We study, under very general conditions and in a variety of geometries, quantum enhancement of transport in open systems. Both static disorder and dephasing associated with dynamical disorder (or finite temperature) are fully included in the analysis. We show that quantum coherence effects may significantly enhance transport in open quantum systems even in the semiclassical regime (where the decoherence rate is greater than the inter-site hopping amplitude), as long as the static disorder is sufficiently strong. When the strengths of static and dynamical disorder are fixed, there is an optimal opening strength at which the coherent transport enhancement is optimized. Analytic results are obtained in two simple paradigmatic tight-binding models of large systems: the linear chain and the fully connected network. The physical behavior is also reflected, for example, in the FMO photosynthetic complex, which may be viewed as being intermediate between these paradigmatic models. We furthermore show that a nonzero dephasing rate assists transport in an open linear chain when the disorder strength exceeds a critical value, and obtain this critical disorder strength as a function of the degree of opening.

1.
J. M.
Moix
,
M.
Khasin
, and
J.
Cao
,
New journal of Physics
15
, p.
085010
(
2013
).
2.
K.
Higgins
,
S.
Benjamin
,
T.
Stace
,
G.
Milburn
,
B. W.
Lovett
, and
E.
Gauger
,
Nature Communications
5
(
2014
).
3.
M.
Sarovar
and
K. B.
Whaley
,
New journal of Physics
15
, p.
013030
(
2013
).
4.
J.
Grad
,
G.
Hernandez
, and
S.
Mukamel
,
Physical Review A
37
, p.
3835
(
1988
).
5.
F. C.
Spano
and
S.
Mukamel
,
The Journal of Chemical Physics
91
,
683
700
(
1989
).
6.
G.
Celardo
and
L.
Kaplan
,
Physical Review B
79
, p.
155108
(
2009
).
7.
G.
Celardo
,
A.
Smith
,
S.
Sorathia
,
V.
Zelevinsky
,
R.
SenKov
, and
L.
Kaplan
,
Physical Review B
82
, p.
165437
(
2010
).
8.
G. G.
Giusteri
,
F.
Mattiotti
, and
G. L.
Celardo
,
Physical Review B
91
, p.
094301
(
2015
).
9.
G. L.
Celardo
,
P.
Poli
,
L.
Lussardi
, and
F.
Borgonovi
,
Physical Review B
90
, p.
085142
(
2014
).
10.
G. L.
Celardo
,
G. G.
Giusteri
, and
F.
Borgonovi
,
Physical Review B
90
, p.
075113
(
2014
).
11.
A. F.
Sadreev
and
I.
Rotter
,
Journal of Physics A: Mathematical and General
36
, p.
11413
(
2003
).
12.
P.
Rebentrost
,
M.
Mohseni
,
I.
Kassal
,
S.
Lloyd
, and
A.
Aspuru-Guzik
,
New journal of Physics
11
, p.
033003
(
2009
).
13.
P.
Rebentrost
,
M.
Mohseni
, and
A.
Aspuru-Guzik
,
The Journal of Physical Chemistry B
113
,
9942
9947
(
2009
).
14.
M. B.
Plenio
and
S. F.
Huelga
,
New journal of Physics
10
, p.
113019
(
2008
).
15.
S.
Lloyd
,
M.
Mohseni
,
A.
Shabani
, and
H.
Rabitz
, arXiv preprint arXiv:1111.4982 (
2011
).
16.
G. L.
Celardo
,
F.
Borgonovi
,
M.
Merkli
,
V. I.
Tsifrinovich
, and
G. P.
Berman
,
The Journal of Physical Chemistry C
116
,
22105
22111
(
2012
).
17.
Y.
Zhang
,
G. L.
Celardo
,
F.
Borgonovi
, and
L.
Kaplan
,
Physical Review E
95
, p.
022122
(
2017
).
18.
J.
Wu
,
R. J.
Silbey
, and
J.
Cao
,
Physical Review Letters
110
, p.
200402
(
2013
).
19.
F.
Caruso
,
A. W.
Chin
,
A.
Datta
,
S. F.
Huelga
, and
M. B.
Plenio
,
The Journal of Chemical Physics
131
, p.
09B612
(
2009
).
20.
Y.
Zhang
,
G. L.
Celardo
,
F.
Borgonovi
, and
L.
Kaplan
, ArXiv e-prints (
2017
), arXiv:1706.09524.
21.
G.
Celardo
,
A.
Biella
,
L.
Kaplan
, and
F.
Borgonovi
,
Fortschritte der Physik
61
,
250
260
(
2013
).
22.
A.
Biella
,
F.
Borgonovi
,
R.
Kaiser
, and
G.
Celardo
,
EPL (Europhysics Letters)
103
, p.
57009
(
2013
).
23.
V.
Sokolov
and
V.
Zelevinsky
,
Nuclear Physics A
504
,
562
588
(
1989
).
24.
V.
Sokolov
and
V.
Zelevinsky
,
Physics Letters B
202
,
10
14
(
1988
).
25.
I.
Rotter
,
Reports on Progress in Physics
54
, p.
635
(
1991
).
26.
V.
Sokolov
and
V.
Zelevinsky
,
Annals of Physics
216
,
323
350
(
1992
).
27.
G.
Celardo
,
F.
Izrailev
,
V.
Zelevinsky
, and
G.
Berman
,
Physics Letters B
659
,
170
175
(
2008
).
28.
G.
Celardo
,
F.
Izrailev
,
V.
Zelevinsky
, and
G.
Berman
,
Physical Review E
76
, p.
031119
(
2007
).
29.
S.
