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We theoretically analyze the differential cross sections (DCSs) for the state-to-state reaction, H + HD(vi = 0, ji = 0, mi = 0) → H2(vf = 0, jf = 1,2,3, mf = 1,..,jf) + D, over the whole range of scattering angles, where v, j, and m are the vibrational, rotational, and helicity quantum numbers for the initial and final states. The analysis extends and complements previous calculations for the same state-to-state reaction, which had jf = 0,1,2,3 and mf = 0, as reported by Xiahou, C.; Connor, J. N. L. Phys. Chem. Chem. Phys. 2021, 23, 13349-13369. Motivation comes from the state-of-the-art experiments and simulations of Yuan et al. Nature Chem. 2018, 10, 653-658 who have measured, for the first time, fast oscillations in the small-angle region of the degeneracy-averaged DCSs for jf = 1 and 3 as well as slow oscillations in the large-angle region. We start with the partial wave series (PWS) for the scattering amplitude expanded in a basis set of reduced rotation matrix elements. Then our main theoretical tools are two variants of Nearside-Farside (NF) theory applied to six transitions: (1) We apply unrestricted, restricted, and restrictedΔ NF decompositions to the PWS including resummations. The restricted and restrictedΔ NF DCSs correctly go to zero in the forward and backward directions when mf > 0, unlike the unrestricted NF DCSs, which incorrectly go to infinity. We also exploit the Local Angular Momentum theory to provide additional insights into the reaction dynamics. Properties of reduced rotation matrix elements of the second kind play an important role in the NF analysis, together with their caustics. (2) We apply an approximate N theory at intermediate and large angles, namely, the Semiclassical Optical Model of Herschbach. We show there are two different reaction mechanisms. The fast oscillations at small angles (sometimes called Fraunhofer diffraction/oscillations) are an NF interference effect. In contrast, the slow oscillations at intermediate and large angles are an N effect, which arise from a direct scattering, and are a "distorted mirror image" mechanism. We also compare these results with the experimental data.

Celestial amplitudes represent 4D scattering of particles in boost, rather than the usual energy-momentum, eigenstates and hence are sensitive to both UV and IR physics. We show that known UV and IR properties of quantum gravity translate into powerful constraints on the analytic structure of celestial amplitudes. For example the soft UV behavior of quantum gravity is shown to imply that the exact four-particle scattering amplitude is meromorphic in the complex boost weight plane with poles confined to even integers on the negative real axis. Would-be poles on the positive real axis from UV asymptotics are shown to be erased by a flat space analog of the AdS resolution of the bulk point singularity. The residues of the poles on the negative axis are identified with operator coefficients in the IR effective action. Far along the real positive axis, the scattering is argued to grow exponentially according to the black hole area law. Exclusive amplitudes are shown to simply factorize into conformally hard and conformally soft factors. The soft factor contains all IR divergences and is given by a celestial current algebra correlator of Goldstone bosons from spontaneously broken asymptotic symmetries. The hard factor describes the scattering of hard particles together with the boost-eigenstate clouds of soft photons or gravitons required by asymptotic symmetries. These provide an IR safe $\mathcal{S}$-matrix for the scattering of hard particles., 43 pages

The K-matrix approach is mostly used when analyzing the overlapping resonances. It provides unitarity of the scattering matrix, however, its parameters are not physical quantities; the resonant and background contributions cannot be separated; and the scattering amplitudes have zeros between the positions of resonances. The parameters of the Breit—Wigner (BW) functions are the masses and widths of resonances; however, the sum of such functions violates unitarity. We construct a unitary S-matrix by taking into account the interference of BW functions. In the examples presented in the paper, these two approaches are compared.

We discuss the extent to which the often assumed independence of the phase of the elastic scattering amplitude from momentum transfer in the domain of only small $$t$$ constrains the dependence of the phase on $$t$$ in general. Based on analyticity, we prove that if the scattering amplitude phase is independent of the transferred momentum in the domain of its small values in strong couplings, then this remains the case in the whole physical domain. Moreover, if such independence holds in any domain of physical energies including values infinitely close to the first inelastic threshold from below, then the whole scattering amplitude vanishes. We also discuss the relation between the dependence of the phase on $$t$$ and the size of the interaction domain.

We study the two-dimensional scattering of a quantum particle by the force center acting on this particle via a superposition of a Coulomb potential and a power-law potential V0r−β with the exponent β ∈ (1,2). We find the explicit low-energy asymptotic forms of all partial phases and scattering amplitudes.

