Asymptotic Universality Research Articles

On Asymptotic Universality of Strong Interactions at Large Distances

On Asymptotic Universality of Strong Interactions at Large Distances

Disentangling sources of quantum entanglement in quench dynamics

Quantum entanglement may have various origins ranging from solely interaction-driven quantum correlations to single-particle effects. Here, we explore the dependence of entanglement on time-dependent single-particle basis transformations in fermionic quantum many-body systems, thus aiming at isolating single-particle sources of entanglement growth in quench dynamics. Using exact diagonalization methods, for paradigmatic non-integrable models we compare to the standard real space cut various physically motivated bipartitions. Moreover, we search for a minimal entanglement basis using local optimization algorithms, which at short to intermediate post-quench times yields a significant reduction of entanglement beyond a dynamical Hartree-Fock solution. In the long-time limit, we identify an asymptotic universality of entanglement for weakly interacting systems, as well as a cross-over from dominant real-space to momentum-space entanglement in Hubbard-models undergoing an interaction quench. Finally, we discuss the relevance of our findings for the development of tensor network based algorithms for quantum dynamics.

Mean equation based scaling analysis of fully-developed turbulent channel flow with uniform heat generation

Multi-scale analysis of the mean equation for passive scalar transport is used to investigate the asymptotic scaling structure of fully developed turbulent channel flow subjected to uniform heat generation. Unlike previous studies of channel flow heat transport with fixed surface temperature or constant inward surface flux, the present flow has a constant outward wall flux that accommodates for the volumetrically uniform heat generation. This configuration has distinct analytical advantages relative to precisely elucidating the underlying self-similar structure admitted by the mean transport equation. The present analyses are advanced using direct numerical simulations (Pirozzoli et al., 2016) that cover friction Reynolds numbers up to δ+=4088 and Prandtl numbers ranging from Pr=0.2–1.0. The leading balances of terms in the mean equation are determined empirically and then analytically described. Consistent with its asymptotic universality, the logarithmic mean temperature profile is shown analytically to arise as a similarity solution to the mean scalar equation, with this solution emerging (as δ+→∞) on an interior domain where molecular diffusion effects are negligible. In addition to clarifying the Reynolds and Prandtl number influences on the von Kármán constant for temperature, kθ, the present theory also provides a couple of self-consistent ways to estimate, kθ. As with previous empirical observations, the present analytical predictions for kθ indicate values that are larger than found for the mean velocity von Kármán constant. The potential origin of this is briefly discussed.

Extremal surfaces in de Sitter spacetime

We study extremal surfaces in de Sitter space in the Poincare slicing in the upper patch, anchored on spatial subregions at the future boundary ${\cal I}^+$, restricted to constant boundary Euclidean time slices (focussing on strip subregions). We find real extremal surfaces of minimal area as the boundaries of past lightcone wedges of the subregions in question: these are null surfaces with vanishing area. We also find complex extremal surfaces as complex extrema of the area functional, and the area is not always real-valued. In $dS_4$ the area is real. The area has structural resemblance with entanglement entropy in a dual $CFT$. There are parallels with analytic continuation from the Ryu-Takayanagi expressions for holographic entanglement entropy in $AdS$. We also discuss extremal surfaces in the $dS$ black brane and the de Sitter "bluewall" studied previously. The $dS_4$ black brane complex surfaces exhibit a real finite cutoff-independent extensive piece. In the bluewall geometry, there are real surfaces that go from one asymptotic universe to the other through the Cauchy horizons.

