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Accardi L., Lu Y.G., Volovich I. — Quantum Theory and Its Stochastic Limit
Accardi L., Lu Y.G., Volovich I. — Quantum Theory and Its Stochastic Limit

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Название: Quantum Theory and Its Stochastic Limit

Авторы: Accardi L., Lu Y.G., Volovich I.

Аннотация:

"The subject of this book is a new mathematical technique, the stochastic limit developed for solving nonlinear problems in quantum theory involving systems with infinitely many degrees of freedom (typically quantum fields or gases in the thermodynamic limit). This technique is condensed into some easily applied rules (called "stochastic golden rule") which allow us to single out the dominating contributions to the dynamical evolution of systems in regimes involving long times and small effects. In the stochastic limit the original Hamiltonian theory is approximated using a new Hamiltonian theory which is singular. These singular Hamiltonians still define a unitary evolution and the new equations give much more insight into the relevant physical phenomena than the original Hamiltonian equations. Especially, one can explicitly compute multitime correlations (e.g. photon statistics) or coherent vectors, which are beyond the reach of typical asymptotic techniques, as well as deduce in the Hamiltonian framework the widely used stochastic Schrodinger equation and the master equation." This monograph is well suited as a textbook in the emerging field of stochastic limit techniques in quantum theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 473

Добавлена в каталог: 15.04.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$u^{0}_{-t}-1$-cocycle      47
$X^{\varepsilon}$      58
$\delta$-function of an operator      8
$\delta$-functions on the standard simplex      227
$\mathcal{N}$-type blocks      267
$\mathcal{P}_{\Omega}$-Fock module      345
2-point functions      73
A- and $A^{+}$-type blocks      267
Analytical condition      163
Anderson model      352
Anisotropic renormalization group method      370
Annihilators      58
Anti — Fock representation      80
Anti — Fock state      61
Asymptotically effective interacting Hamiltonian      261
Asymptotically effective interaction Hamiltonian      276
Backward transport coefficient      33
Basic analytical condition      120
Block      278
Block normal ordering theorem      449
Block principle      278
Blue shifts      144
Bogoliubov      49
Bogoliubov transformation      269
Bogoliubov — Shirkov approach      370
Bohr frequencies      122
Bohr frequencies, positive and negative ~      159
Boltzmann algebra      371
Boltzmann field      58
Born approximation      52
Bose — Einstein condensation      79
Bose — Einstein density      78
Boson field      58
Boson Fock fields      72
Boson Fock white noise      76
Boson Gaussianity      72
Boson, finite temperature white noise      79
Bound states      120
Bra vectors      269
Breit Wigner complex poles      370
Brownian motion      77
Canonical commutation relations      4 395
Canonical decomposition of $H_{0} + H_{I}$      43
Canonical representation of the thermal Gaussian state      80
Carrier frequency      103
Cascades with reed photons      387
Catalan number      448
Causal commutator rule      226
Causal Ito table      172
Caused Fourier transform      158
Cavity QED      169
Central limit theorem      30
chemical potential      78
Cheshire cat effect      161 181
Chronological (or time-ordered) product      237
Chronological stochastic limit      108
Classical Gaussian random field      97
Classical Hamiltonian systems      33
Classical jump Markov process      133
Classical Markov (jump) process      186
Classical white noise      76
Collective vectors      28 48 453
Commutant of a      172
Commutation relations      58
Composite system      118
Conditioned expectation      206
Conjugated vertices      375
Conjugation operator      269
Connected components      396
Connected correlators      355
Connected diagrams      354 375
Converge      48
Convergence in the distribution sense      6
Convergence in the sense of matrix elements      28
Convergence of chronological correlator      107
Convergence of fields in the sense of correlators      85
Correlators      58
Correlators, invariance      60
creators      58
Cutoff      124
Cutoff-free      184
Damped harmonic oscillator      100
Decay rates      140
Decoherence      137 182 194
Detailed balance      200
Dipole approximation      116
Dipole interaction Hamiltonian      162
Dipole-type interactions      121
Discrete spectrum embedded in the continuum      94
Dispersion relations      141
Double integral lemma      431
Drift      166
Drift coefficient      128
Dual space $\overline{\mathcal{H}}_{1}$      269
Dynamical system      11
Dynamically q-deformed fields      290
Effective 1—particle Hamiltonian      126
Effective fields      157
Einstein formula      167
electric field      117
electromagnetic field      253
Energy exponent      375
Energy fluctuations      102
Energy shell scalar product      140
Energy shift      142
Energy surface      140
Entangled or interacting commutation relations      370
Entangled rescaled fields      290 371
Entanglement      373
Environment      24
Equilibrium states at inverse temperature $\beta$      68
Evolution on any algebra      61
expectation value      57
Exponential decay      135
External lines      226 375
Factorization theorem      403
Fast degrees of freedom      14
Fermi block theorem, first ~      414
Fermi block theorem, second ~      415
Fermi momentum      352
Fermi sphere      356
Fermi surface      140
Fermi — Dirac density      78
Filtering problem      206 213
First connected component theorem      401
