Non-Bloch dynamics and topology in a classical nonequilibrium process - INSPIRE

DataBETA

Non-Bloch dynamics and topology in a classical nonequilibrium process

Jun 19, 2023

13 pages

Published in:

Phys.Rev.B 109 (2024) 20, L201121

Published: May 15, 2024

e-Print:

2306.11105 [quant-ph]

DOI:

10.1103/PhysRevB.109.L201121 (publication)

View in:

ADS Abstract Service

reference search6 citations

Citations per year

Abstract: (APS)

The non-Hermitian skin effect refers to the accumulation of eigenstates near the boundary in open boundary lattice models, which can be systematically characterized using the non-Bloch band theory. Here, we apply the non-Bloch band theory to investigate the stochastic reaction-diffusion process by mapping it to a non-Hermitian Kitaev chain. We exactly obtain the open boundary spectrum and the generalized Brillouin zone and identify a robust zero mode arising from the non-Bloch topology. Notably, distinct from its Hermitian counterpart in the quantum context, the zero mode supports anomalous dynamical crossover in the Markov process. We quantitatively demonstrate the intriguing dynamical effects through the spectral decomposition of the Hamiltonian on the non-Bloch eigenstates, and we confirm our findings by conducting stochastic simulations with high accuracy. Our study highlights the significant role and the general role of non-Bloch topology in nonequilibrium dynamics.

Note:

6+13 pages, 3+2 figures

References(68)

Figures(8)

[1]

Random and cooperative sequential adsorption

J.W. Evans
(
- Ames Lab and
- Iowa State U.
)

- Rev.Mod.Phys. 65 (1993) 1281-1329
•
DOI:
- 10.1103/RevModPhys.65.1281

[2]

Exact solutions for stochastic adsorption-desorption models and catalytic surface processes

M.D. Grynberg
,
T.J. Newman
,
R.B. Stinchcombe

- Phys.Rev.E 50 (1994) 957
•
DOI:
- 10.1103/PhysRevE.50.957

[3]

Dynamic correlation functions of adsorption stochastic systems with diffusional relaxation

M.D. Grynberg
,
R.B. Stinchcombe

- Phys.Rev.Lett. 74 (1995) 1242
•
DOI:
- 10.1103/PhysRevLett.74.1242

[4]

Dynamics of adsorption-desorption processes as a soluble problem of many fermions

M.D. Grynberg
,
R.B. Stinchcombe

- Phys.Rev.E 52 (1995) 6013
•
DOI:
- 10.1103/PhysRevE.52.6013

[5]

Diffusion-annihilation in the presence of a driving field

G.M. Schutz

- J.Phys.A 28 (1995) 3405
•
DOI:
- 10.1088/0305-4470/28/12/014

[6]

Stochastic non-equilibrium systems

R. Stinchcombe

- Adv.Phys. 50 (2001) 431
•
DOI:
- 10.1080/00018730110099650

[7]

Diffusion–annihilation dynamics in one spatial dimension

J.E. Santos
,
G.M. Schütz
,
R.B. Stinchcombe

- J.Chem.Phys. 105 (1996) 2399
•
DOI:
- 10.1063/1.472107

[8]

Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation

- J.Stat.Mech. 2110 (2021) 103102
•
e-Print:
- 2105.08828
•
DOI:
- 10.1088/1742-5468/ac22f8

[9]

Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries

F.H.L. Essler
,
V. Rittenberg

- J.Phys.A 29 (1996) 3375
•
DOI:
- 10.1088/0305-4470/29/13/013

[10]

Dynamics of nonequilibrium processes: Surface adsorption, reaction-diffusion kinetics, ordering and phase separation

V. Privman

- Trends Stat. Phys. 1 (1994) 89

[11]

(, Amsterdam, )

A. Schadschneider
,
D. Chowdhury
,
K. Nishinari

[12]

Reaction-diffusion waves in biology

V. Volpert
,
S. Petrovskii

- Phys.Life Rev. 6 (2009) 267
•
DOI:
- 10.1016/j.plrev.2009.10.002

[13]

Reaction - diffusion processes, critical dynamics and quantum chains

- Annals Phys. 230 (1994) 250-302
•
e-Print:
- hep-th/9302112
•
DOI:
- 10.1006/aphy.1994.1026

[14]

(, Boca Raton, FL, ), pp

M. Henkel

[15]

Non-Hermitian physics

Yuto Ashida
(
- Tokyo U., Appl. Phys. Dept.
)
,
Zongping Gong
(
- Tokyo U.
)
,
Masahito Ueda
(
- Tokyo U. and
- Wako, RIKEN
)

- Adv.Phys. 69 (2021) 3, 249-435
•
e-Print:
- 2006.01837
•
DOI:
- 10.1080/00018732.2021.1876991

[16]

Exceptional topology of non-Hermitian systems

Emil J. Bergholtz
(
- Stockholm U.
)
,
Jan Carl Budich
(
- Dresden, Tech. U., ITP
)
,
Flore K. Kunst
(
- Stockholm U. and
- Munich, Max Planck Inst. Quantenopt.
)

- Rev.Mod.Phys. 93 (2021) 1, 015005
•
e-Print:
- 1912.10048
•
DOI:
- 10.1103/revmodphys.93.015005

[17]

Edge States and Topological Invariants of Non-Hermitian Systems

- Phys.Rev.Lett. 121 (2018) 8, 086803
•
DOI:
- 10.1103/physrevlett.121.086803

[18]

Non-Hermitian Chern Bands

- Phys.Rev.Lett. 121 (2018) 13, 136802
•
DOI:
- 10.1103/PhysRevLett.121.136802

[19]

Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems

- Phys.Rev.Lett. 121 (2018) 2, 026808
•
DOI:
- 10.1103/PhysRevLett.121.026808

[20]

Anatomy of skin modes and topology in non-Hermitian systems

- Phys.Rev.B 99 (2019) 20, 201103
•
DOI:
- 10.1103/PhysRevB.99.201103

[21]

Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits

et al.

- Nature Phys. 16 (2020) 7, 747-750
•
DOI:
- 10.1038/s41567-020-0922-9

[22]

Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems

- Phys.Rev.Lett. 123 (2019) 17, 170401
•
DOI:
- 10.1103/PhysRevLett.123.170401

[23]

Probing non-Hermitian skin effect and non-Bloch phase transitions

Stefano Longhi

- Phys.Rev.Res. 1 (2019) 2, 023013
•
DOI:
- 10.1103/PhysRevResearch.1.023013

[24]

Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points

- Phys.Rev.B 97 (2018) 12, 121401
•
DOI:
- 10.1103/PhysRevB.97.121401

[25]

Topological Origin of Non-Hermitian Skin Effects

- Phys.Rev.Lett. 124 (2020) 8, 086801
•
DOI:
- 10.1103/PhysRevLett.124.086801

1-25 of 68
1
2
3
25 / page