A Thermal–Quantum Crossover Model for Mid-Infrared Modulation of Neuronal Excitability

A THERMAL–QUANTUM CROSSOVER MODEL FOR
MID-INFRARED MODULATION OF NEURONAL EXCITABILITY
A PREPRINT
En ic Espel Sanchez
Depa men o Physics
Uni e si y o Helsinki, 00560 Helsinki, Finland
No embe 19, 2025
ABSTRACT
Vol age-ga ed ion channels in neu ons open when a ga ing coo dina e c osses a ee-ene gy ba ie
ha is sha ply sensi i e o he local ansmemb ane ol age, ypically o e ens o hund eds o
milli ol s o e ec i e bias. We model he channel po e as a nanoscale dielec ic ca i y ha suppo s
elec omagne ic ield modes whose ol age luc ua ions include bo h classical ( he mal) and quan um
(ze o-poin ) con ibu ions. We show ha hese con ibu ions a e sepa a ed by a single he mal–
quan um c osso e equency
ωc= 2kBT/ℏ
, which a physiological empe a u e lies in he long-
wa eleng h mid-in a ed (
∼23 µm
). Abo e
ωc
, he ze o-poin (quan um) con ibu ion domina es
he ol age a iance ac oss he po e. In a simple ba ie -limi ed WKB pic u e o channel ga ing, his
enhanced a iance lowe s he e ec i e ba ie and p oduces an exponen ial inc ease in he p edic ed
channel opening p obabili y.
We ca y his c osso e scale consis en ly om a ini e- empe a u e ield- heo e ic desc ip ion,
h ough an e ec i e ga ing Hamil onian ha couples a ol age-sensi i e coo dina e o elec omagne ic
luc ua ions, and in o an expe imen ally es able p edic ion a he cellula le el. Speci ically, he
amewo k p edic s ha neu onal i ing h esholds ( heobase cu en and spike-ini ia ion ol age) will
exhibi a localized dip unde wo complemen a y condi ions: (i) du ing abso bed-dose–equalized
mid-in a ed s imula ion, as a unc ion o illumina ion equency; and (ii) a a ixed long-wa eleng h
illumina ion nea
23 µm
while he ba h empe a u e is swep , p ecisely a he empe a u e
T⋆
whe e
he illumina ion equency ma ches
ωc(T⋆)=2kBT⋆/ℏ
. We ou line whole-cell pa ch-clamp and
in a ed neu al s imula ion p o ocols — including as memb ane he mome y, TTX block, and
powe no maliza ion o con ol o bulk hea ing — ha can alsi y hese p edic ions. Ou analysis
links nanoscale elec omagne ic luc ua ions o mac oscopic neu onal exci abili y in a way ha is, in
p inciple, es able wi h exis ing mid-/ a -in a ed neu omodula ion ha dwa e.
Plain-language summa y
Wha is he idea? The iny wa e - illed po es (ion channels) in neu ons a e ne e pe ec ly quie . Hea makes he
elec ic ield wiggle (classical noise), and quan um mechanics adds i s own wiggle e en a ze o empe a u e (quan um
noise). We show ha he e is a single equency, ωc= 2kBT/ℏ, ha cleanly sepa a es hese wo kinds o noise.
Why does ha ma e ? When he jiggling has mo e quan um cha ac e (abo e
ωc
), i can mo e e ec i ely help he
channel c oss he ene gy ba ie o open. This could lowe he ol age needed o a neu on o i e!
How could you es i ? Shine mid-in a ed ligh on neu ons and sweep only he equency. The i ing h eshold should
dip nea ωc. Because ωcis se by empe a u e, cooling o wa ming he p epa a ion should mo e he dip in locks ep.
