Large deviations and phase transitions in spectral linear statistics of Gaussian random matrices

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2FCZ______%3A_____%2F24%3AN0000098" target="_blank" >RIV/CZ______:_____/24:N0000098 - isvavai.cz</a>

Výsledek na webu

<a href="https://iopscience.iop.org/article/10.1088/1751-8121/ad1e1a" target="_blank" >https://iopscience.iop.org/article/10.1088/1751-8121/ad1e1a</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8121/ad1e1a" target="_blank" >10.1088/1751-8121/ad1e1a</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Large deviations and phase transitions in spectral linear statistics of Gaussian random matrices

Popis výsledku v původním jazyce

We evaluate, in the large-N limit, the complete probability distribution P(A,m) of the values A of the sum & sum;(N)(i=1)|lambda(i)|(m), where lambda(i) (i=1,2,& mldr;,N) are the eigenvalues of a Gaussian random matrix, and m is a positive real number. Combining the Coulomb gas method with numerical simulations using a matrix variant of the Wang-Landau algorithm, we found that, in the limit of N ->infinity, the rate function of P(A,m) exhibits phase transitions of different characters. The phase diagram of the system on the (A,m) plane is surprisingly rich, as it includes three regions: (i) a region with a single-interval support of the optimal spectrum of eigenvalues, (ii) a region emerging for m<2 where the optimal spectrum splits into two separate intervals, and (iii) a region emerging for m>2 where the maximum or minimum eigenvalue ``evaporates" from the rest of eigenvalues and dominates the statistics of A. The phase transition between regions (i) and (iii) is of second order. Analytical arguments and numerical simulations strongly suggest that the phase transition between regions (i) and (ii) is of (in general) fractional order p=1+1/|m-1|, where 02 occur at the ground state of the Coulomb gas which corresponds to the Wigner's semicircular distribution.

Název v anglickém jazyce

Large deviations and phase transitions in spectral linear statistics of Gaussian random matrices

Popis výsledku anglicky

We evaluate, in the large-N limit, the complete probability distribution P(A,m) of the values A of the sum & sum;(N)(i=1)|lambda(i)|(m), where lambda(i) (i=1,2,& mldr;,N) are the eigenvalues of a Gaussian random matrix, and m is a positive real number. Combining the Coulomb gas method with numerical simulations using a matrix variant of the Wang-Landau algorithm, we found that, in the limit of N ->infinity, the rate function of P(A,m) exhibits phase transitions of different characters. The phase diagram of the system on the (A,m) plane is surprisingly rich, as it includes three regions: (i) a region with a single-interval support of the optimal spectrum of eigenvalues, (ii) a region emerging for m<2 where the optimal spectrum splits into two separate intervals, and (iii) a region emerging for m>2 where the maximum or minimum eigenvalue ``evaporates" from the rest of eigenvalues and dominates the statistics of A. The phase transition between regions (i) and (iii) is of second order. Analytical arguments and numerical simulations strongly suggest that the phase transition between regions (i) and (ii) is of (in general) fractional order p=1+1/|m-1|, where 02 occur at the ground state of the Coulomb gas which corresponds to the Wigner's semicircular distribution.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Projekt

—

Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Physics A: Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Svazek periodika

57

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

31

Strana od-do

065001 (1-31)

Kód UT WoS článku

001154489000001

EID výsledku v databázi Scopus

2-s2.0-85184029025