Pre-Big Bang, space-time structure, asymptotic Universe

Planck and other recent data in Cosmology and Particle Physics can open the way to controversial analyses concerning the early Universe and its possible ultimate origin. Alternatives to standard cosmology include pre-Big Bang approaches, new space-time geometries and new ultimate constituents of matter. Basic issues related to a possible new cosmology along these lines clearly deserve further exploration. The Planck collaboration reports an age of the Universe t close to 13.8 Gyr and a present ratio H between relative speeds and distances at cosmic scale around 67.3 km/s/Mpc. The product of these two measured quantities is then slightly below 1 (about 0.95), while it can be exactly 1 in the absence of matter and cosmological constant in patterns based on the spinorial space-time we have considered in previous papers. In this description of space-time we first suggested in 1996-97, the cosmic time t is given by the modulus of a SU(2) spinor and the Lundmark-Lemaitre-Hubble (LLH) expansion law turns out to be of purely geometric origin previous to any introduction of standard matter and relativity. Such a fundamental geometry, inspired by the role of half-integer spin in Particle Physics, may reflect an equilibrium between the dynamics of the ultimate constituents of matter and the deep structure of space and time. Taking into account the observed cosmic acceleration, the present situation suggests that the value of 1 can be a natural asymptotic limit for the product H t in the long-term evolution of our Universe up to possible small corrections. In the presence of a spinorial space-time geometry, no ad hoc combination of dark matter and dark energy would in any case be needed to get an acceptable value of H and an evolution of the Universe compatible with observation. The use of a spinorial space-time naturally leads to unconventional properties for the space curvature term in Friedmann-like equations. It therefore suggests a major modification of the standard cosmology based on general relativity. In the new cosmology thus introduced, the contribution of the space curvature to the value of H 2 is positive definite independently of the apparent sign of this curvature, and has a much larger value than the standard curvature term. Then, a cosmological constant is no longer required. The spinorial space-time also generates automatically for each comoving observer a privileged space direction that, together with parity violation, may explain the anisotropies observed in WMAP and Planck data. Contrary to frequent statements, such a signature would not be a strange phenomenon. The effect emerges directly from the use of two complex space-time coordinates instead of the conventional four real ones, and the privileged direction would correspond to the phase of the cosmic spinor. We remind here our previous work on the subject and further discuss some cosmological implications of the spinorial space-time.

Pre-big bang collapsing universe from modern Kaluza–Klein theory of gravity

We study the collapse of the universe described by a scalar field spherically symmetric collapse of a system described by a massless scalar field from a 5D Riemann-flat canonical metric, on which we make a dynamical foliation on the extra space-like dimension. The asymptotic universe (absent of singularities) results to be finite in size and energy density, with an vacuum dominated equation of state. The important result here obtained is that the asymptotic back-reaction effects are given by a negative constant: 12[11+ψ˙2+1ψ˙2]〈(δφ¯˙)2〉+12a2〈(∇→δφ)2〉|t→∞=−8Λ03πG.

Some recent advances in theory and simulation of fractional diffusion processes

To offer an insight into the rapidly developing theory of fractional diffusion processes, we describe in some detail three topics of current interest: (i) the well-scaled passage to the limit from continuous time random walk under power law assumptions to space-time fractional diffusion, (ii) the asymptotic universality of the Mittag–Leffler waiting time law in time-fractional processes, (iii) our method of parametric subordination for generating particle trajectories.

Asymptotic universality in the vibrational spectra of amorphous single-component systems

We have numerically investigated the vibrational spectra of bulk single-component systems for which the potential energy depends only on the positions of the constituent units and is of the form of a sum over pairs. When the width of the potential well describing the two-body interaction is reduced progressively, our results suggest that the shape of the entire spectrum in the amorphous state approaches a limit that is independent of the explicit functional form of the potential. We use this observation of asymptotic universality to explain the quasiuniversal nature of vibrational spectra that has been observed in recent experimental studies of bulk molecular glasses [Chumakov et al., Phys. Rev. Lett. 92, 245508 (2004)].

Power transfer in non-linear gravitational clustering and asymptotic universality

Abstract We study the non-linear gravitational clustering of collisionless particles in an expanding background using an integro-differential equation for the gravitational potential. In particular, we address the question of how the non-linear mode–mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale. We show that the dynamical equation allows self-similar evolution for the gravitational potential φk(t) in Fourier space of the form φk(t) = F(t)D(k) where the function F(t) satisfies a second-order non-linear differential equation. We analyse the relevant solutions of this equation, thereby determining the asymptotic time evolution of the gravitational potential and density contrast. The analysis suggests that both F(t) and D(k) have well-defined asymptotic forms indicating that the power transfer leads to a universal power spectrum at late times. The analytic results are compared with numerical simulations, showing good agreement over the range at which we could test them.

