Non-hermitian quantum mechanics

Non-Hermitian Quantum Mechanics

Volumn 9780521889728, Issue , 2011, Pages 1-394

  Moiseyev, Nimrod ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC PHYSICS; MECHANICS; QUANTUM THEORY; REFRACTIVE INDEX; STUDENTS;

ATOMIC AND MOLECULAR PHYSICS; COMPLEX POTENTIALS; GRADUATE STUDENTS; NON-HERMITIAN QUANTUM MECHANICS; NUMERICAL CALCULATION; PARITYTIME SYMMETRIES; QUANTUM FIELD THEORY; RESONANCE PHENOMENA;

HAMILTONIANS;

EID: 84928755209     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511976186     Document Type: Book

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130. N. Moiseyev, P. Froelich and E. Watkins, Resonances by the complex coordinate method with Hermitian Hamiltonian II: error estimates, J. Chem. Phys. 80, 3623–3628 (1984).
131. P. Froelich and N. Moiseyev, Resonances by the complex coordinate method with Hermitian Hamiltonian III: autoionization, J. Chem. Phys. 81, 1352–1354 (1984).
132. E. Engdahl and N. Moiseyev, Resonances by the complex coordinate method with Hermitian Hamiltonian IV: the linear correlation procedure, J. Chem. Phys. 84, 1379–1384 (1986).
133. E. Davidson, E. Engdahl and N. Moiseyev, New bounds to resonance eigenvalues, Phys. Rev. A 33, 2436–2439 (1986).
134. U. Peskin, O. E. Alon and N. Moiseyev, The solution of the time-dependent Schr¨odinger equation by the (t, t') method: multiphoton ionization/dissociation probabilities in different gauges of the electromagnetic potentials, J. Chem. Phys. 100, 7310 (1994).
135. J. W. Pang, D. Neuhauser and N. Moiseyev, Photoabsorption probability for a system governed by a time-dependent Hamiltonian through the (t, t’) formalism, J. Chem. Phys. 106, 6839–6847 (1997).
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145. U. Peskin and N. Moiseyev, The complex coordinate scattering theory and the Kohn variational method: a general formulation and application to long range potentials, J. Chem. Phys. 97, 6443–6450 (1992).
146. E. Narevicius and N. Moiseyev, Trapping of an electron due to molecular vibrations, Phys. Rev. Lett. 84, 1681–1684 (2000).
147. N. Moiseyev, R. Santra, J. Zobeley and L. S. Cederbaum, Fingerprints of the nodal structure of autoionizing vibrational wave functions in clasters: interatomic Coulombic decay in Ne dimer, J. Chem. Phys, 114, 7351–7360 (2001).
148. E. Narevicius, P. Serra and N. Moiseyev, Critical phenomena associated with self-orthogonality in non-Hermitian quantum mechanics, Europhys. Lett. 62, 789–794 (2003).
149. E. Narevicius and N. Moiseyev, Non-Hermitian quantum mechanics: formalism and applications, Fundamental World of Quantum Chemistry 2, 1–32 (2003).
150. P. Zdanska, H. R. Sadeghpour, N. Moiseyev, Non-Hermitian diabatic formulation of antiproton collision: protonium formation, J. Phys. B: At. Mol. Opt. Phys. 37, L35–L41 (2004).
151. E. Narevicius, N. Moiseyev, H. R. Sadeghpour and L. S. Cederbaum, Extremely narrow peaks in predissociation of sodium dimer due to rovibronic coupling, J. Chem. Phys, 121, 3527–3532 (2004).
152. N. Moiseyev, T. Maniv, R. Elber and R. B. Gerber, Lifetimes of rotational resonances in molecule-surface scattering: quantum versus classical results, Mol. Phys. 55, 1369–1381 (1985).
153. T. Maniv, E. Engdahl and N. Moiseyev, Application of the complex rotation method to the study of resonance states of atoms at a corrugated surface, J. Chem. Phys. 86, 1048–1054 (1987).
154. E. Engdahl, T. Maniv and N. Moiseyev, Complex quasiprobability for atoms trapped on surfaces: a novel application of the complex coordinate method, J. Chem. Phys. 88, 5864–5870 (1988).
155. A. Ben-Ephraim, M. Folman, J. Heidberg and N. Moiseyev, Predesorption of CO from the sodium chloride (100) surface: study by the complex coordinate method, J. Chem. Phys. 89, 3840–3846 (1988).
156. N. Moiseyev, Complex scaling applied to trapping of atoms and molecules on solid surfaces, in E. Br¨andas and N. Elander, eds. Resonances, the Unifying Route Towards the Formulation of Dynamical Processes. Lecture Notes in Physics, Berlin, Springer-Verlag, 1989.
