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1.
M. Combescot O. Betbeder-Matibet 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,55(1):63-76
The purpose of this paper is to show how the diagrammatic expansion
in fermion exchanges of scalar products of N-composite-boson
(“coboson”) states can be obtained in a practical way. The hard
algebra on which this expansion is based, will be given in an independent publication.
Due to the composite nature of the particles, the scalar products
of N-coboson states do not reduce to a set of Kronecker symbols, as
for elementary bosons, but contain subtle exchange terms between two or
more cobosons. These terms originate from Pauli exclusion between the
fermionic components of the particles. While our many-body
theory for composite bosons leads to write these scalar products as
complicated sums of products of “Pauli scatterings” between
two cobosons, they in fact correspond to fermion exchanges
between any number P of quantum particles, with
2 ≤P≤N. These P-body exchanges are nicely represented by the
so-called “Shiva diagrams”, which are topologically different from
Feynman diagrams, due to the intrinsic many-body nature of the Pauli
exclusion from which they originate. These Shiva diagrams in fact
constitute the novel part of our composite-exciton many-body theory
which was up to now missing to get its full
diagrammatic representation. Using them, we can now “see” through
diagrams the physics of any quantity in which enters N interacting
excitons — or more generally N composite bosons —, with fermion
exchanges included in an
exact — and transparent — way. 相似文献
2.
M. Combescot 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(3):289-303
We reconsider the procedure
developed for atoms a few decades ago by Girardeau, in the light of
the composite-boson many-body theory we recently proposed. The
Girardeau's procedure makes use of a so called “unitary Fock-Tani
operator” which in an exact way transforms one composite bound
atom into one bosonic “ideal” atom. When used to transform the
Hamiltonian of interacting atoms, this operator generates an extremely
complex set of effective scatterings between ideal bosonic atoms and free
fermions which makes the transformed Hamiltonian impossible to write
explicitly, in this way forcing to some truncation. The scatterings
restricted to the ideal-atom subspace are shown to read rather simply in
terms of the two elementary scatterings of the composite-boson many-body
theory, namely, the energy-like direct interaction scatterings
— which describe fermion interactions without fermion exchange — and
the dimensionless Pauli scatterings — which describe fermion exchanges
without fermion interaction. We here show
that, due to a fundamental difference in the scalar products of
elementary and composite bosons, the Hamiltonian expectation
value for N ground state atoms
obtained by staying in the ideal-atom subspace and working
with boson operators only, differ from the exact ones even for N = 2 and
a mapping to the ideal-atom subspace performed, as advocated, from
the fully antisymmetrical atomic state, i.e., the state which obeys the
so-called “subsidiary condition”. This shows that, within this
Girardeau's procedure too, we cannot completely forget the underlying
fermionic components of the particles if we want to correctly describe
their interactions. 相似文献
3.
M. Combescot W. Pogosov 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(2):161-181
We present a many-body theory for Frenkel excitons which takes into account their composite nature exactly. Our approach is
based on four commutators similar to the ones we previously proposed for Wannier excitons. They allow us to calculate any
physical quantity dealing with N excitons in terms of “Pauli scatterings” for carrier exchange in the absence of carrier interaction
and “interaction scatterings” for carrier interactions in the absence of carrier exchange. We show that Frenkel excitons have
a novel “transfer assisted exchange scattering”, specific to these excitons. It comes from indirect Coulomb processes between
localized atomic states. These indirect processes, commonly called “electron-hole exchange” in the case of Wannier excitons
and most often neglected, are crucial for Frenkel excitons, as they are the only ones responsible for the excitation transfer.
We also show that in spite of the fact that Frenkel excitons are made of electrons and holes on the same atomic site, so that
we could naively see them as elementary particles, they definitely are composite objects, their composite nature appearing
through various properties, not always easy to guess. The present many-body theory for Frenkel excitons is thus going to appear
as highly valuable to securely tackle their many-body physics, as in the case of nonlinear optical effects in organic semiconductors. 相似文献
4.
M. Combescot O. Betbeder-Matibet 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(1):33-46
This paper contains a detailed calculation of the photoinduced current density at third order in the coupling between a semiconductor
and a multifrequency photon field, starting from its standard textbook expression which reads in terms of a triple commutator.
