scholarly journals Quantum scattering on a delta potential in ghost-free theory

2018 ◽  
Vol 782 ◽  
pp. 688-693 ◽  
Author(s):  
Jens Boos ◽  
Valeri P. Frolov ◽  
Andrei Zelnikov
Keyword(s):  
Quantum Scattering ◽  
Delta Potential ◽  
Free Theory

An analytical solution for quantum scattering through a $${\cal P}{\cal T}$$-symmetric delta potential

2021 ◽  
Vol 16 (4) ◽  
Author(s):  
Ying-Tao Zhang ◽  
Shan Jiang ◽  
Qingming Li ◽  
Qing-Feng Sun
Keyword(s):  
Analytical Solution ◽  
Quantum Scattering ◽  
Delta Potential

scholarly journals Symmetry-induced nonlocal divergence-free currents in two-dimensional quantum scattering

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
M. A. Metaxas ◽  
P. Schmelcher ◽  
F. K. Diakonos
Keyword(s):  
Quantum Scattering ◽  
Two Dimensional ◽  
Divergence Free

scholarly journals Superconformal boundaries in 4 − ϵ dimensions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Aleix Gimenez-Grau ◽  
Pedro Liendo ◽  
Philine van Vliet
Keyword(s):  
Three Dimensional ◽  
Spacetime Dimension ◽  
Perfect Agreement ◽  
Bootstrap Analysis ◽  
First Order ◽  
Free Theory ◽  
First Order Correction ◽  
Free Parameters ◽  
Superconformal Theories ◽  
Zumino Model

Abstract Boundaries in three-dimensional $$ \mathcal{N} $$ N = 2 superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining 2d boundary algebra exhibits $$ \mathcal{N} $$ N = (0, 2) or $$ \mathcal{N} $$ N = (1) supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $$ \mathcal{N} $$ N = (1) supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the ϵ-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a super-symmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.

scholarly journals Complexity growth in integrable and chaotic models

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Vijay Balasubramanian ◽  
Matthew DeCross ◽  
Arjun Kar ◽  
Yue Li ◽  
Onkar Parrikar
Keyword(s):  
Time Evolution ◽  
Evolution Operator ◽  
Linear Growth ◽  
Conjugate Points ◽  
Majorana Fermions ◽  
Time Evolution Operator ◽  
Free Theory ◽  
Group Manifold ◽  
Geodesic Length ◽  
Evolution Trajectory

Abstract We use the SYK family of models with N Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by the appearance and accumulation of conjugate points, which signal the presence of shorter geodesics intersecting the time evolution trajectory. By explicitly locating such “shortcuts” through analytical and numerical methods, we demonstrate that: (a) in the free theory, time evolution encounters conjugate points at a polynomial time; consequently complexity growth truncates at O($$ \sqrt{N} $$ N ), and we find an explicit operator which “fast-forwards” the free N-fermion time evolution with this complexity, (b) in a class of interacting integrable theories, the complexity is upper bounded by O(poly(N)), and (c) in chaotic theories, we argue that conjugate points do not occur until exponential times O(eN), after which it becomes possible to find infinitesimally nearby geodesics which approximate the time evolution operator. Finally, we explore the notion of eigenstate complexity in free, integrable, and chaotic models.

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

scholarly journals Ab initio investigation of the CO–N2 quantum scattering: The collisional perturbation of the pure rotational R(0) line in CO

2021 ◽  
Vol 154 (5) ◽  
pp. 054314
Author(s):  
Hubert Jóźwiak ◽  
Franck Thibault ◽  
Hubert Cybulski ◽  
Piotr Wcisło
Keyword(s):  
Ab Initio ◽  
Quantum Scattering

scholarly journals Relativistic quantum scattering on a cone

2001 ◽  
Vol 18 (8) ◽  
pp. 1555-1566 ◽  
Author(s):  
J Spinelly ◽  
E R Bezerra de Mello ◽  
V B Bezerra
Keyword(s):  
Relativistic Quantum ◽  
Quantum Scattering
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