We study the gravity-mediated scattering of scalar fields based on a parameterisation of the Lorentzian quantum effective action. We demonstrate that the interplay of infinite towers of spin zero and spin two poles at imaginary squared momentum leads to scattering amplitudes that are compatible with unitarity bounds, causal, and scale-free at trans-Planckian energy. Our construction avoids introducing non-localities or the massive higher-spin particles that are characteristic in string theory., v2: various small improvements/clarifications, version accepted for publication

Purpose. This article is dedicated to the study of phase shifts for single-channel neutron-proton scattering. The phase shifts, which are obtained in the variable phase approach, are studied. For the approximation of phase shifts, a function — 2019 is used in the form of a known formula for a parabolic-type quadratic function y(x)=a+bx+cx2 , which was proposed by M.A. Dolgopolov, L.A. Minin and V.A. Rabotkin in the study of phase shifts for the Paris potential. It is necessary to find the coefficients a, b, c for y(x) when approximating the np- scattering phases for the Argonne v18 potential. Methods. Approximation is used to find the coefficients of the function y(x). Find the optimal values of the coefficients a, b, c at a minimum value χ 2 . Results. An approximation of the neutron-proton scattering phases obtained by various methods for the phenomenological nucleon-nucleon potential Argonne v18 was made. The calculated coefficients of this function obtained for phase shifts by means of the variable phase approach are compared with the results of the approximation of the scattering phases from the original paper. For illustration graphs are given for phase shifts for four spin states for the np- system ( 1S0, 3P1, 1D2, 3D2). Conclusions. The obtained coefficients for the function y(x) can be used to calculate the values of the scalar scattering amplitude, the full cross-section and the partial scattering amplitude for any phase value within the energy interval for the approximation carried out. In next studies one can obtain and compare the coefficients and parameters of approximation for scattering phases for other modern phenomenological nucleon-nucleon potentials. Keywords: variable phase approach, nucleon-nucleon scattering, approximation, phase shifts, Arg

In the framework of nonstationary scattering theory, we study the formation of an entangled state of two identical nonrelativistic spin-1/2 particles as a result of their elastic scattering. The measure of particle entanglement in the final channel is described using pair concurrence. For the indicated quantitative criterion, we obtain general expressions in terms of the direct and exchange scattering amplitudes in the cases of pure and mixed spin states of the pair in the initial channel. We consider the violation of Bell’s inequality in the final channel. We show that as a result of a collision between unpolarized particles, a Werner spin state of the pair forms, which is entangled if the singlet component of the angular differential scattering cross section in the center-of-mass reference frame exceeds the triplet component. We use the process of free electron-electron scattering as an example to illustrate the developed formalism.

The post-Minkowskian expansion of Einstein's general theory of relativity has received much attention in recent years due to the possibility of harnessing the computational power of modern amplitude calculations in such a classical context. In this brief review, we focus on the post-Minkowskian expansion as applied to the two-body problem in general relativity without spin, and we describe how relativistic quantum field theory can be used to greatly simplify analytical calculations based on the Einstein-Hilbert action. Subtleties related to the extraction of classical physics from such quantum mechanical calculations highlight the care which must be taken when both positive and negative powers of Planck's constant are at play. In the process of obtaining classical results in both Einstein gravity and supergravity, one learns new aspects of quantum field theory that are obscured when using units in which Planck's constant is set to unity. The scattering amplitude approach provides a self-contained framework for deriving the two-body scattering valid in all regimes of energy. There is hope that the full impact of amplitude computations in this field may significantly alter the way in which gravitational wave predictions will advance in the coming years., Comment: 35 pages, see also the overview article. v2: minor corrections, published version

We describe a systematic framework for finding the conservative potential of compact binary systems with spin based on scattering amplitudes of particles of arbitrary spin and effective field theory. An arbitrary-spin formalism is generally required in the classical limit. By matching the tree and one-loop amplitudes of four spinning particles with those of a suitably chosen effective field theory, we obtain the spin1-spin2 terms of a two-body effective Hamiltonian through O(G2) and valid to all orders in velocity. Solving Hamilton's equations yields the impulse and spin changes of the individual bodies. We write them in a surprisingly compact form as appropriate derivatives of the eikonal phase obtained from the amplitude. It seems likely this structure persists to higher orders. We also point out various double-copy relations for general spin., Physical Review D, 104 (6), ISSN:1550-7998, ISSN:0556-2821, ISSN:1550-2368