A The mal–Quan um C osso e Model o Mid-In a ed Modula ion o Neu onal Exci abili yA PREPRINT
A B ie In oduc ion
Quan um phenomena once conside ed negligible a physiological condi ions ha e now been po en ially implica ed in
pho osyn hesis, a ian magne o ecep ion, and deba ed in ol ac ion [
1
–
4
]. These p eceden s mo i a ed a ocused sea ch
o quan um e ec s in neu obiology, speci ically in he ol age luc ua ions ha go e n he opening o sodium (Na
+
)
and po assium (K+) channels [5, 6].
The easoning is simple: he nano-scale geome y and sensi i e na u e o ion channels and hei selec i i y il e s, could
gene a e he pe ec condi ions o e y small a ia ions and luc ua ions ha ing g ea e and mo e no iceable e ec s.
As such, he cen al idea o his pape is ha bo h ze o-poin and he mal elec omagne ic luc ua ions gene a e ol age
swings o a simila o de as channel ga ing h esholds (
∼10
–
200
mV depending on geome y) [
7
–
9
]. C ucially, he
ela i e weigh o quan um e sus he mal noise is con olled by a simple scale
ωc≡2kBT
ℏ≈8.2×1013 ad s−1(T= 310 K)(1)
which alls in he mid-in a ed (
≈23 µm
wa eleng h). The ollowing sec ions de elop he heo e ical backbone; wi h a
inal sec ion desc ibing a possible expe imen ha di ec ly unes ωac oss ωc.
Quan um Field–Modula ed Neu al Exci abili y: A Th eshold–F equency F amewo k
We s a by modeling he channel po e as a cylind ical dielec ic ca i y o leng h
d
and ela i e pe mi i i y
ϵ
. We see
ha o a single mode o equency ωcon ined o olume V∼d3, he elec ic- ield oo -mean-squa e ampli ude is
Eq= ℏω
2ϵ0ϵ V,∆Vq(ω;d) = Eqd= ℏω
2ϵ0ϵ d.(2)
(Fo ield quan iza ion and EM ene gy pa i ion, see e.g. [
10
,
11
].) Classically, a mode has o al ene gy
kBT
, and he
elec ic pa con ibu es kBT/2(c . luc ua ion–dissipa ion [12]). The e o e, he analogous ol age luc ua ion is
∆V h(T;d) = kBT
ϵ0ϵ d.(3)
Equa ing Eqs. 2 and 3 yields he c osso e equency
ωc(T) = 2kBT
ℏ,(4)
abo e which quan um luc ua ions should domina e.
He =H0−λ qe ˆ
X∆V( ),(5)
We now de ine he ( wo-sided, angula - equency) ol age powe spec al densi y (PSD)
SV V (ω)≡Z∞
−∞
dτ eiωτ ⟨∆V( )∆V( +τ)⟩= 2ℏωco h
ℏω
2kBTRe Ze (ω),(6)
whe e
Ze (ω)
subsumes geome y and ma e ial esponse; in he classical limi
SV V (ω)→4kBTRe Ze (ω)
. We use
a wo-sided PSD e sus
ω
wi h uni s
V2·s
(i.e.,
V2
pe ad/s). Thus
ωc
dema ca es a quan um-domina ed egime
(ℏω≫kBT) om a he mal one.
Applying Caldei a–Legge , o weak, app oxima ely Ma ko ian coupling he pu e-dephasing a e is
Γϕ=λ2q2
e
2ℏ2SV V (ω=0), τd≡Γ−1
ϕ=2ℏ2
λ2q2
e SV V (ω=0) .(7)
Fo a ini e-band p ocess one may eplace
SV V (0)
by a il e -weigh ed in eg al; ou conclusions nea
ωc
a e unchanged.
Now i we ea he ca i y ield as a scala po en ial
A0
in he Lo enz gauge, we can embed he ini e- empe a u e QFT.
