Cloning in nonlinear Hamiltonian quantum and hybrid mechanics
D. Arsenovic; N. Buric; D. B. Popovic; M. Radonjic; S. Prvanovic
2014-11-17
Possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is then demonstrated that the addition of the cloning machine, treated as a quantum or as a classical system, makes the cloning possible by nonlinear Hamiltonian evolution. However, a special type of quantum-classical theory, known as the mean-field Hamiltonian hybrid mechanics, does not admit cloning by natural evolution. The latter represents an example of a theory where it appears to be possible to communicate between two quantum systems at super-luminal speed, but at the same time it is impossible to clone quantum pure states.
Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation
NASA Astrophysics Data System (ADS)
Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter
2013-08-01
The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.
A modal-Hamiltonian interpretation of quantum mechanics
Olimpia Lombardi; Mario Castagnino
2008-02-04
The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties.
On the modification of Hamiltonians' spectrum in gravitational quantum mechanics
Pouria Pedram
2010-03-14
Different candidates of Quantum Gravity such as String Theory, Doubly Special Relativity, Loop Quantum Gravity and black hole physics all predict the existence of a minimum observable length or a maximum observable momentum which modifies the Heisenberg uncertainty principle. This modified version is usually called the Generalized (Gravitational) Uncertainty Principle (GUP) and changes all Hamiltonians in quantum mechanics. In this Letter, we use a recently proposed GUP which is consistent with String Theory, Doubly Special Relativity and black hole physics and predicts both a minimum measurable length and a maximum measurable momentum. This form of GUP results in two additional terms in any quantum mechanical Hamiltonian, proportional to $\\alpha p^3$ and $\\alpha^2 p^4$, respectively, where $\\alpha \\sim 1/M_{Pl}c$ is the GUP parameter. By considering both terms as perturbations, we study two quantum mechanical systems in the framework of the proposed GUP: a particle in a box and a simple harmonic oscillator. We demonstrate that, for the general polynomial potentials, the corrections to the highly excited eigenenergies are proportional to their square values. We show that this result is exact for the case of a particle in a box.
P. K. Biswas
We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical QM-molecular-mechanical MM calculations. To remedy the nonphysical QM\\/MM Coulomb interaction at short distances arising from a point electrostatic potential ESP charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge
P. K. Biswas; V. Gogonea
2005-01-01
We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical (QM)-molecular-mechanical (MM) calculations. To remedy the nonphysical QM\\/MM Coulomb interaction at short distances arising from a point electrostatic potential (ESP) charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge
Hamiltonian statistical mechanics
Dorje C. Brody; David C. P. Ellis; Darryl D. Holm
2008-09-15
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterised by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.
Juan Sebastián Ardenghi; Mario Castagnino; Olimpia Lombardi
2010-12-05
The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) elds. In this case we propose that the actual- valued observables are the Casimir operators of the Poincar\\'e group and of the group U(1) of the internal symmetry of the theory. Moreover, we also show that the magnitudes that acquire actual values in the relativistic and in the non-relativistic cases are correctly related through the adequate limit.
Positive-operator-valued measures in the Hamiltonian formulation of quantum mechanics
NASA Astrophysics Data System (ADS)
Arsenovi?, D.; Buri?, N.; Popovi?, D. B.; Radonji?, M.; Prvanovi?, S.
2015-06-01
In the Hilbert space formulation of quantum mechanics, ideal measurements of physical variables are discussed using the spectral theory of Hermitian operators and the corresponding projector-valued measures (PVMs). However, more general types of measurements require the treatment in terms of positive-operator-valued measures (POVMs). In the Hamiltonian formulation of quantum mechanics, canonical coordinates are related to PVM. In this paper the results of an analysis of various aspects of applications of POVMs in the Hamiltonian formulation are reported. Several properties of state parameters and quantum observables given by POVMs or represented in an overcomplete basis, including the general Hamiltonian treatment of the Neumark extension, are presented. An analysis of the phase operator, given by the corresponding POVMs, in the Hilbert space and the Hamiltonian frameworks is also given.