This work explores scattering amplitudes that couple two-particle systems via a single external current insertion, $2+\mathcal{J}\to 2$. Such amplitudes can provide structural information about the excited QCD spectrum. We derive an exact analytic representation for these reactions. From these amplitudes, we show how to rigorously define resonance and bound-state form-factors. Furthermore, we explore the consequences of the narrow-width limit of the amplitudes as well as the role of the Ward-Takahashi identity for conserved vector currents. These results hold for any number of two-body channels with no intrinsic spin, and a current with arbitrary Lorentz structure and quantum numbers. This work and the existing finite-volume formalism provide a complete framework for determining this class of amplitudes from lattice QCD., 35 pages, 13 figures

We comment on phase selection of the scattering amplitude, emphasizing that the elastic overlap function should have a central impact parameter profile at high energies and highlighting the role of the reflective scattering mode at the LHC energies. Emerging problems with the use of peripheral impact parameter dependence of the elastic overlap function are explicitly indicated. Their solution is an elimination of the phases connected to peripheral form of the elastic overlap function. Contrary, we adhere to a relative peripheral form of the {\it inelastic} overlap function with an additional new feature of a maximum at nonzero value of the impact parameter at the highest energies. Phenomenologically, the dynamics of hadron scattering is motivated by a hadron structure with a hard central core presence., Comment: 13 pages, 2 figures, revised version

An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $- \alpha \cos (\theta)/r^2$ at large distances. Due to its long-range character, it modifies the properties of angular wave functions, which are no longer given by spherical harmonics. In addition, an effective centrifugal potential in the radial equation can become attractive for low angular momenta. In this paper, we develop a general framework for an ion-dipole reactive scattering, focusing on the regime of large $\alpha$. We introduce modified spherical harmonics as solutions of the angular part of the Schr\"odinger equation and derive several useful approximations in the limit of large $\alpha$. We present a formula for the scattering amplitude expressed in terms of the modified spherical harmonics and we derive expressions for the elastic and reactive collision rates. The solutions of the radial equation are given by Bessel functions, and we analyse their behaviour in two distinct regimes corresponding, basically, to attractive and repulsive long-range centrifugal potentials. Finally, we study reactive collisions in the universal regime, where the short-range probability of loss or reaction is equal to unity., Comment: 19 pages, 11 figures, 5 appendices

Focusing on three-pion states with maximal isospin (π^{+}π^{+}π^{+}), we present the first nonperturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.

Motivated by the desire to understand chaos in the $S$-matrix of string theory, we study tree level scattering amplitudes involving highly excited strings. While the amplitudes for scattering of light strings have been a hallmark of string theory since its early days, scattering of excited strings has been far less studied. Recent results on black hole chaos, combined with the correspondence principle between black holes and strings, suggest that the amplitudes have a rich structure. We review the procedure by which an excited string is formed by repeatedly scattering photons off of an initial tachyon (the DDF formalism). We compute the scattering amplitude of one arbitrary excited string and any number of tachyons in bosonic string theory. At high energies and high mass excited state these amplitudes are determined by a saddle-point in the integration over the positions of the string vertex operators on the sphere (or the upper half plane), thus yielding a generalization of the "scattering equations". We find a compact expression for the amplitude of an excited string decaying into two tachyons, and study its properties for a generic excited string. We find the amplitude is highly erratic as a function of both the precise excited string state and of the tachyon scattering angle relative to its polarization, a sign of chaos., Comment: 65 pages, 11 figures; published version

QCD bound states share many properties with QED atoms. Thus hadrons are routinely classified in terms of their valence quarks, similarly to atoms. QED bound state perturbation theory differs in important aspects from the more familiar expansion of scattering amplitudes. Experts regard QED atoms as being “essentially non-perturbative”, even though physical quantities such as binding energies may be calculated perturbatively. The non-perturbative aspects of hadrons may be analogous to those of atoms. A summary of the contents of these lectures is provided.