The ini e-TEuclidean ac ion is
SE[A0] = ϵ0ϵ
2Zβℏ
0
dτZV(∇A0)2+1
c2∂τA02,(8)
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A The mal–Quan um C osso e Model o Mid-In a ed Modula ion o Neu onal Exci abili yA PREPRINT
wi h he Ma suba a p opaga o
D00(k, iωn) = 1
ϵ0ϵ
1
k2+ω2
n/c2,(9)
ep oducing Eqs. 2–3 upon summing o e
n
[
16
,
17
]. Impo an ly, and su p isingly, he same o de o magni ude o
ωc
eme ges as he scale sepa a ing n= 0 ( he mal) om n= 0 (quan um) con ibu ions, ying ou ield- heo e ic pic u e
back o he Hamil onian desc ip ion.
We know ha he channel opens when he ga ing coo dina e unnels h ough a ee-ene gy ba ie
U(x)
. Fo an
ene gy-independen ba ie o heigh U0and wid h d, he WKB p obabili y is
P(ω)∝exp−2d
ℏq2mU0−qe ∆V(ω),(10)
and because
∆V(ω)
g ows as
√ω
[Eq. 2],
P
is exponen ially sensi i e o equencies nea and abo e
ωc
, po en ially
leading o he sha p h eshold-like beha iou [20, 21].
Expe imen al P oposals
O e iew
We will implemen wo complemen a y es s o he h eshold- equency hypo hesis:
(A)
Abso bed-dose–equalized equency sweep (3–12
µ
m): Uses an exis ing mid-IR QCL band, bu equalizes
abso bed dose (peak memb ane
∆T
) a each equency o emo e spec al abso p ion bias. This p o ides a igo ous
nega i e/limi ed-band es .
(B)
Tempe a u e- acking c osso e a a ixed wa eleng h. To make he c osso e es able wi hin physiological
empe a u es, we ix he illumina ion nea he p edic ed h eshold band and sweep he ba h empe a u e. Speci ically,
we use a single-mode a -IR/THz sou ce a
λ= 23.0µm
(i.e.,
ω= 2πc/λ ≈8.19 ×1013 s−1
), which lies close o
he heo e ical ωc(T)=2kBT/ℏa ound body empe a u e. The equali y ω=ωc(T)occu s a
T⋆=ℏω
2kB≈313 K (40◦C) o λ= 23.0µm.
We hold
λ
ixed and s ep
T
om
298
–
314 K
in
1 K
inc emen s. A each
Tj
we e-equalize abso bed dose by
uning he inciden powe
P⋆(Tj)
so ha he peak memb ane empe a u e ise
∆Tpeak
ma ches a p ese a ge
wi hin
±15%
. I he amewo k is co ec , esponse me ics (e.g.,
∆I heo
,
V h eshold
) will exhibi a dip/in lec ion
as Tjc osses T⋆, e lec ing he swi ch in dominance be ween quan um and classical ield luc ua ions a ωc.
Op ionally (used when a ailable) a long-wa eleng h sou ce (18–30
µ
m QCL o THz line) ha can di ec ly span he
15–60 µm window a ound λc≈23 µm.
Common Readou and Endpoin s
P ima y endpoin (cu en -clamp). Measu e spike h eshold ( heobase) and F–I cu es in whole-cell cu en -clamp.
Fo each condi ion we:
• Injec 1 s cu en s eps (o s ai case) wi h 5–10 pA inc emen s o map i ing p obabili y s. cu en .
• De ine heobase as he minimal cu en elici ing ≥50% spike p obabili y ac oss 10 epea s.
• Repo ∆I heo (change om baseline) and ∆V h eshold ( om amp p o ocols).
Seconda y endpoin s.
•Vol age-clamp Na+a ailabili y and kine ics (sepa a e blocks) o ack channel-le el e ec s.
• Spike iming ji e and ISI s a is ics unde noisy cu en injec ion (dynamic h eshold).
Powe /dose ope a ing poin . The e a e wo possible egimes, adhe ence o one means s icking o i ac oss equen-
cies/ empe a u es:
(i) Low-∆T egime: Ta ge ∆Tpeak = 0.2±0.05 K a he memb ane.