Identifying mechanisms in the control of quantum dynamics through Hamiltonian encoding
Mitra, Abhra [Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544 (United States); Rabitz, Herschel [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States)
2003-03-01
A variety of means are now available to design control fields for manipulating the evolution of quantum systems. However, the underlying physical mechanisms often remain obscure, especially in the cases of strong fields and high quantum state congestion. This paper proposes a method to quantitatively determine the various pathways taken by a quantum system in going from the initial state to the final target. The mechanism is revealed by encoding a signal in the system Hamiltonian and decoding the resultant nonlinear distortion of the signal in the system time-evolution operator. The relevant interfering pathways determined by this analysis give insight into the physical mechanisms operative during the evolution of the quantum system. A hierarchy of mechanism identification algorithms with increasing ability to extract more detailed pathway information is presented. The mechanism identification concept is presented in the context of analyzing computer simulations of controlled dynamics. As illustrations of the concept, mechanisms are identified in the control of several simple, discrete-state quantum systems. The mechanism analysis tools reveal the roles of multiple interacting quantum pathways to maximally take advantage of constructive and destructive interference. Similar procedures may be applied directly in the laboratory to identify control mechanisms without resort to computer modeling, although this extension is not addressed in this paper.
NASA Astrophysics Data System (ADS)
Yelnykov, Oleksandr V.
This thesis addresses three topics: calculation of the invariant measure for the pure Yang-Mills configuration space in (3 + 1) dimensions, Hamiltonian analysis of the pure Chern-Simons theory on the noncommutative plane and noncommutative quantum mechanics in the presence of singular potentials. In Chapter 1 we consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parameterized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom. We develop an approximate calculation of the volume element on the gauge-invariant configuration space. We also make a rough estimate of the ratio of 0++ glueball mass and the square root of string tension by comparison with (2 + 1)-dimensional Yang-Mills theory. In Chapter 2 the Hamiltonian analysis of the pure Chern-Simons theory on the noncommutative plane is performed. We use the techniques of geometric quantization to show that the classical reduced phase space of the theory has nontrivial topology and that quantization of the symplectic structure on this space is possible only if the Chern-Simons coefficient is quantized. Also we show that the physical Hilbert space of the theory is one-dimensional and give an explicit expression for the vacuum wavefunction. This vacuum state is found to be related to the noncommutative Wess-Zumino-Witten action. And finally in Chapter 3 we address the question of two-dimensional quantum mechanics in the presence of delta-function potentials which is known to be plagued by UV divergences resulting from the singular nature of the potentials in question. The two particularly interesting examples of this kind are non-relativistic spin zero particles in delta-function potential and Dirac particles in Aharonov-Bohm magnetic background. We show that by extending the corresponding Schrodinger and Dirac equations onto the flat noncommutative space a well-defined quantum theory can be obtained. Complete analytic solution is found in both cases. In the limit of vanishing noncommutativity we recover the standard expressions corresponding to certain self-adjoint extensions of the Hamiltonians in question.
Local Hamiltonians in quantum computation
Nagaj, Daniel
2008-01-01
In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time- dependent Hamiltonian. I show that to succeed using ...
FAST TRACK COMMUNICATION: Hamiltonian statistical mechanics
NASA Astrophysics Data System (ADS)
Brody, Dorje C.; Ellis, David C. P.; Holm, Darryl D.
2008-12-01
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve towards those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterized by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.
Entropic Dynamics: from Entropy and Information Geometry to Hamiltonians and Quantum Mechanics
Ariel Caticha; Daniel Bartolomeo; Marcel Reginatto
2014-12-17
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the "quantum potential" that leads to the Schroedinger equation follows naturally from information geometry.
