Nimrod Moiseyev

Nimrod Moiseyev (b. October 1947 in Haifa, Hebrew language) is an Israeli professor of theoretical chemistry & physics at Technion International School.

His research focuses on the foundations of quantum mechanics with applications for selected systems.

Quantum mechanics describes systems as Wave function and Operator (physics, which provide various observables, such as the energy of the system, average Positioning system, etc.

The standard Formalism (philosophy of mathematics) of quantum mechanics, described for example in Paul Dirac book on The Principles of Quantum mechanics [1], is based on a special class of operators, called Self-adjoint operators.

The Hermitian property of an operator implies imposing boundary conditions on the wave-functions.

Using Hermitian operators ensures that the Eigenvalues and eigenvectors are real and that the amplitude of the Wave function of Bound state| decay to zero at the asymptote, i.e., very far from the Center of mass of the system.

Nowadays, the eigenvalues of many-electron Molecule are routinely calculated by List of quantum chemistry and solid-state physics software for the Electronic structure of Bound state..

Atomic and molecular systems in a metastable Resonance (particle physics) state have sufficient energy to break into two or more subsystems but do not break immediately, that is, they have finite lifetime.

The calculations of such states cannot be done using the same boundary conditions as for bound states, which are imposed on the time-independent Schrödinger equation.

This is due to the fact that one needs to look for solutions that represent an outgoing spherical waves at infinity.

Such boundary conditions are complex, which make the eigenfunctions exponentially diverge at asymptote, unlike bound states.

Thus, the wave-functions are not square integrable and therefore, cannot be normalized (they are not part of the Hilbert space).

Notably, using outgoing boundary conditions makes the physical Hamiltonian non-Hermitian. (See, for example, Section 132 in the book of Landau and Lifshitz on Non-Relativistic Quantum Mechanics [2]).

In 1928 Gamow [3] developed a theory of resonances (quasi-stationary or finite-lifetime metastable states) for alpha decay of heavy nuclei.

However, his theory is based on eigenfucntions that are not square integrable (not part of the Hilbert space).

Later, in 1971, the derivation of complex scaling transformations by Balslev and Combes [4], and Simon [5] enabled to Calculation|calculate resonance solutions that are square integrable (and are part of a Generalization|generalized Hilbert space).

These Function (mathematics)|functions can be normalized.

## Contents

* 1 Major Contributions To Science
* 2 Books
* 3 Prizes & Awards
* 4 Visiting Academic Positions
* 5 Education
* 5.1 References
* 5.2 External links

# Major Contributions To Science[edit]

During his postdoctoral studies in Madison, Nimrod Moiseyev, together with Frank Weinhold and Phil Certain, derived a variational principle for non-Hermitian complex scaled Hamiltonian path|Hamiltonians [6], and later, jointly with Joe Hirschfelder, he introduced a generalization of complex scaling transformations [7].

These derivations provide a formal justification for using numerical methods, originally developed for calculating bound states, for computing atomic and molecular autoionization resonances.

Later, upon starting his own research group at Technion, Nimrod Moiseyev and his colleagues developed such methods and applied them to discover metastable states in a range of systems from molecular hydrogen anion [8] to RNA nucleobase (the uracil anion) [9] through optical devices [10].

Nimrod Moiseyev coined terms that are used to describe basic concepts in non-Hermitian quantum mechanics.

First, the complex-product, replacing Paul Dirac|Dirac’s Scalar (physics)|scalar product, which is used in standard (Hermitian) quantum mechanics [6].

Second, self-orthogonality [6,11], resulting from non-Hermitian degeneracy that corresponds to physical phenomena that cannot be predicted or explained by the standard (Hermitian) quantum mechanics. For example, time asymmetric switch from one state to another [12] rather than accumulating a topological Berry Phase as in the Hermitian case.

He also coined the term universal-RFCAP [13], a reflection-free complex absorption potential, which enables the calculations of resonance decay rates and energies for any system without using energy dependent fitting parameters.

He also invented the term SECS (smooth-exterior-complex-scaling) [13,14]. SECS is used to avoid the difficulties in calculating molecular resonances.

Also, he introduced RVP (the resonances via Pade approach) [15].