(ii)
Mode a e INS-like egime: Ta ge
∆Tpeak = 2.0±0.2
K o la ge e ec sizes while con olling o he mal
con ounds.
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A The mal–Quan um C osso e Model o Mid-In a ed Modula ion o Neu onal Exci abili yA PREPRINT
High-bandwid h he mome y (memb ane-local). Replace/augmen he he mocouple wi h a memb ane-bound
luo escen he mome e (e.g. Rhodamine B o Eu-complex), sampled a
≥
10 kHz ia epi luo escence. Calib a e
luo escence s. empe a u e in si u (0.1 K esolu ion). Use he he mocouple only as a slow absolu e e e ence.
Ma e ials and Appa a us
• Whole-cell pa ch ig (Axopa ch-class ampli ie ) and up igh mic oscope wi h epi luo escence pa h.
• Mid-IR QCL, unable 3–12 µm (25–100 THz) o Pa (A).
•
Fixed-line sou ce o Pa (B): single-mode a -IR/THz QCL nea 23.0 µm, di e ence- equency mid-IR
sou ce.
• Op ional long-λsou ce (i a ailable, o Pa B): 18–30 µm QCL o THz line.
• ZnSe OAP op ics; beam expande ; ach oma ic ocusing o educe λ-dependen spo changes.
• Ge manium (o some pola ize -based) a iable a enua o wi h known spec al ansmission.
•Beam p o ile o kni e-edge se up a he sample plane o e i y spo size a each λ.
• 50 µm blackened shield a ound pipe e ip and Ag/AgCl e e ence o supp ess pho oelec ic a i ac s.
• FTIR o g a ing spec ome e on a 1% pick-o o absolu e equency e i ica ion.
• MCT (o py oelec ic) de ec o on a 9% pick-o o inciden powe moni o ing.
•Memb ane-bound luo escen he mome e dye and calib a ion s anda ds.
• Tempe a u e-con olled pe usion chambe wi h ±0.05 K s abili y and logging.
Abso bed-Dose–Equalized F equency Sweep (3–12 µm)
Ra ionale. Wa e /p o ein abso p ion and op ics h oughpu a y s ongly wi h
λ
. We equalize he s imulus a he
memb ane by holding ∆Tpeak cons an ac oss equencies, (no jus he inciden powe ).
Calib a ion: equalizing abso bed dose.
1.
Fo each cen e equency
νi
(s ep ac oss 3–12
µ
m), measu e he local memb ane
∆Tpeak(νi, P)
s. pulse
powe Pusing he luo escen he mome e (single 10–20 ms pulse).
2. Fi a mono onic calib a ion P⋆(νi)such ha ∆Tpeak(νi, P⋆)=∆T a ge (choose egime (i) o (ii) abo e).
3.
Ve i y spo diame e a he sample plane is wi hin
±10%
ac oss
νi
; adjus ocus/expansion o s abilize
geome y.
P o ocol.
1. Baseline (no ligh ): Cu en -clamp heobase + F–I; hen ol age-clamp sodium ac i a ion/inac i a ion.
2.
Randomized
ν
-sweep: Fo each
νi
, we deli e an op ical pulse ain (e.g., 10 ms pulses, 2 s IPI) a
P⋆(νi)
and collec :
• Cu en -clamp: heobase and amp-de i ed V h eshold (10-15 ials each).
• Simul aneous as he mome y o con i m ∆Tpeak wi hin a ge band.
3. Reco e y block: Repea baseline.
Con ols.
(i) 1 µM TTX o es Na+-dependence o any h eshold shi .
(ii) Op ical da k con ol: shu e closed bu un ull p o ocol.
(iii) Fa -IR/THz illumina ion con ol (i a ailable) a ma ched abso bed ∆Tpeak.
(i )
Fo a pho oelec ic a i ac con ol: illumina e ba h away om he cell; illumina e he pipe e unde a black shield
o ensu e no elec ical pickup.