157. E. Engdahl and N. Moiseyev, Perturbation analysis of gas-surface diffractive selective adsorption resonance states, Mol. Phys. 66, 465–478 (1989).
158. E. Engdahl, T. Maniv and N. Moiseyev, Gas-surface scattering cross section by the complex coordinate method, J. Chem. Phys. 94, 6330–6333 (1991).
159. U. Peskin and N. Moiseyev, Gas/surface complex coordinate scattering theory: HD/Ag(111), HD/Pt(111) rotationally inelastic transition intensities, J. Chem. Phys. 96, 2347–2355 (1992).
160. U. Peskin and N. Moiseyev, The complex coordinate scattering theory: broken inversion symmetry of corrugated surfaces in helium diffraction from Cu(115), J. Chem. Phys. 97, 2804–2808 (1992).
161. U. Peskin and N. Moiseyev, The complex coordinate scattering theory and its application to the study of the surface asymmetry effect in helium diffraction from copper, Int. J. Quantum. Chem. 46, 343–363 (1993).
162. A. K. Gupta and N. Moiseyev, Trapping of molecules by highly rotational excitations, Chem. Phys. 338, 113–120 (2007).
163. N. Moiseyev, F. Bensch and H. J. Korsch, Multiphoton dissociation or ionization partial widths and branching ratios for time-periodic systems, Phys. Rev. A 42, 4045–4049 (1990).
164. F. Bensch, H. J. Korsch and N. Moiseyev, Decay dynamics of a time-periodic quantum system, J. Phys. B 24, 1321–1341 (1991).
165. N. Ben-Tal, N. Moiseyev, C. Leforestier and R. Kosloff, Positions, lifetimes, and partial widths of metastable quasienergy states by solving the time-dependent complex-scaled Schr¨odinger equation, J. Chem. Phys. 94, 1636–1642 (1991).
166. F. Bensch, H. J. Korsch and N. Moiseyev, Simple method for constructing the ionization spectra of driven time-periodic Hamiltonians, Phys. Rev. A 43, 5145–5148 (1991).
167. U. Peskin and N. Moiseyev, The solution of the time-dependent Schrödinger equation by the (t, t‘) method: theory, computational algorithm and applications, J. Chem. Phys. 99, 4590–4596 (1993).
168. N. Moiseyev, The solution of the time-dependent Schr¨odinger equation by the (t, t’) method: complex scaled multiphoton ionization/dissociation resonance wave functions are square integrable, J. Chem. Phys. 101, 9716–9718 (1994).
169. I. Vorobeichik and N. Moiseyev, State-to-state transition probabilities for time-dependent Hamiltonians using complex absorbing potentials, J. Phys. B 31, 645–656 (1998).
170. I. Gilary, A. Fleischer and N. Moiseyev, Calculations of time-dependent observables in non-Hermitian quantum mechanics: the problem and a possible solution, Phys. Rev. A 72, 012117/1–012117/8 (2005).
171. A. Fleischer and N. Moiseyev, Adiabatic theorem for non-Hermitian time-dependent open systems. Phys. Rev. A 72, 032103/1–032103/11 (2005).
172. N. Ben-Tal, N. Moiseyev, R. Kosloff and C. Cerjan, Harmonic generation in ionizing systems by the time-dependent complex coordinate Floquet Method, J. Phys. B 26, 1445–1461 (1993).
173. U. Peskin and N. Moiseyev, Time-independent scattering theory for time-periodic hamiltonians: formulation and complex scaling calculations of above-threshold -ionization spectra, Phys. Rev. A 49, 3712–7318 (1994).
174. N. Moiseyev, M. Chrysos, O. Atabek and R. Lefebvre, harmonic generation in molecular systems: application to H2+ in intense laser fields, J. Phys. B 28, 2007–2019 (1995).
175. N. Moiseyev and F. Weinhold, High harmonic generation spectra of neutral helium by the complex-scaled (t, t’) method: role of dynamical electron correlation, Phys. Rev. Lett., 78, 2100–2103 (1997).
176. P. Zdanska, V. Averbukh and N. Moiseyev, High harmonic generation spectra of aligned benzene in circular polarized laser field, J. Chem. Phys. 118, 8726–8738 (2003).
177. N. Moiseyev and M. Lein, Non-Hermitian quantum mechanics for high-order harmonic generation spectra, J. Phys. Chem. A 107, 7181–7188 (2003).