Quantum Hamiltonian Complexity
Sevag Gharibian; Yichen Huang; Zeph Landau; Seung Woo Shin
2014-09-15
We survey the growing field of Quantum Hamiltonian Complexity, which includes the study of Quantum Constraint Satisfaction. In particular, our aim is to provide a computer science-oriented introduction to the subject in order to help bridge the language barrier between computer scientists and physicists in the field. As such, we include the following in this paper: (1) The motivations and history of the field, (2) a glossary of condensed matter physics terms explained in computer-science friendly language, (3) overviews of central ideas from condensed matter physics, such as indistinguishable particles, mean field theory, tensor networks, and area laws, and (4) brief expositions of selected computer science-based results in the area. For example, as part of the latter, we provide a novel information theoretic presentation of Bravyi's polynomial time algorithm for Quantum 2-SAT.
Paul Benioff
1980-01-01
In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each numberN and Turing machineQ there exists a HamiltonianHNQ and a class of appropriate initial states such that if c is such an initial state, then?QN(t)=exp(-1HNQt)?QN(0) correctly describes at timest3,t6,?,t3N model states that correspond to the completion of
A Hamiltonian for quantum copying
Dima Mozyrsky; Vladimir Privman; Mark Hillery
1997-05-10
We derive an explicit Hamiltonian for copying the basis up and down states of a quantum two-state system - a qubit - onto n "copy" qubits initially all prepared in the down state. In terms of spin components, for spin-1/2 particle spin states, the resulting Hamiltonian involves n- and (n+1)-spin interactions. The case n=1 also corresponds to a quantum-computing controlled-NOT gate.
Anisimov, Victor M; Cavasotto, Claudio N
2011-06-23
To build the foundation for accurate quantum mechanical (QM) simulation of biomacromolecules in an aqueous environment, we undertook the optimization of the COnductor-like Screening MOdel (COSMO) atomic radii and atomic surface tension coefficients for different semiempirical Hamiltonians adhering to the same computational conditions recently followed in the simulation of biomolecular systems. This optimization was achieved by reproducing experimental hydration free energies of a set consisting of 507 neutral and 99 ionic molecules. The calculated hydration free energies were significantly improved by introducing a multiple atomic-type scheme that reflects different chemical environments. The nonpolar contribution was treated according to the scaled particle Claverie-Pierotti formalism. Separate radii and surface tension coefficient sets have been developed for AM1, PM3, PM5, and RM1 semiempirical Hamiltonians, with an average unsigned error for neutral molecules of 0.64, 0.66, 0.73, and 0.71 kcal/mol, respectively. Free energy calculation of each molecule took on average 0.5 s on a single processor. The new sets of parameters will enhance the quality of semiempirical QM calculations using COSMO in biomolecular systems. Overall, these results further extend the utility of QM methods to chemical and biological systems in the condensed phase. PMID:21585215
Simplifying quantum double Hamiltonians using perturbative gadgets
Robert Koenig
2010-02-09
Perturbative gadgets were originally introduced to generate effective k-local interactions in the low-energy sector of a 2-local Hamiltonian. Extending this idea, we present gadgets which are specifically suited for realizing Hamiltonians exhibiting non-abelian anyonic excitations. At the core of our construction is a perturbative analysis of a widely used hopping-term Hamiltonian. We show that in the low-energy limit, this Hamiltonian can be approximated by a certain ordered product of operators. In particular, this provides a simplified realization of Kitaev's quantum double Hamiltonians.
The Stability of Quantum Concatenated Code Hamiltonians
D. Bacon
2008-07-01
Protecting quantum information from the detrimental effects of decoherence and lack of precise quantum control is a central challenge that must be overcome if a large robust quantum computer is to be constructed. The traditional approach to achieving this is via active quantum error correction using fault-tolerant techniques. An alternative to this approach is to engineer strongly interacting many-body quantum systems that enact the quantum error correction via the natural dynamics of these systems. Here we present a method for achieving this based on the concept of concatenated quantum error correcting codes. We define a class of Hamiltonians whose ground states are concatenated quantum codes and whose energy landscape naturally causes quantum error correction. We analyze these Hamiltonians for robustness and suggest methods for implementing these highly unnatural Hamiltonians.