Expec ed ou comes. I equency pe se is causal,
∆I heo(ν)
shows a dip localized in
ν
; i he mal-only, he cu e
la ens a e dose equaliza ion.
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A The mal–Quan um C osso e Model o Mid-In a ed Modula ion o Neu onal Exci abili yA PREPRINT
Tempe a u e-T acking C osso e a Fixed Wa eleng h
Ra ionale. Keep ω ixed and sweep Tso ha ωc(T)c osses ω. P edic ion: a h eshold dip when ω≈ωc(T).
Se up.
• Fix λ(e.g. 23.0 µm). Compu e ω= 2πc/λ.
• We choose a biologically easible empe a u e ange (e.g., 298–314 K) wi h cell- iabili y checks.
P o ocol.
1. Fo each Tj, measu e cu en -clamp heobase wi h/wi hou illumina ion ( andomized o de ).
2. T ack ∆I heo(Tj)and ∆V h eshold(Tj).
Expec ed ou comes. A empe a u e-locked mode a e dip in h eshold a
T⋆
whe e
ω≈ωc(T⋆)=2kBT⋆/ℏ
; he dip
should shi linea ly wi h Ti he c osso e go e ns he e ec .
Fu u e Al e na i e: In Vi o Op ical Neu omodula ion in Zeb a ish La ae
Why? I would demons a e beha io al ele ance and issue pene a ion limi s.
• 5-dp Tg(ela l3:GCaMP6s) zeb a ish a e immobilised in aga ose [29].
•
The mid-IR beam (expanded o
50 µ
m) is scanned ac oss he hindb ain mo o nuclei while wo–pho on calcium
imaging eco ds neu onal ac i i y.
•
The Tail- lick equency se es as a beha io al endpoin , expec ed o inc ease by
∼30
% upon
ω≳ωc
illumina ion.
A posi i e esul should cons i u e di ec e idence o quan um- ield con ibu ions o neu al exci abili y.
Discussion and Ou look
By h eading he h eshold equency
ωc
h ough e e y le el o heo y— om ol age a iances o Hamil onian coupling,
p opaga o s uc u e, and unnelling p obabili y—we o e a cohe en , alsi iable s o yline.
Fu he mo e, and c ucially, because
ωc= 2kBT/ℏ
is a uni e sal he mal–quan um c osso e scale, any biomolecula
nanodomain ha (i) suppo s ield modes in he mid-IR and (ii) couples hose modes elec os a ically o a ba ie -limi ed
unc ional coo dina e could exhibi analogous h eshold beha io . Ion-channel ga ing p o ides a conc e e wo ked
example; i should no be pigeonholed, b oade applicabili y o enzyme ac i e si es, allos e ic pocke s, o agg ega ion
nuclei emains an open, es able ques ion, and a no el a enue o quan um neu obiology.
Howe e , i is impo an o acknowledge ha , while ou h eshold- equency amewo k e eals a p e iously o e looked
quan um con ibu ion o ion-channel ga ing, we emphasize ha highe -le el cogni i e and emo ional p ocesses emain
well desc ibed by es ablished, la gely classical neu al-ne wo k models. Any unc ional ole o quan um luc ua ions a
he ci cui o beha io al le el emains specula i e and demands dedica ed in es iga ion.
Appendix A: De i a ions Unde lying he Abs ac
A.1 Se up and no a ion
We modeled he channel po e as a homogeneous dielec ic nanodomain o ela i e pe mi i i y
ε
and cha ac e is ic
leng h
d
( anspo e di ec ion). A single elec omagne ic (EM) no mal mode o angula equency
ω
con ined o olume
V
is ea ed as a ha monic oscilla o . We ake he ansmemb ane ol age luc ua ion as
∆V≡Rd
0E∥(x)dx ≈E d
o
a slowly a ying longi udinal ield.