Due to a major intrinsic problem linked to this triple commutator, such a derivation has been made possible quite recently
only, thanks to the tools developed in the composite-boson many-body theory we have recently constructed. The photoinduced
current density is shown to ultimately read in a compact form, in terms of the “Pauli scatterings” and “Coulomb scatterings”
for exciton-exciton interactions introduced in this theory. Representation of this third order response in Shiva diagrams,
which visualize interactions between excitons, is also given to better grasp the physics of the various contributions. 相似文献
5.
The aim of this paper is to clarify the conceptual difference which
exists between the interactions of composite bosons and the interactions
of elementary bosons. A special focus is made on the physical processes
which are missed when composite bosons are replaced by elementary bosons.
Although what is here said directly applies to excitons, it is also valid
for composite bosons in other fields than semiconductor physics. We, in
particular, explain how the two elementary scatterings – Coulomb and
Pauli – of our many-body theory for composite excitons, can be extended
to a pair of fermions which is not an Hamiltonian eigenstate – as for
example a pair of trapped electrons, of current interest in quantum
information. 相似文献
6.
W. Pogosov M. Combescot 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(2):183-192
By using the composite many-body theory for Frenkel excitons we have recently developed, we here derive the ground state energy
of N Frenkel excitons in the Born approximation through the Hamiltonian mean value in a state made of N identical Q = 0 excitons. While this quantity reads as a density expansion in the case of Wannier excitons, due to many-body effects induced
by fermion exchanges between N composite particles, we show that the Hamiltonian mean value for N Frenkel excitons only contains
a first order term in density, just as for elementary bosons. Such a simple result comes from a subtle balance, difficult
to guess a priori, between fermion exchanges for two or more Frenkel excitons appearing in Coulomb term and the ones appearing
in the N exciton normalization factor – the cancellation being exact within terms in 1/Ns where Ns is the number of atomic sites in the sample. This result could make us naively believe that, due to the tight binding approximation
on which Frenkel excitons are based, these excitons are just bare elementary bosons while their composite nature definitely
appears at various stages in the precise calculation of the Hamiltonian mean value. 相似文献
7.
8.
We here consider an exciton i embedded in a
sea of N identical excitons 0. If the
excitons are taken as true bosons, a bosonic
enhancement factor N is
found for i=0. If the
exciton composite nature is kept, this enhancement not only exists
for i=0, but also for any exciton
having a center of mass momentum equal to the
sea exciton momentum. This physically
comes from the fact that an exciton with such a
momentum can be transformed into a
sea exciton by Pauli scattering, i.e., carrier exchange with the
sea, making this exciton i not so much
different from a sea exciton. This possible
scattering, directly linked to the composite nature of
the excitons, is irretrievably lost when the
excitons are bosonized. The underlying interest of this work is in fact the calculation of
the scalar products of N-exciton states, which turns out to be quite tricky,
due to possible carrier exchanges between excitons. This work actually
constitutes a crucial piece of our many-body theory for interacting
composite bosons, because all physical effects involving composite bosons
ultimately end by the calculation of such scalar products. The skeleton
diagrams we here introduce to represent them, allow
to visualize many-body effects linked to carrier exchanges in an easy way.
They are conceptually different from Feynman
diagrams, because of the special feature of the Pauli
scatterings which originate from
boson statistics departure. 相似文献
9.
N. Andrenacci P. Pieri G.C. Strinati 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,13(4):637-642
We consider a system of fermions in the continuum case at zero temperature, in the strong-coupling limit of a short-range
attraction when composite bosons form as bound-fermion pairs. We examine the density dependence of the size of the composite
bosons at leading order in the density (“dilute limit”), and show on general physical grounds that this size should decrease with increasing density, both in three and two dimensions. We then compare with the analytic zero-temperature mean-field
solution, which indeed exhibits the size shrinking of the composite bosons both in three and two dimensions. We argue, nonetheless,
that the two-dimensional mean-field solution is not consistent with our general result in the “dilute limit”, to the extent
that mean field treats the scattering between composite bosons in the Born approximation which is known to break down at low
energy in two dimensions.
Received 3 June 1999 and Received in final form 29 July 1999 相似文献
10.
O. Betbeder-Matibet M. Combescot 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,31(4):517-523
Pauli exclusion between the carriers of N excitons induces novel many-body effects, quite different from the ones generated by Coulomb interaction. Using our commutation
technique for interacting close-to-boson particles, we here calculate the Hamiltonian expectation value in the N-ground-state-exciton state. Coulomb interaction enters this quantity at first order only by construction; nevertheless, due
to Pauli exclusion, subtle many-body effects take place, which give rise to terms in (Na
x
3/)n with n ≥ 2. An exact procedure to get these density dependent terms is given.
