We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.
The physical consequences of the relativistic and nonrelativistic approaches to describe the energy levels of electrons which propagate in a static homogeneous magnetic field are considered. It is shown that for a given strength of the magnetic field, the quantized energy levels of the electrons calculated by nonrelativistic and relativistic equations differ substantially, up to few orders of magnitude for a magnetic field of about 1 Tesla. Experimental verification to resolve the discrepancy would be very welcome.
We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues may be determined analytically. Applied to two-particle bound states, it turns out that in this way a nonrelativistic treatment may indeed be able to simulate relativistic effects. Within the framework of hadron spectroscopy, this lucky circumstance may be an explanation for the sometimes extremely good predictions of nonrelativistic potential models even i…
We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues may be determined analytically. Applied to two-particle bound states, it turns out that in this way a nonrelativistic treatment may indeed be able to simulate relativistic effects. Within the framework of hadron spectroscopy, this lucky circumstance may be an explanation for the sometimes extremely good predictions of nonrelativistic potential models even i…
We examine string (vortex) formation at a quench for a weakly-coupled global U(1) theory when the excitation spectrum is non-relativistic. It is so similar to vortex production in the corresponding relativistic plasma as to reinforce arguments for the similarity of vorheptex production in the early universe and in low-temperature many-body physics.
The relativistic amplitude for the direct knock-out contribution to $\left( γ, p \right)$ reactions on nuclei is reduced to a nonrelativistic form using an effective Pauli reduction scheme. The reduction is carried out to second order in the inverse nucleon mass. It is found that the interaction Hamiltonian appearing in the nonrelativistic amplitude has significant dependence, starting at second order, on the vector and scalar mean nuclear potentials. These strong medium modifications are absent in traditional nonrelativistic calculations. Detailed comparisons show that these modifications are…
The confinement mechanism earlier proposed by author is applied to describe the (possible) ground state of toponium $η_t$. For this aim the nonperturbative consistent approach is elaborated in both relativistic and nonrelativistic cases. The study entails estimates for parameters of the confining SU(3)-gluonic field in the above quarkonium, those estimates being also consistent with possible width of decay $η_t\to2γ$. The corresponding estimates of the gluon concentrations, electric and magnetic colour field strengths are also adduced for the mentioned field at the scales of toponium.
The fractional parentage expansion method is extended from $SU(2)_{f}$ nonrelativistic to $SU(3)_{f}$ and relativistic dibaryon calculations. A transformation table between physical bases and symmetry bases for the $SU(3)_{f}$ dibaryon is provided. A program package has been written for dibaryon calculation based on the fractional parentage expansion method.
We investigate the connection between relativistic potential models for quark-antiquark bound states and the nonrelativistic models that have been used successfully to fit and predict the spectra of relativistic systems. We use Martin's operator inequality \sqrt{p^2+m^2} <= (p^2+M^2+m^2)/2M to motivate the approximation of the relativistic kinetic energy terms in the spinless Salpeter equation by expressions of the nonrelativistic form M+ε+p^2/2M for each quark. To investigate the validity of the resulting approximation numerically, we generate energy spectra for q\bar{q} mesons composed of tw…
We discuss the phenomena of symmetry non-restoration and inverse symmetry breaking in the context of multi-scalar field theories at finite temperatures and present its consequences for the relativistic Higgs-Kibble multi-field sector as well as for a nonrelativistic model of hard core spheres. For relativistic scalar field models, it has been shown previously that temperature effects on the couplings do not alter, qualitatively, the phase transition pattern. Here, we show that for the nonrelativistic analogue of these models inverse symmetry breaking, as well as symmetry non-restoration, canno…
Nonthermal fixed point for massless scalar field theories
Institute for Theoretical Physics, Heidelberg University（海德堡大学理论物理研究所）；Institute for Theoretical Physics, University of Tübingen（蒂宾根大学理论物理研究所）；Department of Physics, University of Konstanz（康斯坦茨大学物理系）；Institute of Physics, Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学物理研究所）
