Random Matrix Theory of resonances: An overview

Fyodorov, Yan V.

doi:10.1109/ursi-emts.2016.7571486

Cited by 9 publications

(15 citation statements)

References 46 publications

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“…In particular, for a wave reflecting off of a potential, the transmission factor will have a jump at the resonance energy, and each such jump in the phase angle gives a time delay, see e.g. [15,16].…”

Section: Jhep05(2021)048mentioning

confidence: 99%

“…In order for the excited string to have the correct mass, M 2 = p 2 = 2(N 1), we ose q such that e p • q = 1. q (3.7) t follows, we explicitly work out the form of these vertex operators, essentially reviewing ction in [99,43]. 15 We start in Sec. 3.1 with the N = 1 state, • A 1 |0i, and then the states: l-one and level-two states {sec31} section we construct the vertex operators for the states at level N = 1 and at level make more sense for p = e p + Nq.…”

Section: Building Excited States {Sec3}mentioning

confidence: 99%

“…In what follows, we explicitly work out the form of these vertex operators, essentially revie the construction in [99,43]. 15 We start in Sec.…”

Section: Building Excited Statesmentioning

confidence: 99%

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Chaotic scattering of highly excited strings

Gross

Rosenhaus

2021

J. High Energ. Phys.

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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.

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Section: Jhep05(2021)048mentioning

confidence: 99%

Section: Building Excited States {Sec3}mentioning

confidence: 99%

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Chaotic scattering of highly excited strings

Gross

Rosenhaus

2021

J. High Energ. Phys.

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“…Section III is devoted to the derivation of exact joint distribution of eigenvalues and eigenfunctions of matrix M in Eq. (3). It is demonstrated that for any rank-one perturbation such distribution equals the unperturbed joint distribution of invariant matrix G without the confinement term (4).…”

Section: Introductionmentioning

confidence: 96%

“…reviews [1]- [3] and references therein). One of the simplest and widely used RM predictions is the statement that resonance widths are distributed as modulus square of RM eigenfunctions.…”

Section: Introductionmentioning

confidence: 99%

Modification of the Porter-Thomas Distribution by Rank-One Interaction

Bogomolny

2017

Phys. Rev. Lett.

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The Porter-Thomas (PT) distribution of resonance widths is one of the oldest and simplest applications of statistical ideas in nuclear physics. Previous experimental data confirmed it quite well but recent and more careful investigations show clear deviations from this distribution. To explain these discrepancies the authors of Ref. [12], [PRL 115, 052501 (2015)], argued that to get a realistic model of nuclear resonances is not enough to consider one of the standard random matrix ensembles which leads immediately to the PT distribution but it is necessary to add a rank-one interaction which couples resonances to decay channels. The purpose of the paper is to solve this model analytically and to find explicitly the modifications of the PT distribution due to such interaction. Resulting formulae are simple, in a good agreement with numerics, and could explain experimental results.

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Scattering in Quantum Dots via Noncommutative Rational Functions

Erdős

Krüger

Nemish

2021

Ann. Henri Poincaré

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In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via $$N\ll M$$ N ≪ M channels, the density $$\rho $$ ρ of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio $$\phi := N/M\le 1$$ ϕ : = N / M ≤ 1 ; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit $$\phi \rightarrow 0$$ ϕ → 0 , we recover the formula for the density $$\rho $$ ρ that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any $$\phi <1$$ ϕ < 1 but in the borderline case $$\phi =1$$ ϕ = 1 an anomalous $$\lambda ^{-2/3}$$ λ - 2 / 3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries.

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Random Matrix Theory of resonances: An overview

Cited by 9 publications

References 46 publications

Chaotic scattering of highly excited strings

Chaotic scattering of highly excited strings

Modification of the Porter-Thomas Distribution by Rank-One Interaction

Scattering in Quantum Dots via Noncommutative Rational Functions

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