Universality class of discrete solid-on-solid limited mobility nonequilibrium growth models for kinetic surface roughening

We investigate, using the noise reduction technique, the asymptotic universality class of the well-studied nonequilibrium limited mobility atomistic solid-on-solid surface growth models introduced by Wolf and Villain (WV) and Das Sarma and Tamborenea (DT) in the context of kinetic surface roughening in ideal molecular beam epitaxy. We find essentially all the earlier conclusions regarding the universality class of DT and WV models to be severely hampered by slow crossover and extremely long-lived transient effects. We identify the correct asymptotic universality class(es) that differs from earlier conclusions in several instances.

Hadron diffractive processes: the structure of soft pomeron and colour screening

On the basis of the experimental data on diffractive processes in πp, pp and p¯p collisions at intermediate, moderately high and high energies, we restore the scattering amplitude related to the t-channel exchange by vacuum quantum numbers by taking account of the diffractive s-channel rescatterings. At intermediate and moderately high energies, the t-channel exchange amplitude turns, with a good accuracy, into an effective pomeron which renders the results of the additive quark model. At superhigh energies the scattering amplitude provides a Froissart-type behaviour, with an asymptotic universality of cross sections such as σtot πp/σtot pp→ 1 at s→∞. The quark structure of hadrons being taken into account at the level of constituent quarks, the cross sections of pion and proton (antiproton) in the impact parameter space of quarks, σπ(r 1⊥, r 2⊥; s) and σp(r 1⊥, r 2⊥, r 3⊥; s), are found as functions of s. These cross sections implicate the phenomenon of colour screening: they tend to zero at |r i⊥−r k⊥|→ 0. The effective colour screening radius for pion (proton) is found for different s. The predictions for the diffractive cross sections at superhigh energies are presented.

Fluid-magnet universality: Renormalization-group analysis ofφ5operators

The question of a possible difference between the universality classes of fluids and Ising-like magnets is addressed by perturbation theory and the renormalization group. The most dangerous possibility is that of an ${\ensuremath{\varphi}}^{5}$ addition to the usual ${\ensuremath{\varphi}}^{4}$ theory. We show that no ${\ensuremath{\varphi}}^{5}$ fixed point exists in the framework of an expansion around $d=\frac{10}{3}$. Further we show that to $O({\ensuremath{\epsilon}}_{4}^{2})$, ${\ensuremath{\epsilon}}_{4}\ensuremath{\equiv}4\ensuremath{-}d$, the ordinary ${\ensuremath{\varphi}}^{4}$ fixed point is stable against the perturbations that mix with ${\ensuremath{\varphi}}^{5}$. Two new correction-to-scaling exponents are found. One of the exponents, ${\ensuremath{\Delta}}_{5}$, is poorly determined with a range of values from 0.5 to 1.0 compatible with the $O({\ensuremath{\epsilon}}_{4}^{2})$ result. However, its positivity rules out a separate fluid fixed point, indicating fluid-magnet asymptotic universality. The second exponent, ${\ensuremath{\Delta}}_{3}$, can be determined exactly: ${\ensuremath{\Delta}}_{3}=1\ensuremath{-}\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta}$. This implies the universal existence of a contribution to the fluid diameter scaling like the internal energy.

XYmodel and the superfluid density in two dimensions

By computing the incremental free energy of the two-dimensional $\mathrm{XY}$ model in a state with a long-wavelength twist of the local short-range order, we evaluate for all $Tl{T}_{c}$ the superfluid density ${\ensuremath{\rho}}_{s}$ for superfluid systems. Spin-wave excitations in the $\mathrm{XY}$ model imply a substantial (nonuniversal) depletion of ${\ensuremath{\rho}}_{s}$ at low temperatures. We find that these contributions do not affect the asymptotic universality; as $T\ensuremath{\rightarrow}{T}_{{c}^{\ensuremath{-}}}$, $\frac{{\ensuremath{\rho}}_{s}}{T}$ becomes universal and we recover the previous results of Nelson and Kosterlitz. In the Appendix we derive the Kosterlitz recursion relations by transforming to a sine-Gordon system and using conventional momentum shell integration techniques.