Inspired by general relativity, we suggest an approach for long-range potential scattering. In scattering theory, there is a general theory for short-range potential scattering, but there is no general theory for long-range potential scattering. This is because the scattering boundary conditions for all short-range potentials are the same, but for different long-range potentials, they are different. In this paper, by introducing tortoise coordinates, we convert long-range potential scattering to short-range potential scattering. This allows us to deal with long-range potential scattering as short-range potential scattering. An explicit expression of the scattering wave function for long-range potential scattering is presented, in which the scattering wave function is represented by the tortoise coordinate and the scattering phase shift. We show that the long-range potential scattering wave function is just the short-range potential scattering wave function with a replacement of a common coordinate by a tortoise coordinate. The approach applies not only to scattering but also applies to bound states. Furthermore, in terms of tortoise coordinates, we suggest a classification scheme for potentials. We also discuss the duality between tortoise coordinates.Inspired by general relativity, we suggest an approach for long-range potential scattering. In scattering theory, there is a general theory for short-range potential scattering, but there is no general theory for long-range potential scattering. This is because the scattering boundary conditions for all short-range potentials are the same, but for different long-range potentials, they are different. In this paper, by introducing tortoise coordinates, we convert long-range potential scattering to short-range potential scattering. This allows us to deal with long-range potential scattering as short-range potential scattering. An explicit expression of the scattering wave function for long-range potential scattering is presented, in which the scattering wave function is represented by the tortoise coordinate and the scattering phase shift. We show that the long-range potential scattering wave function is just the short-range potential scattering wave function with a replacement of a common coordinate by a tortoise coordinate. The approach applies not only to scattering but also applies to bound states. Furthermore, in terms of tortoise coordinates, we suggest a classification scheme for potentials. We also discuss the duality between tortoise coordinates.

arXiv:1802.05245Journal of Mathematical PhysicsDec 1, 20218 citations

Q is for Quantum Entanglement.

Ashley Campbell

Jan 1, 20170 citations

Conformality loss and short-range crossover in long-range conformal field theories

Zhijin Li

We study the conformality loss of theories with long-range interactions. We consider the $O(2)\times O(N)$ multiscalar model with coupling $r^{-d-δ}$ in $d=4-ε$ dimension. We compute the critical exponents of the long-range fixed points (LRFPs) to three loops. The phase diagram of the model is dominated by two processes: the short-range crossover and merger-annihilation of LRFPs. The two processes intersect at the lower edge of the conformal window, below which the LRFPs disappear into the complex plane. We propose a novel scenario for the short-range crossover of complex LRFPs, in which the short-range crossover occurs on a vertical line in the complex plane of $δ$ . The complex marginal operator generates renormalization group flow on the transition line and significantly enriches the short-range crossover of complex LRFPs.We study the conformality loss of theories with long-range interactions. We consider the $O(2)\times O(N)$ multiscalar model with coupling $r^{-d-δ}$ in $d=4-ε$ dimension. We compute the critical exponents of the long-range fixed points (LRFPs) to three loops. The phase diagram of the model is dominated by two processes: the short-range crossover and merger-annihilation of LRFPs. The two processes intersect at the lower edge of the conformal window, below which the LRFPs disappear into the complex plane. We propose a novel scenario for the short-range crossover of complex LRFPs, in which the short-range crossover occurs on a vertical line in the complex plane of $δ$. The complex marginal operator generates renormalization group flow on the transition line and significantly enriches the short-range crossover of complex LRFPs.

arXiv:2409.19392Sep 28, 20242 citations

絡み合い(entanglement)エントロピーはブラックホールエントロピーの起源になり得るか

Shinji Mukohyama A, Masafumi Seriu, Hideo Kodama

Jan 1, 19960 citations

Deterministic Entangled Pairs

ScienceJul 26, 20070 citations

From Light-Cone to Supersonic Propagation of Correlations by Competing Short- and Long-Range Couplings

Catalin-Mihai Halati, Ameneh Sheikhan, Giovanna Morigi +2 more

We investigate the dynamical spreading of correlations in many-body quantum systems with competing short- and global-range couplings. We monitor the nonequilibrium dynamics of the correlations following a quench, showing that for strong short-range couplings the propagation of correlations is dominated at short and intermediate distances by a causal, light-cone dynamics, resembling the purely short-range quantum systems. However, the interplay of short- and global-range couplings leads to a crossover between space-time regions in which the light cone persists to regions where a supersonic, distance-independent spreading of the correlations occurs. We identify the important ingredients needed for capturing the supersonic spreading and demonstrate our findings in systems of interacting bosonic atoms, in which the global-range coupling is realized by a coupling to a cavity light field or atomic long-range interactions, respectively. We show that our results hold in both one and two dimensions and in the presence of dissipation. Furthermore, we characterize the short-time power-law scaling of the distance-independent growth of the density-density correlations.We investigate the dynamical spreading of correlations in many-body quantum systems with competing short- and global-range couplings. We monitor the nonequilibrium dynamics of the correlations following a quench, showing that for strong short-range couplings the propagation of correlations is dominated at short and intermediate distances by a causal, light-cone dynamics, resembling the purely short-range quantum systems. However, the interplay of short- and global-range couplings leads to a crossover between space-time regions in which the light cone persists to regions where a supersonic, distance-independent spreading of the correlations occurs. We identify the important ingredients needed for capturing the supersonic spreading and demonstrate our findings in systems of interacting bosonic atoms, in which the global-range coupling is realized by a coupling to a cavity light field or atomic long-range interactions, respectively. We show that our results hold in both one and two dimensions and in the presence of dissipation. Furthermore, we characterize the short-time power-law scaling of the distance-independent growth of the density-density correlations.

arXiv:2503.13306Physical Review LettersNov 7, 20253 citations

We study the conformality loss of theories with long-range interactions. We consider the

O(2)\times O(N)

multiscalar model with coupling

r^{-d-δ}

d=4-ε

dimension. We compute the critical exponents of the long-range fixed points (LRFPs) to three loops. The phase diagram of the model is dominated by two processes: the short-range crossover and merger-annihilation of LRFPs. The two processes intersect at the lower edge of the conformal window, below which the LRFPs disappear into the complex plane. We propose a novel scenario for the short-range crossover of complex LRFPs, in which the short-range crossover occurs on a vertical line in the complex plane of

δ

. The complex marginal operator generates renormalization group flow on the transition line and significantly enriches the short-range crossover of complex LRFPs.