178. A. Fleischer, V. Averbukh and N. Moiseyev, Non-Hermitian quantum mechanics versus the conventional quantum mechanics: effect of the relative phasing of bichromatic fields on high-order harmonic generation, Phys. Rev. A 69, 043404/1–043404/8 (2004).
179. I. Gilary, P. Zdanska and N. Moiseyev, Ab initio calculation of harmonic generation spectra of helium using a time-dependent non-Hermitian formalism. Phys Rev. A 74, 052505/1–052505/8 (2006).
180. A. Fleischer and N. Moiseyev, Attosecond laser pulse synthesis using bichromatic highorder harmonic generation, Phys. Rev. A 74, 053806/1–053806/7(2006).
181. A. Fleischer and N. Moiseyev, Amplification of high-order harmonics using weak perturbative high-frequency radiation, Phys. Rev. A 77, 010102/1(R)–010102/4(R) (2008).
182. A. Fleischer, A. K. Gupta and N. Moiseyev, Dynamical symmetry analysis of ionization and harmonic generation of atoms in bichromatic laser pulses, Int. J. Quantum Chem. 103, 824–840 (2005).
183. I. Vorobeichik, U. Peskin and N. Moiseyev, Modal losses and design of modal irradiance patterns in an optical fiber by the complex (t, t’) method, J. Opt. Soc. An. B 12, 1133–1141 (1995).
184. A. M. Kenis, I. Vorobeichik and N. Moiseyev, Analysis of an intermediate-mode-assisted optical directional coupler using Bloch theory, IEEE J. Quant. Electron. 36, 563–573 (2000).
185. N. Moiseyev and L. S. Cederbaum, Resonance solutions of the nonlinear Schr¨odinger equation: tunneling lifetime and fragmentation of trapped condensates, Phys. Rev. A 72, 033605/1–033605/8 (2005).
186. N. Moiseyev, L. D. Carr, B. A. Malomed and Y. B. Band. Transition from resonances to bound states in nonlinear systems: application to BEC, J. Phys. B 37, L193–L200 (2004).
187. E. Narevicius and N. Moiseyev, Non-Hermitian formulation of interference effect in scattering experiments, J. Chem. Phys. 113, 6088–6095.
188. E. Narevicius and N. Moiseyev, (2000); Structured photo-absorbtion spectra of ArHCl: fingerprints of overlapping broad resonances, Chem. Phys. Lett. 287, 250–254 (1998).
189. N. Moiseyev, R. Santra, J. Zobeley and L. S. Cederbaum, Fingerprints of the nodal structure of autoionizing vibrational wave functions in clusters: interatomic coulombic decay in Ne dimer, J. Chem. Phys. 114, 7351–7360 (2001).
190. S. Scheit, L. S. Cederbaum and H.-D. Meyer, Time-dependent interplay between electron emission and fragmentation in the interatomic Coulombic decay, J. Chem. Phys. 118, 2092–2107 (2003).
191. N. Moiseyev, S. Scheit and L. S. Cederbaum, Non-Hermitian quantum mechanics: wave packet propagation on autoionizing potential energy surfaces, J. Chem. Phys. 121, 722–725 (2004).
192. N. Moiseyev, P. R. Certain and F. Weinhold, Resonance properties of complex-rotated Hamiltonians, Mol. Phys. 36, 1613–1630 (1978).
193. N. Moiseyev and S. Friedland, The association of resonance states with the incomplete spectrum of finite complex-scaled Hamiltonian matrices, Phys. Rev. A 22, 618–623 (1980).
194. H. P. Breuer, K. Dietz and M. Holthaus, Berry’s phase in quantum optics, Phys. Rev. A 47, 725–728 (1993).
195. O. Latinne, N. J. Kylstra, M. Dörr et-al. Laser-induced degeneracies involving autoionizing states in complex atoms, Phys. Rev. Lett. 74, 46–49 (1995).
196. M. V. Berry and D. H. J. O’Dell, Diffraction by volume gratings with imaginary potentials, J. Phys. A 31, 2093–2101 (1998).
197. W. D. Heiss, M. Müller and I. Rotter, Collectivity, phase transitions, and exceptional points in open quantum systems, Phys. Rev. E 58, 2894–2901 (1998).
198. W. D. Heiss, Phases of wave functions and level repulsion, Eur. Phys. J. D 7, 1 (1999).
199. W. D. Heiss, Repulsion of resonance states and exceptional points, Phys. Rev. E 61, 929–932 (2000).
200. E. Hernández, A. Jáuregui and A. Mondragón, Degeneracy of resonances in a double barrier potential, J. Phys. A 33, 4507–4523 (2000).
