scholarly journals Transseries for causal diffusive systems

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Michal P. Heller ◽  
Alexandre Serantes ◽  
Michał Spaliński ◽  
Viktor Svensson ◽  
Benjamin Withers
Keyword(s):  
Approximation Scheme ◽  
Proper Time ◽  
Gluon Plasma ◽  
Nonequilibrium Dynamics ◽  
Late Time ◽  
Time Behaviour ◽  
Position Space ◽  
Hydrodynamic Modes ◽  
Plasma Dynamics ◽  
Spacetime Region

Abstract The large proper-time behaviour of expanding boost-invariant fluids has provided many crucial insights into quark-gluon plasma dynamics. Here we formulate and explore the late-time behaviour of nonequilibrium dynamics at the level of linearized perturbations of equilibrium, but without any special symmetry assumptions. We introduce a useful quantitative approximation scheme in which hydrodynamic modes appear as perturbative contributions while transients are nonperturbative. In this way, solutions are naturally organized into transseries as they are in the case of boost-invariant flows. We focus our attention on the ubiquitous telegrapher’s equation, the simplest example of a causal theory with a hydrodynamic sector. In position space we uncover novel transient contributions as well as Stokes phenomena which change the structure of the transseries based on the spacetime region or the choice of initial data.

scholarly journals The late-time behaviour of vortic Bianchi type VIII universes

2006 ◽  
Vol 23 (9) ◽  
pp. 3017-3035 ◽  
Author(s):  
Sigbjørn Hervik ◽  
Woei Chet Lim
Keyword(s):  
Bianchi Type ◽  
Late Time ◽  
Time Behaviour ◽  
Type Viii

Long tipping times of a quantum rod

2006 ◽  
Vol 84 (1) ◽  
pp. 19-36 ◽  
Author(s):  
Mark B Lundeberg ◽  
Mark RA Shegelski
Keyword(s):  
Quantum State ◽  
Schrodinger Equation ◽  
Center Of Mass ◽  
Edge Length ◽  
The Other ◽  
Late Time ◽  
Time Behaviour ◽  
Complex Energy ◽  
Energy Eigenstates ◽  
Quantum Rod

We calculate the tipping time of a quantum rod that has a height several times that of the edge length of its square base. We use an expression for the tipping time that has heuristic value, and gives the average time at which, upon measurement, the initially balanced rod is found to tip. We use two methods to calculate the tipping time. One method is to examine the "late time" behaviour of the quantum state of the center of mass of the rod by using an equation that has the form of the time-independent Schrödinger equation except that it involves a "complex energy." The other method uses energy resonances in the eigenstates of the Hamiltonian to determine the tipping time. We use the well-known Wentzel–Kramers–Brillouin approximation to calculate the energy eigenstates. With these methods, we obtain expressions for the tipping time that are valid for very long tipping times. PACS Nos.: 03.65.–w, 03.65.Xp

ASSISTED INFLATION

2002 ◽  
Vol 17 (20) ◽  
pp. 2755-2755
Author(s):  
A. A. COLEY ◽  
R. J. VAN DEN HOOGEN
Keyword(s):  
Perfect Fluid ◽  
Scalar Fields ◽  
Cosmological Models ◽  
Late Time ◽  
Time Behaviour ◽  
Field Curvature ◽  
Scaling Solution ◽  
Dynamical Properties ◽  
Spatially Homogeneous ◽  
Parameter Values

The dynamical properties of spatially homogeneous and isotropic cosmological models containing a barotropic perfect fluid and multiple scalar fields with independent exponential potentials is investigated. It is shown that the assisted inflationary scaling solution is the global late-time attractor for the parameter values for which the model is inflationary, even when curvature and barotropic matter are included. For all other parameter values the multi-field curvature scaling solution is the global late-time attractor (in these solutions the curvature is not dynamically negligible asymptotically). Consequently, in general all of the scalar fields in multi-field models with exponential potentials are non-negligible in late-time behaviour, contrary to what is commonly believed.

scholarly journals Late-time behaviour of the tilted Bianchi type VI h models

2007 ◽  
Vol 24 (15) ◽  
pp. 3859-3895 ◽  
Author(s):  
S Hervik ◽  
R J van den Hoogen ◽  
W C Lim ◽  
A A Coley
Keyword(s):  
Bianchi Type ◽  
Late Time ◽  
Time Behaviour

scholarly journals The First fm/c of Heavy-Ion Collisions

2019 ◽  
Vol 69 (1) ◽  
pp. 447-476 ◽  
Author(s):  
S. Schlichting ◽  
D. Teaney
Keyword(s):  
Heavy Ion Collisions ◽  
Early Time ◽  
Heavy Ion ◽  
Gluon Plasma ◽  
High Energy ◽  
Nonequilibrium Dynamics ◽  
Local Thermal Equilibrium ◽  
Time Dynamics ◽  
Ion Collisions ◽  
The Many