Received 11 February 2002 / Received in final form 30 May 2002 Published online 6 March 2003
RID="a"
ID="a"e-mail: combescot@gps.jussieu.fr 相似文献
11.
M. Combescot X. Leyronas C. Tanguy 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,31(1):17-24
The N-ground-state-exciton normalization factor, namely 〈v| B
0
N
B
0
dagN| v〉 = N!F
N, with B
0
d
ag the exact ground state exciton creation operator, differs from N! because the excitons are not perfect bosons. The quantity FN turns out to be crucial for problems dealing with interacting excitons. Indeed, the excitons feel each other not only through
the Coulomb interaction but also through Pauli exclusion between their components. A quite novel purely Pauli contribution
exists in their many-body effects, which relies directly on FN. Following procedures used in the commutation technique we recently introduced to treat interacting close-to-bosons, and
in the BCS theory of superconductivity, we rederive important relations verified by the FN's. We also give new explicit expressions of FN valid for η = Na
x
3/ small but N
2
a
x
3/ large, as FN does not read in terms of η but Nη, the exciton number N being possibly huge in macroscopic samples. Due to this superextensivity, FN does not appear alone in physical quantities, but through ratios like F
N + p/F
N. We end this work by giving the η expansion of these ratios, useful for all purely Pauli many-body effects.
Received 30 May 2002 / Received in final form 12 October 2002 Published online 27 January 2003
RID="a"
ID="a"e-mail: combescot@gps.jussieu.fr 相似文献
12.
We examine “de Broglie-Bohm” causal trajectories for the two electrons in a nonrelativistic helium atom, taking into account
the spin-dependent momentum terms that arise from the Pauli current. Given that this many-body problem is not exactly solvable,
we examine approximations to various helium eigenstates provided by a low-dimensional basis comprised of tensor products of
one-particle hydrogenic eigenstates.
First to be considered are the simplest approximations to the ground and first-excited electronic states found in every introductory
quantum mechanics textbook. For example, the trajectories associated with the simple 1s(1)1s(2) approximation to the ground state are, to say the least, nontrivial and nonclassical.
We then examine higher-dimensional approximations, i.e., eigenstates Ψ
α
of the Hamiltonian in this truncated basis, and show that ∇
i
S
α
=0 for both particles, implying that only the spin-dependent momentum term contributes to electronic motion. This result is
independent of the size of the truncated basis set, implying that the qualitative features of the trajectories will be the
same, regardless of the accuracy of the eigenfunction approximation.
The electronic motion associated with these eigenstates is quite specialized due to the condition that the spins of the two
electrons comprise a two-spin eigenfunction of the total spin operator. The electrons either (i) remain stationary or (ii)
execute circular orbits around the z-axis with constant velocity. 相似文献
13.
We extend the well-known Cooper’s problem beyond one pair and study how this dilute limit is connected to the many-pair Bardeen-Cooper-Schrieffer
(BCS) condensate. We find that, all over from the dilute to the dense regime of pairs, Pauli blocking induces the same “moth-eaten
effect” as the one existing for composite boson excitons. This effect makes the average pair binding energy decrease linearly
with pair number, bringing it, in the standard BCS configuration, to half the single-pair value. This proves that, at odds
with popular understanding, the BCS gap is far larger than the broken pair energy. The increase comes from Pauli blocking
between broken and unbroken pairs. Possible link between our result and the crossover between the Bose-Einstein condensate
and BCS condensate is also discussed. 相似文献
14.
O. Betbeder-Matibet M. Combescot 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,22(1):17-29
We study the interaction of an exciton with a distant metal, which is the simplest problem on interacting excitons: The semiconductor
and metal electrons being “different” species, we do not have to worry about the tricky consequences of Pauli exclusion between
identical carriers, which appear in any other problem on interacting excitons. We show how the exciton absorption, in the
presence of semiconductor-metal interaction, can be derived in a very simple and transparent way from an exciton diagram procedure,
provided that we use the appropriate exciton-metal interaction vertex, which contains the scattering from an exciton state
to another exciton state under a Coulomb excitation. We also show that the resolution of this problem using standard electron-hole
diagrams is dreadfully complicated at the lowest order in the semiconductor-metal interaction already, preventing a full calculation
of the exciton-metal coupling from this usual technique.