In this approach, energies and lifetimes of autoionizing molecular states, as a function of their geometry, can be computed using standard (Hermitian) quantum chemistry packages, along with analytic dilation into the complex (non-Hermitian) plane.

Using the (t,t’) method that he developed with his then PhD student Uri Peskin [16], he carried out the first ab-initio calculations of high-order harmonic generation spectra (HGS) for helium Atom|atoms in 1998.

This work has put an End time|end to a long standing discussion about the source of HGS by showing that it is obtained from neutral atoms in a photo induced resonance finite lifetime metastable state and not by the cations [17].

Nimrod Moiseyev was also among the pioneers of PT symmetry in optics [18,19]; a phenomenon that was confirmed experimentally two years later by Detlef Kip, :de:Mordechai_Segev|Mordechai (Moti) Segev and :de:Demetrios_N._Christodoulides|Demitris Christodoulides and their co-workers [20].

He also developed the counter intuitive adiabatic theory for cold molecular collisions [21] that enabled analysis of experimental results measured in the lab of Ed Narevicius at Weizmann Institute of Science|Weizmann institute of Science [22].

In 2008 Nimrod Moiseyev together with his postdoctoral fellow Milan Sindelka and his colleague Lorenz S. Cederbaum|Lorenz Cederbaum opened the field of Light / Laser - Induced Conical Intersection (LICI) [23] that in 2016 was observed in experiments conducted by Adi Natan from SLAC Labs [24].

# Books[edit]

1. The book “Non-Hermitian Quantum Mechanics” that Nimrod Moiseyev wrote (Cambridge University Press, 2011. ISBN:978-0-521-88972-8 ) provides a comprehensive description of the foundations of non-Hermitian quantum mechanics with different applications in various fields. For example, it includes Solution|solutions of the Maxwell's equations|Maxwell equations with complex index of refraction, where the Hamiltonian is non-Hermitian even without imposing outgoing boundary conditions as required in the studies of resonance phenomena in nature. Link to this book in Google Scholar
2. The need for non-Hermitian formalism of quantum mechanics is discussed also in a two volumes textbook “Quantum mechanics from foundations to applications” that Nimrod Moiseyev wrote in Hebrew (Magnus Press, Hebrew University of Jerusalem|Hebrew University, 2015. ISBN:978-965-493-773-3).

# Prizes & Awards[edit]

* Medal of CMOA (Centre de Mecanique Ondulatoire Appliquee founded by Louis de Broglie) as a recognition of his contributions to the development of the non-hermitian quantum mechanic”, (2010).
* J. Phys. B: Atomic, Molecular and Optical Physics, dedicated a special issue (# 4, Vol. 42) on resonances to Nimrod Moiseyev on accounts of his ”research with important contributions”, (2009).
* Landau award for Sciences and Research by Mifaal Ha Pais, (2006).
* The Israel Chemistry Society Prize for excellence in research, (2006).
* Golden Medal from the Israeli Chemistry Society for “his pioneering work on resonance states in atoms and molecules and for introducing the theory of non-Hermitian quantum mechanics, which had a remarkable impact on experimental chemistry and physics”
* Alexander von Humboldt Research Award to senior scientists, (2002).
* Yigal Allon Fellow, award for Young Outstanding Scientists in Universities in Israel, (1981).

# Visiting Academic Positions[edit]

Between 1990 to 2016 Nimrod Moiseyev was a visiting professor in the University of Kaisreslautern and Heidelberg University in Germany, Pierre and Marie Curie University (Paris 6) and Paris-Sud University (Orsay) in France, and University of Wisconsin-Madison, UCLA, Pen University and ITAMP at Harvard in USA.

# Education[edit]

1965-69 - Bachelor of Science in Information Technology|B.Sc. in Chemistry, Bar-Ilan University

1970-72 - M.Sc. Thesis on: Isotope enrichment by Gas Chromatography, Weizmann Institute of Science.

1973-77 - D.Sc. Thesis on: Mathematical and Physical Problems in SCF (self-consistent-field) methods, Technion International School|Technion-Israel Institute of Technology.

1977-79 - Research Associate, TCI-Theoretical Chemistry Institute, University of Wisconsin, Madison, USA.

## References[edit]

## External links[edit]

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