A non-relativistic scalar particle moving on a curved surface undergoes a geometric scattering whose behavior is sensitive to the theoretically ambiguous values of the intrinsic and extrinsic curvature coefficients entering the expression for the quantum Hamiltonian operator. This suggests using the scattering data to settle the ambiguity in the definition of the Hamiltonian. It has recently been shown that the inclusion of point defects on the surface enhances the geometric scattering effects. We perform a detailed study of the geometric scattering phenomenon in the presence of line defects for the case that the particle is confined to move on a Gaussian bump and the defect(s) are modeled by delta-function potentials supported on a line or a set of parallel lines normal to the scattering axis. In contrast to a surface having point defects, the scattering phenomenon associated with this system is generically geometric in nature in the sense that for a flat surface the scattering amplitude vanishes for all scattering angles $\theta$ except $\theta=\theta_0$ and $\pi-\theta_0$, where $\theta_0$ is the angle of incidence. We show that the presence of the line defects amplifies the geometric scattering due to the Gaussian bump. This amplification effect is particularly strong when the center of the bump is placed between two line defects., Comment: 18 pages, 5 figures

It is described how quantum field theory went from a theory for calculating the properties of stationary states, in the mold of quantum mechanics, to the scattering-focused theory we know today. This development is located as originating in the 1930s and 40s, primarily in the attempts by Werner Heisenberg and Richard Feynman to find a new theory of relativistic quantum mechanics that gets rid of the notion of state entirely. It is then shown how these attempts formed the conceptual inspiration and the provided the formal tools for the formulation of modern, scattering-based QFT in the late 1940s, in particular by Freeman Dyson (and, to some extent, by E.C.G. Stueckelberg). This transformation of quantum field theory is interpreted as a paradigm shift in a weak sense, where the foundations of the theory remain the same, while the paradigmatic problem to be calculated changes (in this case from energy levels to scattering amplitudes)., This paper was originally published in Studies in the History and Philosophy of Modern Physics, Volume 60 (2017), pp. 46-80. Due to formatting mistakes that appeared only after proof-reading, parts of that paper are garbled. An erratum was published in SHPMP that links to this version, which is the definitive version of the paper

We use complex semiclassical method to compute scattering amplitudes of a point particle in dilaton gravity with a boundary. This model has nonzero minimal black hole mass $M_{cr}$. We find that at energies below $M_{cr}$ the particle trivially scatters off the boundary with unit probability. At higher energies the scattering amplitude is exponentially suppressed. The corresponding semiclassical solution is interpreted as formation of an intermediate black hole decaying into the final-state particle. Relating the suppression of the scattering probability to the number of the intermediate black hole states, we find an expression for the black hole entropy consistent with thermodynamics. In addition, we fix the constant part of the entropy which is left free by the thermodynamic arguments. We rederive this result by modifying the standard Euclidean entropy calculation., Comment: 33 pages, 9 figures

We present that, if unitarizing the B(*)B(*) scattering amplitudes in the constituent interchange model, one can find two bound-state poles for (Itot,Stot)=(0,1) BB* and B*B* system, which correspond to two I(JP)=0(1+) doubly bottomed molecular states. Furthermore, it is noticed that the virtual states in (1,0) BB, (1,1) BB*, (1,0) B*B*, and (1,2) B*B* systems could produce enhancements of the squared moduli of the scattering T matrix just above the related thresholds, which might correspond to I(JP)=1(0+), 1(1+), and 1(2+) doubly bottomed molecular states, respectively. The calculation may be helpful for searching for the doubly bottomed molecular state in future experiments.

Schwarzian quantum mechanics describes the collective IR mode of the SYK model and captures key features of 2D black hole dynamics. Exact results for its correlation functions were obtained in JHEP {\bf 1708}, 136 (2017) [arXiv:1705.08408]. We compare these results with bulk gravity expectations. We find that the semi-classical limit of the out-of-time-order (OTO) four-point function exactly matches with the scattering amplitude obtained from the Dray-'t Hooft shockwave $\mathcal{S}$-matrix. We show that the two point function of heavy operators reduces to the semi-classical saddle-point of the Schwarzian action. We also explain a previously noted match between the OTO four point functions and 2D conformal blocks. Generalizations to higher-point functions, and applications, are discussed., Comment: 37 pages, 6 figures; v3 typos fixed

The present work reviews the results concerning quantum scattering theory of ultrarelativistic electrons in ultrathin crystals and its comparison with analogous classical results. It deals with an intermediate range of thicknesses, large enough for that the particle motion could not be considered as rectilinear but small enough for that the channeling regime of motion was not established. The quantum theory is based both upon the representation of the scattering amplitude as an integral over the surface surrounding the target, and on the so-called operator method of determination of the wave function as a solution of a Schrödinger-like equation. The latter method implies a wide use of the Fourier technique, both in calculation of each next step in the wave packet evolution, and in moving from the spatial coordinates to the angular ones. The authors compare the quantum differential scattering cross-sections with the classical ones in the considered range of crystal thicknesses and show their resemblances, distinctions and the evolution of these distinctions with the change of the particle energy. The simplest variant of quantum scattering theory based upon the eikonal approximation of quantum mechanics is considered. In the paper the quantum differential scattering cross-section was calculated and its affinity with the classical one was demonstrated. In the preparation of these lecture notes the material of the paper [4] was used.