We calculate two-photon exchange amplitudes for the elastic electron-hadron scattering in the nonrelativistic approximation, and obtain analytical formulae for them. Numerical calculations are performed for proton and $^3$He targets. Comparing our numerical results with relativistic calculations, we find that the real part of the amplitude is described well at moderate $Q^2$, but the imaginary part strongly differs from the relativistic result. Thus the nonrelativistic approximation should not be used for calculation of observables which depend on the imaginary part of the amplitude, such as s…
We consider the problem of internal particle state transformation, which is a bound state of several constituents, from the particle's rest frame to the system in which this particle is relativistic. It is assumed that in the rest frame of the composite particle, its internal state can be considered in the nonrelativistic approximation. It is shown, that this internal state is unchanged during the transition from one reference frame to another. Namely, given the particle is spherically symmetric in the rest frame, it remains spherically symmetric in any other reference frame, and does not unde…
We find an exact formula for the thermally averaged cross section times the relative velocity $\langle σv_{\text{rel}} \rangle$ with relativistic Maxwell-Boltzmann statistics. The formula is valid in the effective field theory approach when the masses of the annihilation products can be neglected compared with the dark matter mass and cut-off scale. The expansion at $x=m/T\gg 1$ directly gives the nonrelativistic limit of $\langle σv_{\text{rel}}\rangle$ which is usually used to compute the relic abundance for heavy particles that decouple when they are nonrelativistic. We compare this expansi…
We discuss the nonrelativistic limit of the relativistic Navier-Fourier-Stokes (NFS) theory. The next-to-leading order relativistic corrections to the NFS theory for the Landau-Lifshitz fluid are obtained. While the lowest order truncation of the velocity expansion leads to the usual NFS equations of nonrelativistic fluids, we show that when the next-to-leading order relativistic corrections are included, the equations can be expressed concurrently with two different fluid velocities. One of the fluid velocities is parallel to the conserved charge current (which follows the Eckart definition) …
The nonrelativistic Hamiltonians of scalar, spinor and vector particles in the electromagnetic field are studied by applying the Douglas-Kroll-Hess approach. Their relativistic Hamiltonians are expanded on the potential, and the Hamiltonians containing one- and two-photon potentials are derived. The nonrelativistic Hamiltonians up to $mα^8$ order are obtained by applying Taylor expansion on momentum, and the result of spin-1/2 spinor is coincided with the result obtained by applying scattering matching approach in the Ref.~[Phys. Rev. A {\bf 100}, 012513 (2019)]. Then, the singularities in Ham…
In this paper we develop a formalism for studying the nonrelativistic limit of relativistic field theories in a systematic way. By introducing a simple, nonlocal field redefinition, we transform a given relativistic theory, describing a real, self-interacting scalar field, into an equivalent theory, describing a complex scalar field that encodes at each time both the original field and its conjugate momentum. Our low-energy effective theory incorporates relativistic corrections to the kinetic energy as well as the backreaction of fast-oscillating terms on the behavior of the dominant, slowly v…
We present an effective field theory suitable to describe a non-relativistic particle-antiparticle pair of heavy scalars based on the gauge group SU(3). Its formulation is analogous to that of "velocity NRQCD" (vNRQCD), a non-relativistic effective theory for heavy quark pairs. The matching conditions with scalar QCD and the renormalization group evolution of the effective theory are discussed. The non-relativistic framework proposed here suffices to compute scalar-antiscalar bound state energies at next-to-next-to-leading-logarithmic (NNLL) order and next-to-leading-logarithmic (NLL) threshol…
The structure functions b_{1,2}^D(X) of the deuteron are studied within covariant approach. It is shown that usual nonrelativistic convolution model result in incorrect behavior of this structure functions at small X and violates the exact sum rules. Realistic calculations are carried out with the Bethe-Salpeter amplitude of the deuteron and compared with the nonrelativistic results.