A geome ical ema k. In he main ex we used
V∼d3
o compac ness. Fo a cylind ical po e o adius
a
,
V=πa2d
, which can be subs i u ed whe e e
V
appea s o expose he explici
a
-dependence. Fo p o ein and
con ined-wa e dielec ic conside a ions, see e.g. [30].
5

A The mal–Quan um C osso e Model o Mid-In a ed Modula ion o Neu onal Exci abili yA PREPRINT
A.2 Ze o-poin ol age a iance
The elec ic- ield ene gy o a single mode wi h ( ms) ampli ude Eis
UE=1
2ε0ε E2V. (11)
Fo a quan ized EM mode, he g ound-s a e (ze o-poin ) ene gy is
1
2ℏω
, sha ed equally by elec ic and magne ic pa s,
so ⟨UE⟩0=1
4ℏω. Equa ing he wo gi es
Ezp, ms = ℏω
2ε0ε V,∆Vq(ω;d)≡Ezp, ms d= ℏω
2ε0ε d,(12)
whe e he las equali y used V∼d3. Fo a cylinde , ∆Vq=qℏω d
2ε0ε πa2.
A.3 The mal ol age a iance (an equipa i ion)
Classically, one quad a ic deg ee o eedom a empe a u e
T
ca ies a e age ene gy
kBT/2
. The elec ic pa
con ibu es
⟨UE⟩T=1
2kBT=1
2ε0ε ⟨E2⟩TV, (13)
hence
E h, ms = kBT
ε0ε V,∆V h(T;d)≡E h, ms d= kBT
ε0ε d.(14)
This connec s wi h Johnson–Nyquis noise in conduc o s [13, 14].
A.4 The mal–quan um c osso e equency
The c osso e is de ined by ∆Vq(ωc;d)=∆V h(T;d), which yields
ωc(T) = 2kBT
ℏ.(15)
A T= 310 K, ωc≈8.1×1013 s−1(mid-IR), co esponding o c=ωc/2π≈1.29 ×1013 Hz and λc=c/ c≈23 µm.
A.5 Fini e- empe a u e a iance and he co h ac o
Fo a bosonic mode, he mean ene gy a ini e Tis
⟨H⟩T=ℏω¯n+1
2=ℏω
2co hℏω
2kBT,¯n=1
eℏω/kBT−1.(16)
Since he elec ic and magne ic ene gies a e equal on a e age,
⟨UE⟩T=1
2⟨H⟩T=ℏω
4co hℏω
2kBT=1
2ε0ε ⟨E2⟩TV. (17)
The e o e
⟨E2⟩T=ℏω
2ε0ε Vco hℏω
2kBT,⟨(∆V)2⟩T= ∆V2
q(ω;d) co hℏω
2kBT.(18)
This is an equal- ime a iance pe mode a equency
ω
, no a PSD. I s connec ion o he PSD
SV V (ω)
de ined
in he main ex is he s anda d ela ion
⟨(∆V)2⟩=1
2πR∞
−∞dω SV V (ω)
; inse ing he luc ua ion–dissipa ion o m
SV V (ω)=2ℏωco h(ℏω/2kBT) Re Ze (ω) ep oduces he same co h ac o .
A.6 Euclidean ini e-T ield heo y link and Ma suba a p opaga o
In a homogeneous dielec ic and Lo enz gauge, he scala po en ial A0has Euclidean ac ion
SE[A0] = ε0ε
2Zβℏ
0
dτ ZV
d3xh(∇A0)2+1
c2(∂τA0)2i, β ≡(kBT)−1.(19)
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A The mal–Quan um C osso e Model o Mid-In a ed Modula ion o Neu onal Exci abili yA PREPRINT
Fou ie expansion wi h bosonic Ma suba a equencies ωn= 2πn/(βℏ)gi es he quad a ic ke nel
D00(k, iωn) = 1
ε0ε
1
k2+ω2
n/c2.(20)
Summing o e
n
econs uc s he
co h(ℏω/2kBT)
occupa ion ac o ha appea s in
(18)
[
16
,
17
]. No ably, he
n= 0
(s a ic) Ma suba a sec o encodes he classical (
∝T
) con ibu ion, while
n= 0
e ms encode quan um
luc ua ions—mi o ing he c osso e a ωcin (15).