201. E. Narevicius and N. Moiseyev, Fingerprints of broad overlapping resonances in the e+H2 cross section, Phys. Rev. Lett. 81, 2221–2224 (1998); Trapping of an electron due to molecular vibrations, Phys. Rev. Lett. 84, 1681–1684 (2000).
202. W. D. Heiss and H. L. Harney, The chirality of exceptional points, Eur. Phys. J. D 17, 149–151 (2001).
203. P. Serra, S. Kais and N. Moiseyev, Crossover phenomena and resonances in quantum systems, Phys. Rev. A 64, 062502-062507 (2001).
204. R. Santra and L. S. Cederbaum, Non-Hermitian electronic theory and applications to clusters, Phys. Rep. 368, 1–117 (2002).
205. M. V. Berry and M. R. Dennis, The optical singularities of birefringent dichroic chiral crystals, Proc. R. Soc. Lond. 459, 1261–1292 (2003).
206. E. Narevicius, P. Serra and N. Moiseyev, Critical phenomena associated with self-orthogonality in non-Hermitian quantum mechanics, Europhys. Lett. 62, 789–794 (2003).
207. E. Hernández, A. Jáuregui and A. Mondragón, Jordan blocks and Gamow–Jordan eigenfunctions associated with a degeneracy of unbound states, Phys. Rev. A 67, 022721/1–022721/15 (2003).
208. W. D. Heiss, Exceptional points: their universal occurrence and their physical significance, Czechoslovak J. Phys. 54, 1091–1099 (2004) and references therein. A. Mostafazadeh, Quantum mechanics of Klein–Gordon-type fields and quantum cosmology, Ann. Phys. 309, 1–48 (2004).
209. M. V. Berry, Physics of nonhermitian degeneracies, Czech. J. Phys. 54 1039–1047 (2004).
210. E. Hernández, A. Jáuregui and A. Mondragón, Energy eigenvalue surfaces close to a degeneracy of unbound states: crossings and anticrossings of energies and widths, Phys. Rev. E 72, 026221/1–026221/11 (2005).
211. U. Günther, I. Rotter and B. F. Samsonov, Projective Hilbert space structures at exceptional points, J. Phys. B 40, 8815–8833 (2007).
212. C. M. Bender, Making sense of non-Hermitian Hamiltonians, Rep. Prog. Phys. 70, 947–1018 (2007) and references therein.
213. S. Klaiman, U. Günther and N. Moiseyev, Visualization of branch points in PT-symmetric waveguides, Phys. Rev. Lett. 101, 080402 (2008).
214. U. Günther and B. F. Samsonov, Naimark-dilated PT-symmetric brachistochrone, Phys. Rev. Lett. 101, 230404–230408 (2008).
215. M. V. Berry, Optical lattices with PT symmetry are not transparent, J. Phys. A 41, 244007–244013 (2008).
216. S. Klaiman and N. Moiseyev, Narrow resonances in complex potential energy surfaces, J. Phys. B: At. Mol. Opt. Phys. 42, 044004 (2009).
217. O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides and N. Moiseyev, Nonlinear waves in subwavelength waveguide arrays: evanescent bands and the Phoenix Soliton, Phys. Rev. Lett. 102, 163902 (2009).
218. H. Cartarius, J. Main and G. Wunner, Exceptional points in atomic spectra, Phys. Rev. Lett. 99, 173003 (2007); Exceptional points in the spectra of atoms in external fields, Phys. Rev. A 79, 053408-1-11 (2009).
219. I. Rotter, A non-Hermitian Hamilton operator and the physics of open quantum systems, J. Phys. A 42 153001–153051 (2009) and references therein.
220. S. Y. Lee, Decaying and growing eigenmodes in open quantum systems: biorthogonality and the Petermann factor, Phys. Rev. A 80, 042104–042108 (2009).
221. S. B. Lee, J. Yang, S. Moon et al., Observation of an exceptional point in a chaotic optical microcavity, Phys. Rev. Lett. 103, 134101–134104 (2009).
222. H. Baumgärtel, Analytic Perturbation Theory for Matrices and Operators, Berlin, Akademie-Verlag, 1984 and Operator Theory: Adv. Appl. 15 (1985).
223. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th edn., Oxford, Clarendon Press, 1958.
224. H. Feshbach, Theoretical Nuclear Physics, New York, John Wiley & Sons, Inc., 1992.
225. H. Feshbach, Unified theory of nuclear reactions, Ann. Phys. 5, 357–390 (1958).
226. H. Feshbach, Unified theory of nuclear reactions: II, Ann. Phys. 19, 287–313 (1962).
227. N. Moiseyev, Feshbach resonances: the branching of quantum mechanics into Hermitian and non-Hermitian formalisms, J. Phys. Chem. A. 113, 7660–7666 (2009).