We present an introductory review of the early-time dynamics of high-energy heavy-ion collisions and the kinetics of high-temperature quantum chromodynamic matter. The equilibration mechanisms in the quark–gluon plasma uniquely reflect the nonabelian and ultrarelativistic character of the many-body system. Starting with a brief exposé of the key theoretical and experimental questions, we provide an overview of the theoretical tools employed in weak coupling studies of the early-time nonequilibrium dynamics. We highlight theoretical progress in understanding different thermalization mechanisms in weakly coupled nonabelian plasmas, and discuss their relevance in describing the approach to local thermal equilibrium during the first fm/ c of a heavy-ion collision. We also briefly discuss some important connections to the phenomenology of heavy-ion collisions.

scholarly journals Late-time behaviour of the tilted Bianchi type VI −1/9 models

2007 ◽  
Vol 25 (1) ◽  
pp. 015002 ◽  
Author(s):  
S Hervik ◽  
R J van den Hoogen ◽  
W C Lim ◽  
A A Coley
Keyword(s):  
Bianchi Type ◽  
Late Time ◽  
Time Behaviour

scholarly journals QUANTUM AMPLITUDES IN BLACK-HOLE EVAPORATION: COMPLEX APPROACH AND SPIN-0 AMPLITUDE

2011 ◽  
Vol 20 (02) ◽  
pp. 133-159
Author(s):  
A. N. St. J. FARLEY ◽  
P. D. D'EATH
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Scalar Field ◽  
Boundary Value Problem ◽  
Boundary Data ◽  
Proper Time ◽  
Boundary Value ◽  
Constrained Systems ◽  
Time Interval ◽  
Late Time

This paper is concerned with the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat space–time and weak radiation at a very late time. We evaluate quantum amplitudes (not just probabilities) for transitions from initial to final states. This quantum description shows that no information is lost in collapse to a black hole. Boundary data for the gravitational field and (in this paper) a scalar field are posed on an initial space-like hypersurface ΣI and a final surface ΣF. These asymptotically flat three-surfaces are separated by a Lorentzian proper-time interval T (typically very large), as measured at spatial infinity. The boundary-value problem is made well-posed, both classically and quantum-mechanically, by a rotation of T into the lower-half complex plane: T → |T| exp (- iθ), with 0 < θ ≤ π/2. This corresponds to Feynman's +iϵ prescription. We consider the classical boundary-value problem and calculate the second-variation classical Lorentzian action [Formula: see text] as a functional of the boundary data. Following Feynman, the Lorentzian quantum amplitude is recovered in the limit θ → 0+ from the well-defined complex-T amplitude. Dirac's canonical approach to the quantisation of constrained systems shows that, for locally supersymmetric theories of gravity, the amplitude is exactly semi-classical, namely [Formula: see text] for weak perturbations, apart from delta functionals of the supersymmetry constraints. We treat such quantum amplitudes for weak scalar-field configurations on ΣF, taking (for simplicity) the weak final gravitational field to be spherically symmetric. The treatment involves adiabatic solutions to the scalar wave equation. This considerably extends work reported in previous papers, by giving explicit expressions for the real and imaginary parts of such quantum amplitudes.

scholarly journals String fragmentation with a time-dependent tension

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Nicholas Hunt-Smith ◽  
Peter Skands
Keyword(s):  
Proper Time ◽  
String Tension ◽  
Time Dependent ◽  
Data Sets ◽  
Late Time ◽  
Equilibrium Limit ◽  
Model Independent ◽  
String Fragmentation ◽  
Hadronization Model ◽  
Do So

AbstractMotivated by recent theoretical arguments that expanding strings can be regarded as having a temperature that is inversely proportional to the proper time, $$\tau $$ τ , we investigate the consequences of adding a term $$\propto 1/\tau $$ ∝ 1 / τ to the string tension in the Lund string-hadronization model. The lattice value for the tension, $$\kappa _0 \sim 0.18\,{\mathrm {GeV}}^2\sim 0.9\,{\mathrm {GeV}}/{\mathrm {fm}}$$ κ 0 ∼ 0.18 GeV 2 ∼ 0.9 GeV / fm , is then interpreted as the late-time/equilibrium limit. A generic prediction of this type of model is that early string breaks should be associated with higher strangeness (and baryon) fractions and higher fragmentation $$\langle p_\perp \rangle $$ ⟨ p ⊥ ⟩ values. It should be possible to use archival ee data sets to provide model-independent constraints on this type of scenario, and we propose a few simple key measurements to do so.

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