Sorathia
,
F.
Izrailev
,
V.
Zelevinsky
, and
G.
Celardo
,
Physical Review E
86
, p.
011142
(
2012
).
30.
A.
Ziletti
,
F.
Borgonovi
,
G.
Celardo
,
F.
Izrailev
,
L.
Kaplan
, and
V.
Zelevinsky
,
Physical Review B
85
, p.
052201
(
2012
).
31.
H.
Haken
and
G.
Strobl
,
Zeitschrift für Physik A Hadrons and Nuclei
262
,
135
148
(
1973
).
32.
J.
Cao
and
R. J.
Silbey
,
Journal of Physical Chemistry A
113
,
13825
13838
(
2009
).
33.
T.
Förster
, in
Modern Quantum Chemistry Istanbul Lectures
, Vol.
3
, edited by
O.
Sinanoglu
(
Academic Press
,
New York
,
1965
), pp.
93
137
.
34.
J. A.
Leegwater
,
The Journal of Physical Chemistry
100
,
14403
14409
(
1996
).
35.
G. S.
Engel
,
T. R.
Calhoun
,
E. L.
Read
,
T.-K.
Ahn
,
T.
Mančal
,
Y.-C.
Cheng
,
R. E.
Blankenship
, and
G. R.
Fleming
,
Nature
446
,
782
786
(
2007
).
36.
G.
Panitchayangkoon
,
D.
Hayes
,
K. A.
Fransted
,
J. R.
Caram
,
E.
Harel
,
J.
Wen
,
R. E.
Blankenship
, and
G. S.
Engel
,
Proceedings of the National Academy of Sciences
107
,
12766
12770
(
2010
).
37.
M.
Sarovar
,
A.
Ishizaki
,
G. R.
Fleming
, and
K. B.
Whaley
,
Nature Physics
6
,
462
467
(
2010
).
38.
H.
Hossein-Nejad
and
G. D.
Scholes
,
New journal of Physics
12
, p.
065045
(
2010
).
39.
J.
Strumpfer
,
M.
Sener
, and
K.
Schulten
,
The Journal of Physical Chemistry Letters
3
,
536
542
(
2012
).
40.
H.
Fidder
,
J.
Knoester
, and
D. A.
Wiersma
,
The Journal of Chemical Physics
95
,
7880
7890
(
1991
).
41.
J.
Moll
,
S.
Daehne
,
J. R.
Durrant
, and
D. A.
Wiersma
,
The Journal of Chemical Physics
102
,
6362
6370
(
1995
).
42.
X.
Hu
,
T.
Ritz
,
A.
Damjanović
, and
K.
Schulten
,
The Journal of Physical Chemistry B
101
,
3854
3871
(
1997
).
43.
X.
Hu
,
A.
Damjanović
,
T.
Ritz
, and
K.
Schulten
,
Proceedings of the National Academy of Sciences
95
,
5935
5941
(
1998
).
44.
A.
Olaya-Castro
,
C. F.
Lee
,
F. F.
Olsen
, and
N. F.
Johnson
,
Physical Review B
78
, p.
085115
(
2008
).
45.
R. H.
Dicke
,
Physical Review
93
, p.
99
(
1954
).
46.
M. O.
Scully
and
A. A.
Svidzinsky
,
Science
328
,
1239
1241
(
2010
).
47.
S.
Lloyd
and
M.
Mohseni
,
New journal of Physics
12
, p.
075020
(
2010
).
48.
G. D.
Scholes
,
Chemical Physics
275
,
373
386
(
2002
).
49.
R.
Monshouwer
,
M.
Abrahamsson
,
F.
Van Mourik
, and
R.
Van Grondelle
,
The Journal of Physical Chemistry B
101
,
7241
7248
(
1997
).
50.
D.
Ferrari
,
G.
Celardo
,
G. P.
Berman
,
R.
Sayre
, and
F.
Borgonovi
,
The Journal of Physical Chemistry C
118
,
20
26
(
2013
).
51.
P. W.
Anderson
,
Physical Review
109
, p.
1492
(
1958
).
52.
D.
Heijs
,
V.
Malyshev
, and
J.
Knoester
,
Physical Review Letters
95
, p.
177402
(
2005
).
53.
T.
Shahbazyan
,
M.
Raikh
, and
Z. V.
Vardeny
,
Physical Review B
61
, p.
13266
(
2000
).
54.
G. L.
Celardo
,
P.
Poli
,
L.
Lussardi
, and
F.
Borgonovi
,
Physical Review B
90
, p.
085142
(
2014
).
55.
A. V.
Chechkin
,
R.
Metzler
,
J.
Klafter
, and
V. Y.
Gonchar
, in
Anomalous Transport: Foundations and Applications
, edited by
R.
Klages
,
G.
Radons
, and
I. M.
Sokolov
(
Wiley-VCH
,
2008
), pp.
129
162
.
56.
Y.
Zhang
,
G. L.
Celardo
,
F.
Borgonovi
, and
L.
Kaplan
,
Physical Review E
95
, p.
022122
Feb (
2017
).
57.
F. M.
Izrailev
,
S.
Ruffo
, and
L.
Tessieri
,
Journal of Physics A: Mathematical and General
31
, p.
5263
(
1998
).
58.
C. W.
Beenakker
,
Reviews of Modern Physics
69
, p.
731
(
1997
).
59.
C.
Beenakker
and
H.
van Houten
,
Solid State Physics
44
,
1
228
(
1991
).
60.
V.
May
and
O.
Kühn
,
Charge and energy transfer dynamics in molecular systems
(
John Wiley & Sons
,
2008
).
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