Received 26 February 2001 相似文献
15.
V. P. Neznamov 《Physics of Particles and Nuclei》2012,43(1):36-41
The Standard Model with massive fermions is formulated in the isotopic Foldy-Wouthuysen representation. SU(1) × U(1) — invariance of the theory in this representation is independent of whether fermions possess mass or not, and, consequently,
it is not necessary to introduce interactions between Higgs bosons and fermions. The study discusses a possible relation between
spontaneous breaking of parity in the isotopic Foldy-Wouthuysen representation and the composition of elementary particles
of “dark matter”. 相似文献
16.
L. S. Schulman 《Foundations of Physics》1997,27(12):1623-1636
The quantum Zeno effect (QZE) is often associated with the ironic maxim, “a watched pot never boils”, although the notion
of “watching” suggests a continuous activity at odds with the usual (pulsed measurement) presentation of the QZE. We show
how continuous watching can provide the same halting of decay as the usual QZE, and, for incomplete hindrance, we provide
a precise connection between the interval between projections and the response time of the continuous observer. Thus, watching
closely, but not so closely as to halt the “boiling”, is equivalent to—gives the same degree of partial hindrance as—pulsed
measurements with a particular pulsing rate. Our demonstration is accomplished by treating the apparatus for the continuous
watching as a fully quantum object. This in turn allows us a second perspective on the QZE, in which it is the modified level
structure of the combined system/apparatus Hamiltonian that slows the decay. This and other considerations favor the characterization
“dominated time evolution” for the QZE. 相似文献
17.
M. Combescot M.-A. Dupertuis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(3):459-464
We show that the carrier “antibinding” observed recently in
semiconductor quantum dots, i.e., the fact that the ground state
energy of two electron-hole pairs goes above twice the ground-state
energy of one pair, can entirely be assigned to a charge separation
effect, whatever its origin. In the absence of external electric field, this charge
separation comes from different “spreading-out” of the electron and
hole wavefunctions linked to the finite height of the barriers. When
the dot size shrinks, the two-pair energy always stays below when the
barriers are infinite. On the opposite, because barriers are less
efficient for small dots, the energy of two-pairs in a dot with
finite barriers, ends by behaving like the one in bulk, i.e., by
going above twice the one-pair energy when the pairs get too close.
For a full understanding of this “antibinding” effect, we have also
reconsidered the case of one pair plus one carrier. We find that,
while the carriers just have to spread out of the dot differently for
the “antibinding” of two-pairs to appear, this “antibinding” for
one pair plus one carrier only appears if this carrier is the one
which spreads out the less. In addition a remarkable sum rule exists
between the “binding energies” of two pairs and of one pair plus one carrier. 相似文献
18.
We review the infrared behavior of interacting bosons at zero temperature. After a brief discussion of the Bogoliubov approximation
and the breakdown of perturbation theory due to infrared divergences, we present two approaches that are free of infrared
divergences—Popov’s hydrodynamic theory and the nonperturbative renormalization group—and allow us to obtain the exact infrared
behavior of the correlation functions. We also point out the connection between the infrared behavior in the superfluid phase
and the critical behavior at the superfluid-Mott-insulator transition in the Bose-Hubbard model. 相似文献
19.
Starting from the full group of symmetries of a system we select a discrete subset of transformations which allows to introduce
the Clifford algebra of operators generating new supercharges of extended supersymmetry. The system defined by the Pauli Hamiltonian
is discussed.
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001
Partially supported by the KBN-Grant # 5 P03B056 20. 相似文献
20.
M. Combescot G. J. Zhu 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,79(3):263-274
We propose a many-body formalism for Cooper pairs which has similarities to the one we recently
developed for composite boson excitons (coboson in short). Its Shiva diagram representation evidences
that N Cooper pairs differ from N single pairs through electron exchange only: no direct coupling
exists due to the very peculiar form of the reduced BCS potential. As a first application, we here use this
formalism to derive Richardson’s equations for the exact eigenstates of N Cooper pairs. This derivation
gives hints on why the N(N-1)N(N-1) dependence of the N-pair ground state energy we recently obtained by
solving Richardson’s equations analytically in the low density limit, stays valid up to the dense regime.
No higher order dependence exists under large overlap, a surprising result hard to accept at first. We
also briefly question the BCS wave function ansatz compared to Richardson’s exact form, in the light of our
understanding of coboson many-body effects. 相似文献