By performing resummation of small fermion-antifermion pairs within the pentagon form factor program to scattering amplitudes in planar N = 4 superYang-Mills theory, we construct multichannel conformal blocks within the flux-tube picture for N-sided NMHV polygons. This procedure is equivalent to summation of descendants of conformal primaries in the OPE framework. The resulting conformal partial waves are determined by multivariable hypergeometric series of Lauricella-Saran type., 11 pages, 1 figure

We study string scattering amplitudes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. The four-string scattering amplitudes with three tachyons and an arbitrary string state are calculated. The string field theory yields the string scattering amplitudes evaluated on the world sheet of string scattering whereas the coventional method, based on the first quantized theory brings us the string scattering amplitudes defined on the upper half plane. For the highest spin states, generated by the primary operators, both calculations are in perfect agreement. In this case, the string scattering amplitudes are invariant under the conformal transformation, which maps the string world sheet onto the upper half plane. If the external string states are general massive states, generated by non-primary field operators, we need to take into account carefully the conformal transformation between the world sheet and the upper half plane. We show by an explicit calculation that the string scattering amplitudes calculated by using the deformed cubic string field theory transform into those of the first quantized theory on the upper half plane by the conformal transformation, generated by the Schwarz-Christoffel mapping., Comment: 12 pages, 2 figures, references added

The method for analyzing resonance states based on the harmoni©oscillator representation of scattering equations (HORSE) and on analytic properties of partial-wave scattering amplitudes which has been proposed earlier, is generalized to the case of charged-particle scattering. The method in question is tested by applying it to the model problem of pα scattering and can be used to study resonance states on the basis of microscopic calculations within various versions of the shell model.

The simulation of light scattering by particles on a substrate with the $T$-matrix method relies on the expansion of the scattered field in spherical waves, followed by a plane wave expansion to allow the evaluation of the reflection from the substrate. In practice, the plane wave expansion (i.e., the Sommerfeld integrals) needs to be truncated at a maximal in-plane wavenumber $\kappa_\mathrm{max}$. An appropriate selection of $\kappa_\mathrm{max}$ is essential: counter-intuitively, the overall accuracy can degrade significantly if the integrals are truncated with a too large value. In this paper, we propose an empirical formula for the selection of $\kappa_\mathrm{max}$ and discuss its application using a number of example simulations with dielectric and metallic oblate spheroids on dielectric and metallic substrates. The computed differential scattering cross sections are compared to results obtained from the discrete-sources method., Comment: Accepted manuscript. \copyright 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license, http://creativecommons.org/licenses/by-nc-nd/4.0/

We analyze the microlocal structure of the semi-classical scattering amplitude for Schrodinger operators with a strong magnetic and a strong electric field at non-trapping energies. For this purpose, we develop a framework and establish some of the properties of semi-classical-Fourier-integral-operator-valued pseudodifferential operators and prove that the scattering amplitude is given by such an operator.

We show that when the dynamical dimension of the $\bar{\psi}\psi$ operator is reduced from three to two in a fermion electrodynamics with scaling, a $g(\bar{\psi}\psi)^2+g(\bar{\psi}i\gamma^5\psi)^2$ four-fermion interaction which is dressed by this electrodynamics becomes renormalizable. In the fermion-antifermion scattering amplitude every term in an expansion to arbitrary order in $g$ is found to diverge as just a single ultraviolet logarithm (i.e. no log squared or higher), and is thus made finite by a single subtraction. While not necessary for renormalizability per se, the reduction in the dimension of $\bar{\psi}\psi$ to two leads to dynamical chiral symmetry breaking in the infrared, with the needed subtraction then automatically being provided by the theory itself through the symmetry breaking mechanism, with there then being no need to introduce the subtraction by hand. Since the vector and axial vector currents are conserved, they do not acquire any anomalous dimension, with the four-fermion $(\bar{\psi}\gamma^{\mu}\psi)^2$ and $(\bar{\psi}\gamma^{\mu}\gamma^5\psi)^2$ interactions instead having to be controlled by the standard Higgs mechanism., Comment: 6 pages, 4 figures, Revtex4-1. Rewritten, with no changes in the physics