First vanishing theorem      417
Flip of spin      200
Flow equation      11 47
Flow with explosion      40
Fluctuation-dissipation relation      133
Fock representation      60
Fock state      61
Fokker — Planck equation      35
Form factor      123
Free (or Boltzmannian) algebra      289
Free 1—particle Hamiltonian      62
Free algebra      371
Free evolution      62
Free Fock (or Boltzmannian) white noise      306
Free Hamiltonian      62
Free independence      304
Free massive scalar field      248
Free massless scalar field      250
Free master Hamiltonian      145
Free state      64
Free Wick theorem      289
Friedrichs      50
Fugacity      78
Functional central limit theorem      30 32
Functional integral approach to the stochastic limit      247
Gamma-ray bursts from neutron stars      386
Gamma-ray pulsars      386
Gamma-ray repeaters      386
Gap at the zero eigenvalue      136
Gauge transformations of the first kind      61
Gauge-invariant state      61
Gaussian field      59
General noncrossing principle      448
Generalized dipole approximation      123
Generalized random fields      58
Generalized rotating-wave approximation      125
Generalized susceptibility      192
Generalized susceptivity      167
Generalized Wick theorem      60
Generic quantum system      173
Gibbs state      68
GKSL generator      132
Glauber dynamics      200
Grand canonical state      78
Green functions      354 380
Green — Kubo — Mori theory      17
Ground state      353
Half-bandwidth      103
Half-planar      377
Hamiltonian, free ~      4
Hamiltonian, rescaled interaction      19
Heat bath      24
Heisenberg equation      10
Heisenberg equation in the interaction, representation      11
Heisenberg evolution      10
Heisenberg-Euler effective Lagrangian      386
Hilbert modules      265
Hilbert transform      142
Homogeneization problem      45
Hot free algebra      321
Hot free algebra relations      333
Independent      59
Index of refraction      386
Input algebra      211
Input processes      212
Input—output channels      205
Integrable in the sense of distributions      87 156
Interacting commutation relations      372
Interacting particle systems      196
Interaction representation      9
Internal lines      226 379
Interpolation problem      206
Intertwiner property      337
Invariance principle      30
Inverse lifetime of the vacuum      135
Ionized states      121
Ising model      199
Ket vectors      269
KMS condition      68
Langevin equation, backward or outer white noise      23
Langevin equation, forward or inner white noise      23
Langevin equation, quantum ~      29
Large N limit      368
Large N limit for SU(N) invariant gauge theory      371
Left and right multiplication      335
Level systems      174
Liouville equation      10
Liouvillian      33
Local quantum field theory      384
Locality      83
Localized left unitary evolution      211
Localized left unitary multiplicative, functional      211
Long chain      425
Loop variables      375
Low density      15
Low-density limit      255
Macroscopic quantum coherence      179
Magnetic field      117
Markov semigroup      172
Markovian approximation      27
Markovian cocycle      145
Markovian generator      172
Martingale term      166
Master equation      27 132
Master field      93
Maxwell's equations with radiative corrections      386
Mean zero gauge-invariant white noise      165
Measurement      216
Measurement apparatus      24
Minimal coupling      113
Mixed moments      58
Module commutation relations      289
Multiple integral lemma      438
Multiple-simplex theorem      435
Multiplicative interaction      121
N-particle vectors      73
n-point functions      58
Noise      24
Non-time-consecutive pairings      222
Non-time-consecutive theorem      417
Nonconnected diagram      354
Noncrossing pair partition      293 446
Nondemolition measurements      217
Nondemolition process      215
Nonequilibrium quantum field theory      162 369
Nonstationary white noises      201
Normal ordering theorem      448
Normally ordered form of the white noise Hamiltonian      128
Normally ordered free equation      307
Normally ordered Langevin white noise equation      132
Number vectors      73
Off-resonance condition      182
One-parameter automorphism group      10
One-parameter unitary group      4
Open system      24
Operator density of particles      371
Operator valued transport coefficient      17
Orthogonalization principle      280
Output field      212
Pair partition      446
Pair partitions      60
Parametric Down Conversion      390
Parity operator      9 269
Partial expectation      26
Partition of the identity      172
Photon splitting      386
Photon splitting in a strong magnetic field      386
Photon-splitting cascades in a magnetic field      372
Plane waves      138
Polarization index      114
Polarization vectors      114
Polaron model      320
Polynomial decay      319
Polynomial interactions      251
Polynomial interactions with cutoff      262
Prediction problem      206
Prigogine      55
Projection on the diagonal algebra      42
Propagator      9
Pseudo-eigenstates      137
Purely oscillatory behaviours      135 9
Q-deformed correlators      293
Q-deformed module relations      290
Q-deformed module Wick Theorem      296
Q-Gaussian Equilibrium States      70
QED in an external field      385
Quantum (Boltzmannian or free), stochastic differential equation      309
Quantum central limit theorems      86
Quantum coherence      195
Quantum dissipative and irreversible, phenomena      8
Quantum transport coefficient      16
Quasi free states      64
Quasi-free evolution      67
Quasi-standard models      265
Rainbow graphs      285
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