Taking advantage of a semirelativistic and a full relativistic representation of the quark propagator in an external field we present an unified derivation of the semirelativistic potential and of a Bethe-Salpeter like equation for the quark-antiquark system. We consider three different models for the evaluation of the Wilson loop: the Modified Area Law model (MAL), the Stochastic Vacuum Model (SVM) and the Dual QCD (DQCD). We compare the corresponding potentials and show that they all agree at the short and the long distances. In the case of the Bethe-Salpeter equation we treat explicitly onl…
Graphene's isolation launched explorations of fundamental relativistic physics originating from the planar honeycomb lattice arrangement of the carbon atoms, and of potential technological applications in nanoscale electronics. Bottom-up fabricated atomically-precise segmented graphene nanoribbons, SGNRs, open avenues for studies of electrical transport, coherence, and interference effects in metallic, semiconducting, and mixed GNRs, with different edge terminations. Conceptual and practical understanding of electric transport through SGNRs is gained through nonequilibrium Green's function (NE…
A method is presented for deriving the nonrelativistic quantum hamiltonian of a free massive fermion from the relativistic lagrangian of the Lorentz-violating standard-model extension. It permits the extraction of terms at arbitrary order in a Foldy-Wouthuysen expansion in inverse powers of the mass. The quantum particle hamiltonian is obtained and its nonrelativistic limit is given explicitly to third order.
Nonrelativstic effective field theories have shown to be a useful framework to describe systems of weakly bound particles. This work focuses on the matching procedure to the underlying relativistic theory. The concept of a physical mass in the absence of explicit Lorentz symmetry and the matching conditions for S-matrix elements and Green's functions are discussed in general for scalar particles. The effective Lagrangians of the pure particle and anti-particle sectors are constructed explicitely for a Yukawa-type interaction of a heavy and a light scalar field. Using the proper matching, it is…
The number of nonrelativistic axions can be changed by inelastic reactions that produce photons or relativistic axions. Any odd number of axions can annihilate into two photons. Any even number of nonrelativistic axions can scatter into two relativistic axions. We calculate the rate at which axions are lost from axion stars from these inelastic reactions. In dilute systems of axions, the dominant inelastic reaction is axion decay into two photons. In sufficiently dense systems of axions, the dominant inelastic reaction is the scattering of four nonrelativistic axions into two relativistic axio…
We present a systematic study of the leading twist structure functions of the deuteron, F_2^D, b_{1,2}^D and g_1^D in a fully relativistic approach. Our study is based on a realistic Bethe-Salpeter amplitude for the deuteron, which is obtained as a solution to the homogeneous Bethe-Salpeter equation with a realistic NN kernel. Particular effort is made to connect the structure functions to the densities of the appropriate charges and currents. This allows for a systematic comparison between the relativistic and nonrelativistic calculations, by analysing the same densities in both approaches. T…
We carry out a comparative study of electronic properties of 2D electron gas (2DEG) in a magnetic field of an infinitesimally thin solenoid with relativistic dispersion as in graphene and quadratic dispersion as in semiconducting heterostructures. The problem of ambiguity of the zero mode solutions of the Dirac equation is treated by considering of a finite radius flux tube which allows to select unique solutions associated with each $\mathbf{K}$ point of graphene's Brillouin zone. Then this radius is allowed to go to zero. On the base of the obtained in this case analytical solutions in the A…
At the end of inflation, the inflaton field decays into an initially nonthermal population of relativistic particles which eventually thermalize. We consider the production of dark matter from this relativistic plasma, focusing on the prethermal phase. We find that for a production cross section $σ(E)\sim E^n$ with $n> 2$, the present dark matter abundance is produced during the prethermal phase of its progenitors. For $n\le 2$, entropy production during reheating makes the nonthermal contribution to the present dark matter abundance subdominant compared to that produced thermally. As specific…
We discuss the resolution of an inconsistency between lattice background field methods and nonrelativistic QED matching conditions. In particular, we show that lack of on-shell conditions in lattice QCD with time-dependent background fields generally requires that certain operators related by equations of motion should be retained in an effective field theory to correctly describe the behavior of Green's functions. The coefficients of such operators in a nonrelativistic hadronic theory are determined by performing a robust nonrelativistic expansion of QED for relativistic scalar and spin-half …
Spins of relativistic fermions are related to their orbital degrees of freedom. In order to quantify the effect of hybridization between relativistic and nonrelativistic degrees of freedom on spin-orbit coupling, we focus on the spin-orbital (SO) crossed susceptibility arising from spin-orbit coupling. The SO crossed susceptibility is defined as the response function of their spin polarization to the "orbital" magnetic field, namely the effect of magnetic field on the orbital motion of particles as the vector potential. Once relativistic and nonrelativistic fermions are hybridized, their SO cr…