The near-collinear expansion of scattering amplitudes in maximally supersymmetric Yang-Mills theory at strong coupling is governed by the dynamics of stings propagating on the five sphere. The pentagon transitions in the operator product expansion which systematize the series get reformulated in terms of matrix elements of branch-point twist operators in the two-dimensional O(6) nonlinear sigma model. The facts that the latter is an asymptotically free field theory and that there exists no local realization of twist fields prevents one from explicit calculation of their scaling dimensions and operator product expansion coefficients. This complication is bypassed making use of the equivalence of the sigma model to the infinite-level limit of WZNW models perturbed by current-current interactions, such that one can use conformal symmetry and conformal perturbation theory for systematic calculations. Presently, to set up the formalism, we consider the O(3) sigma model which is reformulated as perturbed parafermions., Comment: 16 pages, 4 figures

We present a formulation and mathematical justification of the method of amplitude functions. This method allows solving the radial problem of the two-dimensional scattering of a quantum particle by the sum of a Coulomb potential and a certain short-range or long-range central potential.

Effects of the quantum interference in collisions of particles have a twofold nature: they arise because of the auto-correlation of a complex scattering amplitude and due to spatial coherence of the incoming wave packets. Both these effects are neglected in a conventional scattering theory dealing with the delocalized plane waves, although they sometimes must be taken into account in particle and atomic physics. Here, we study the role of a transverse coherence length of the packets, putting special emphasis on the case in which one of the particles is twisted, that is, it carries an orbital angular momentum $\ell\hbar$. In $ee, ep$, and $pp$ collisions the interference results in corrections to the plane-wave cross sections, usually negligible at the energies $\sqrt{s} \gg 1$ GeV but noticeable for smaller ones, especially if there is a twisted hadron with $|\ell| > 10^3$ in initial state. Beyond the perturbative QCD, these corrections become only moderately attenuated allowing one to probe a phase of the hadronic amplitude as a function of $s$ and $t$. In this regime, the coherence effects can compete with the loop corrections in QED and facilitate testing the phenomenological models of the strong interaction at intermediate and low energies., 3 figures

We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion mass $M\approx 200\;$MeV in Ref. [1]. Using the relativistic three-particle quantization condition, we find $\sim 2 \sigma$ evidence for a nonzero value for the contact part of the three-$\pi^+$ ($I=3$) scattering amplitude. We also compare our results to leading-order chiral perturbation theory. We find good agreement at threshold, and some tension in the energy dependent part of the three-$\pi^+$scattering amplitude. We also find that the two-$\pi^+$ ($I=2$) spectrum is fit well by an $s$-wave phase shift that incorporates the expected Adler zero., Comment: Corrected Figs S1 and S2 in supplementary material. Main text and conclusions unchanged

In quantum electrodynamics, we are typically interested in computing the scattering matrix for processes involving the interaction between electrons, positrons and photons. Basically, there are three fundamental kinds of processes involved here, one Compton scattering involving the process in which an electron emits absorbs a photon, moves further and then reemits the absorbed photon and moves further and we are interested in computing the scattering amplitude.

Scattering theory is a standard tool for the description of transport phenomena in mesoscopic systems. Here, we provide a detailed derivation of this method for nano-scale conductors that are driven by oscillating electric or magnetic fields. Our approach is based on an extension of the conventional Lippmann-Schwinger formalism to systems with a periodically time dependent Hamiltonian. As a key result, we obtain a systematic perturbation scheme for the Floquet scattering amplitudes that describe the transition of a transport carrier through a periodically driven sample. Within a general multi-terminal setup, we derive microscopic expressions for the mean values and time-integrated correlation functions, or zero-frequency noise, of matter and energy currents, thus unifying the results of earlier studies. We show that this framework is inherently consistent with the first and the second law of thermodynamics and prove that the mean rate of entropy production vanishes only if all currents in the system are zero. As an application, we derive a generalized Green-Kubo relation, which makes it possible to express the response of any mean currents to small variations of temperature and chemical potential gradients in terms of time integrated correlation functions between properly chosen currents. Finally, we discuss potential topics for future studies and further reaching applications of the Floquet scattering approach to quantum transport in stochastic and quantum thermodynamics., Comment: 17 pages, 3 figures

Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium's optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper., Comment: 44 pages, 9 figures, 122 equations, 32 references, 13 appendices

We present two methods to pin down the internal structure of hadron resonances from the quantities which can in principle be determined by experimental observables in a model-independent manner. One method is to relate the internal structure of a quasibound state with the scattering length and eigenenergy based on the generalized weak-binding relation. The other method is to find a trace of the origin of resonances in the analytic structure of the scattering amplitude. Utilizing both the methods, we conclude that the high-mass pole of Λ(1405) is dominated by the \(\bar{K}N\) component, and the low-mass pole originates from the dynamics in the πΣ channel.

