-95009.p

Intrinsic ripples in graphene

The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.Comment: 14 pages, 6 figure

Parameters of Pseudo-Random Quantum Circuits

Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random circuits, with the goal of identifying relevant trade-offs and optimizing convergence. The parameters we explore include the choice of single- and two-qubit gates, the topology of the underlying physical qubit architecture, the probabilistic application of two-qubit gates, as well as circuit size, initialization, and the effect of control constraints. Building on the equivalence between pseudo-random circuits and approximate $t$-designs, a Markov matrix approach is employed to analyze asymptotic convergence properties of pseudo-random second-order moments to a 2-design. Quantitative results on the convergence rate as a function of the circuit size are presented for qubit topologies with a sufficient degree of symmetry. Our results may be theoretically and practically useful to optimize the efficiency of random state and operator generation.Comment: 17 pages, 14 figures, 2 Appendice

The heterotic string at high temperature (or with strong supersymmetry breaking)

Perturbative heterotic string theory develops a single complex tachyonic mode beyond the Hagedorn temperature. We calculate the quartic effective potential for this tachyonic mode at the critical temperature. Equivalently, we determine the quartic effective potential for strong supersymmetric breaking via anti-perdiodic boundary conditions for fermions on a small circle. We give many details of the heterotic tachyon scattering amplitudes, including a unitarity check to fix all normalization constants. We discuss difficulties in obtaining an effective action valid at all radii. We argue that in certain variables, the quartic term in the potential is radius independent. Speculations on the properties of a new strongly curved phase that could occur after tachyon condensation are offered.Comment: 22 pages; v2: minor corrections, references adde

Shaping black holes with free fields

Starting from a metric Ansatz permitting a weak version of Birkhoff's theorem we find static black hole solutions including matter in the form of free scalar and p-form fields, with and without a cosmological constant \Lambda. Single p-form matter fields permit multiple possibilities, including dyonic solutions, self-dual instantons and metrics with Einstein-Kaelher horizons. The inclusion of multiple p-forms on the other hand, arranged in a homogeneous fashion with respect to the horizon geometry, permits the construction of higher dimensional dyonic p-form black holes and four dimensional axionic black holes with flat horizons, when \Lambda<0. It is found that axionic fields regularize black hole solutions in the sense, for example, of permitting regular -- rather than singular -- small mass Reissner-Nordstrom type black holes. Their cosmic string and Vaidya versions are also obtained.Comment: 38 pages. v2: minor changes, published versio

Evidence for topological defects in a photoinduced phase transition

Upon excitation with an intense ultrafast laser pulse, a symmetry-broken ground state can undergo a non-equilibrium phase transition through pathways dissimilar from those in thermal equilibrium. Determining the mechanism underlying these photo-induced phase transitions (PIPTs) has been a long-standing issue in the study of condensed matter systems. To this end, we investigate the light-induced melting of a unidirectional charge density wave (CDW) material, LaTe$_3$. Using a suite of time-resolved probes, we independently track the amplitude and phase dynamics of the CDW. We find that a quick ($\sim\,$1$\,$ps) recovery of the CDW amplitude is followed by a slower reestablishment of phase coherence. This longer timescale is dictated by the presence of topological defects: long-range order (LRO) is inhibited and is only restored when the defects annihilate. Our results provide a framework for understanding other PIPTs by identifying the generation of defects as a governing mechanism

Self-shaping of oil droplets via the formation of intermediate rotator phases upon cooling.

Revealing the chemical and physical mechanisms underlying symmetry breaking and shape transformations is key to understanding morphogenesis. If we are to synthesize artificial structures with similar control and complexity to biological systems, we need energy- and material-efficient bottom-up processes to create building blocks of various shapes that can further assemble into hierarchical structures. Lithographic top-down processing allows a high level of structural control in microparticle production but at the expense of limited productivity. Conversely, bottom-up particle syntheses have higher material and energy efficiency, but are more limited in the shapes achievable. Linear hydrocarbons are known to pass through a series of metastable plastic rotator phases before freezing. Here we show that by using appropriate cooling protocols, we can harness these phase transitions to control the deformation of liquid hydrocarbon droplets and then freeze them into solid particles, permanently preserving their shape. Upon cooling, the droplets spontaneously break their shape symmetry several times, morphing through a series of complex regular shapes owing to the internal phase-transition processes. In this way we produce particles including micrometre-sized octahedra, various polygonal platelets, O-shapes, and fibres of submicrometre diameter, which can be selectively frozen into the corresponding solid particles. This mechanism offers insights into achieving complex morphogenesis from a system with a minimal number of molecular components.European Research Council (Grant ID: EMATTER 280078), European networks COST MP 1106 and 1305 and the capacity building project BeyondEverest of the European Commission (Grant ID: 286205)This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/nature1618