A.7 E ec i e coupling, dephasing, and a decohe ence imescale
Le he ele an ga ing coo dina e couple o ol age luc ua ions ia
Hin =−λ qe ˆ
X∆V( ),(21)
whe e
qe
is an e ec i e displaced cha ge and
ˆ
X
dis inguishes al e na i e sys em con igu a ions (e.g. along a eac ion
coo dina e). Fo Gaussian ol age noise wi h PSD
SV V (ω)
and weak, app oxima ely Ma ko ian coupling, he
pu e-dephasing a e is
Γϕ=λ2q2
e
2ℏ2SV V (0), τd≃2ℏ2
λ2q2
e SV V (0) .(22)
He e
ω⋆= 0
co esponds o quasi-s a ic dephasing; mo e gene ally one may use a il e -weigh ed in eg al i he sys em
selec s a ini e band.
A.8 Semiclassical unnelling dependence on ω
Conside ba ie -limi ed ga ing along
x
wi h an ene gy-independen ba ie o heigh
U0
and wid h
d
. In he p esence o
an e ec i e bias qe ∆V(ω) ha lowe s he ba ie , he WKB ansmission p obabili y o E≪U0−qe ∆Vis
P(ω)∝exp"−2
ℏZd
0
dx q2mU0−qe ∆V(ω)−Eg#≈exp−2d
ℏq2mU0−qe ∆V(ω).(23)
Using
(12)
,
∆V(ω)∝√ω
in he quan um-domina ed egime, so
P(ω)
is exponen ially sensi i e o
ω
nea and abo e
ωc[20, 21].
A.9 Mul imode gene aliza ion and b oadening
Fo a ealis ic (disc e e) se o ca i y modes indexed by
m
wi h equencies
ωm
and geome y-dependen ol age
pa icipa ion ac o s, he a iance is
⟨(∆V)2⟩T=X
m
∆V2
q,m co hℏωm
2kBT,(24)
which b oadens he sha pness o he c osso e i he mode densi y a ound
ωc
is app eciable. In he con inuum limi , he
sum can be eplaced by an in eg al wi h an app op ia e densi y o s a es and lineshape.
A.10 Dimensional and ( ai ly) concise limi ing checks
(a)
∆V2
q∼ℏω
ε0ε d
has uni s o
V2
; (b)
∆V2
h ∼kBT
ε0ε d
also
V2
; (c)
ωc
in
(15)
is linea in
T
and
ℏ−1
as expec ed; (d)
(18) eco e s (14) o ℏω≪kBTand (12) o ℏω≫kBT.
Acknowledgemen s
I g a e ully acknowledge discussions and me hodological insigh s om he published wo k o E. Duco Jansen,
A. Mahade an-Jansen, J. Wells, M. Che no , and S. Shoham, whose pionee ing s udies on in a ed neu al s imula ion
and pho o he mal sa e y c i e ia di ec ly in o med he expe imen al design desc ibed he e. The elec ophysiological
amewo k ollows he pa ch-clamp echniques de eloped by B. Sakmann, E. Nehe , O. P. Hamill, and F. J. Sigwo h.
Guidance on mid-in a ed lase sou ces and ins umen a ion d aws on he wo k o M. Razeghi, C. F. Gmachl, and Y. Yao
in he ield o quan um-cascade lase s. The concep o luo escen mic o- he mome y is indeb ed o J. Richa ds-Ko um
and colleagues.
7
A The mal–Quan um C osso e Model o Mid-In a ed Modula ion o Neu onal Exci abili yA PREPRINT
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