Recently, we have proposed an unusual mechanism of superconducting current that is specific for quantum Hall edge channels connected to superconducting electrodes. We have shown that the supercurrent can be mediated by a nonlocal electron-electron interaction that provides an opportunity for a long-distance information transfer in the direction opposite to the electron flow. A convenient model for such interaction is that of an external circuit. The consideration has been performed for the case of a single channel. In order to facilitate the experimental verification and the observation of peculiar features of the effect, in this paper, we provide a more detailed description of the phenomenon and extend the results to more sophisticated setups. We establish that the dynamical phase contributes to superconducting interference; this being the manifestation of the channel chirality. We consider setups that include the scattering between quantum Hall channels of opposite direction and multiple superconducting contacts. For a single quantum Hall constriction, we derive a general and comprehensive relation for the interaction-induced supercurrent in terms of scattering amplitudes and demonstrate the nonlocal nature of the current by considering its sensitivity to scattering. In multiterminal setups, we reveal the characteristic phase dependences of the supercurrents explaining those in terms of interference of Andreev reflection processes. For more complex setups encompassing, at least, two constrictions, we find an interplay between noninteracting and interaction-induced currents and contributions of more complex interference processes.

In this work, we use an extension of the quantization condition, given in Ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the two-particle K matrix that required the absence of two-particle bound states or narrow two-particle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the K-matrix-like quantity that enters the quantization condition. With this in hand, we extend previous numerical studies of the quantization condition to explore the finite-volume signature for a variety of two- and three-particle interactions. We determine the spectrum for parameters such that the system contains both dimers (two-particle bound states) and one or more trimers (in which all three particles are bound), and also for cases where the two-particle subchannel is resonant. We also show how the quantization condition provides a tool for determining infinite-volume dimer-particle scattering amplitudes for energies below the dimer breakup. We illustrate this for a series of examples, including one that parallels physical deuteron-nucleon scattering. All calculations presented here are restricted to the case of three identical scalar particles., Comment: 42 pages, 16 figures, CERN-TH-2019-129, JLAB-THY-19-3011. Minor clarification and updated references

We calculate a class of polarized fermion string scattering amplitudes (PFSSA) at arbitrary mass levels. We discover that, in the hard scattering limit, the functional forms of the non-vanishing PFSSA at each fixed mass level are independent of the choices of spin polarizations. This result justifies and extends Gross conjecture on high energy string scattering amplitudes to the fermionic sector. In addition, this peculiar property of hard PFSSA is to be compared with the usual spin polarization dependence of the hard polarized fermion field theory scatterings., Comment: 15 pages, no figure

We study the universal far from equilibrium dynamics of magnons in Heisenberg ferromagnets. We show that such systems exhibit universal scaling in momentum and time of the quasiparticle distribution function, with the universal exponents distinct from those recently observed in Bose-Einstein condensates. This new universality class originates from the SU(2) symmetry of the Hamiltonian, which leads to a strong momentum-dependent magnon-magnon scattering amplitude. We compute the universal exponents using the Boltzmann kinetic equation and incoherent initial conditions that can be realized with microwave pumping of magnons. We compare our numerical results with analytic estimates of the scaling exponents and demonstrate the robustness of the scaling to variations in the initial conditions. Our predictions can be tested in quench experiments of spin systems in optical lattices and pump-probe experiments in ferromagnetic insulators such as yttrium iron garnet., 5 pages, 3 figures

We study the bending of gravitons that pass near a massive object like the Sun, using scattering amplitudes in which the Sun is represented by a massive scalar particle. Our results complete previous work on the bending angles of massless spin-0, spin-$\frac{1}{2}$ and spin-1 particles, and provides more evidence for the violation of the equivalence principle at the quantum level, in the sense that the quantum corrections to bending angles for massless particles with different spins are different. We provide a universal expression for the bending angle in terms of coefficients of triangle and bubble integrals in the amplitudes in the low energy limit. We also compare bending angles for scalar, photon and graviton projectiles under different circumstances., 6 Pages, 1 figure, 1 Ancillary file for coefficients of Integrals. v2, with typoes corrected. PRD version

Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrodinger equation with the modified Rosen—Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.

We consider a charged quantum particle moving in a two-dimensional plane in the three-dimensional coordinate space and scattering on an immovable Coulomb center in the same plane. We derive and investigate expansions of the wave function and of all radial wave functions of the particle in integer powers of the wave number and in Bessel functions of a real order. We prove that finite sums of such expansions are asymptotic in the low-energy limit.

Some aspects of Aomoto's generalized hypergeometric functions on Grassmannian spaces $Gr(k+1,n+1)$ are reviewed. Particularly, their integral representations in terms of twisted homology and cohomology are clarified with an example of the $Gr(2,4)$ case which corresponds to Gauss' hypergeometric functions. The cases of $Gr(2, n+1)$ in general lead to $(n+1)$-point solutions of the Knizhnik-Zamolodchikov (KZ) equation. We further analyze the Schechtman-Varchenko integral representations of the KZ solutions in relation to the $Gr(k+1, n+1)$ cases. We show that holonomy operators of the so-called KZ connections can be interpreted as hypergeometric-type integrals. This result leads to an improved description of a recently proposed holonomy formalism for gluon amplitudes. We also present a (co)homology interpretation of Grassmannian formulations for scattering amplitudes in ${\cal N} = 4$ super Yang-Mills theory., Comment: 51 pages; v2. reference added; v3. minor corrections, published version

We show that the formation/evaporation of Black Holes (BH) unitarizes quantum gravity at all the orders of the perturbation theory. Non-perturbative quantum effects save the scattering amplitudes from any polynomial divergences. Such a phenomena is intimately related to the dynamical emergence of an effective non-locality as well as emergent modifications of the Heisenberg's uncertainty principle. The BH production de-localizes quantum gravity vertices and propagators as a consequence of its holographically stored entropy. In this sense, quantum gravity is a superrenormalizable theory, although non-locality is hidden in its action., Comment: few typos fixed, all results are unchanged

Calculations of high multiplicity Higgs amplitudes exhibit a rapid growth that may signal an end of perturbative behavior or even the need for new physics phenomena. As a step toward this problem we consider the quantum mechanical equivalent of 1→n scattering amplitudes in a spontaneously broken ϕ4-theory by extending our previous results on the quartic oscillator with a single minimum [Phys. Rev. D 98, 096007 (2018)] to transitions ⟨n|x^|0⟩ in the symmetric double-well potential with quartic coupling λ. Using recursive techniques to high order in perturbation theory, we argue that these transitions are of exponential form ⟨n|x^|0⟩∼exp(F(λn)/λ) in the limit of large n and λn fixed. We apply the methods of “exact perturbation theory” put forward by Serone et al. in [Phys. Rev. D 96, 021701 (2017); J. High Energy Phys. 05 (2017) 056] to obtain the exponent F and investigate its structure in the regime where tree-level perturbation theory violates unitarity constraints. We find that the resummed exponent is in agreement with unitarity and rigorous bounds derived by Bachas [Nucl. Phys. B377, 622 (1992)].

I consider non-relativistic bosons interacting via pairwise potentials with infinite scattering length and supporting no two-body bound states. To lowest order in effective field theory, these conditions lead to non-interacting bosons, since the coupling constant of the Lieb-Liniger model vanishes identically in this limit. Since any realistic pairwise interaction is not a mere delta function, the non-interacting picture is an idealisation indicating that the effect of interactions is weaker than in the case of off-resonant potentials. I show that the leading order correction to the ground state energy for more than two bosons is accurately described by the lowest order three-body force in effective field theory that arises due to the off-shell structure of the two-body interaction. For natural two-body interactions with a short-distance repulsive core and an attractive tail, the emergent three-body interaction is repulsive and, therefore, three bosons do not form any bound states. This situation is analogous to the two-dimensional repulsive Bose gas, when treated using the lowest-order contact interaction, where the scattering amplitude exhibits an unphysical Landau pole. The avoidance of this state in the three-boson problem proceeds in a way that parallels the two-dimensional case. These results pave the way for the experimental realisation of one-dimensional Bose gases with pure three-body interactions using ultracold atomic gases., 9 pages, 2 figures, accepted version. Added detailed discussion of the Faddeev equations

In this letter, we study the implications of unitary completion of quantum gravity on the low energy spectrums, through an infinite set of unitarity bounds on the forward-limit scattering amplitudes. In three dimensions, we find that light states with charge-to-mass ratio $z$ greater than $1$ can only be consistent if there exists other light states, preferably neutral. Applied to the compactification of the Standard Model, where the low energy couplings are dominated by the electron with $|z|\sim 10^{22}$, this provides a novel understanding of the need for light neutrinos., 5+2 pages, 2+2 figures