Universal two-body-Hamiltonian quantum computing
NASA Astrophysics Data System (ADS)
Nagaj, Daniel
2012-03-01
We present a Hamiltonian quantum-computation scheme universal for quantum computation. Our Hamiltonian is a sum of a polynomial number (in the number of gates L in the quantum circuit) of constant-norm, time-independent, two-body interaction terms. Furthermore, each qubit in the system interacts only with a constant number of other qubits in a three-layer, geometrically local layout. The computer runs in three steps—it starts in a simple initial product state, evolves according to a time-independent Hamiltonian for time of order L2 (up to logarithmic factors), and finishes with a two-qubit measurement. Our model improves previous universal two-local-Hamiltonian constructions, as it avoids using perturbation gadgets and large energy-penalty terms in the Hamiltonian, which would result in a large required run time.
Quantum Markov Networks and Commuting Hamiltonians
Winton Brown; David Poulin
2012-06-04
Quantum Markov networks are a generalization of quantum Markov chains to arbitrary graphs. They provide a powerful classification of correlations in quantum many-body systems---complementing the area law at finite temperature---and are therefore useful to understand the powers and limitations of certain classes of simulation algorithms. Here, we extend the characterization of quantum Markov networks and in particular prove the equivalence of positive quantum Markov networks and Gibbs states of Hamiltonians that are the sum of local commuting terms on graphs containing no triangles. For more general graphs we demonstrate the equivalence between quantum Markov networks and Gibbs states of a class of Hamiltonians of intermediate complexity between commuting and general local Hamiltonians.
Hamiltonian Quantum Cellular Automata in 1D
Daniel Nagaj; Pawel Wocjan
2008-08-14
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process. We only require the ability to prepare an initial computational basis state which encodes both the quantum circuit and its input. The computational process is then carried out by the autonomous Hamiltonian time evolution. After a time polynomially long in the size of the quantum circuit has passed, the result of the computation is obtained with high probability by measuring a few qudits in the computational basis. This result also implies that there cannot exist efficient classical simulation methods for generic translationally invariant nearest-neighbor Hamiltonians on qudit chains, unless quantum computers can be efficiently simulated by classical computers (or, put in complexity theoretic terms, unless BPP=BQP).
Hamiltonian Quantum Cellular Automata in 1D
Nagaj, Daniel
2008-01-01
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process. We only require the ability to prepare an initial computational basis state which encodes both the quantum circuit and its input. The computational process is then carried out by the autonomous Hamiltonian time evolution. After a time polynomially long in the size of the quantum circuit has passed, the result of the computation is obtained with high probability by measuring a few qudits in the computational basis. This result also implies that there cannot exist efficient classical simulation methods for generic translationally invariant nearest-neighbor Hamiltonians on qudit chains, unless quantum computers can be efficiently simulated by classical computers (or, put in complexity theoretic terms, unless BPP=BQP).
Quaternionic Formulation of Supersymmetric Quantum Mechanics
Seema Rawat; O. P. S. Negi
2007-03-18
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with the results of quantum mechanics.
NASA Astrophysics Data System (ADS)
Kuna, Maciej; Naudts, Jan
2010-01-01
The unitary operators U( t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic techniques in this context and elaborate the theory for SU(2) and SU(1,1). In these cases we give explicit formulae for obtaining general solutions from special ones. We show that the constructions known as Magnus expansion and Wei—Norman expansion correspond with different representations of the rotation group. A simpler construction is obtained when representing rotations in terms of Euler angles. Progress can be made if one succeeds in finding a nontrivial special solution of the equations of motion. Then the general solution can be derived by means of the Lie theory. The problem of evaluating the evolution of the system is translated from a noncommutative integration in the sense of Dyson into an ordinary commutative integration. The two main applications of our method are reviewed, namely the Bloch equations and the harmonic oscillator with time-dependent frequency. Even in these well-known examples some new results are obtained.
Entanglement Hamiltonians for quantum spin chains
NASA Astrophysics Data System (ADS)
Thomale, Ronny; Rachel, Stephan; Arovas, Daniel; Bernevig, B. Andrei
2011-03-01
We report on our analysis of entanglement phenomena in gapped and gapless quantum spin chains. In particular we discuss criteria of correspondence between entanglement spectra and Hamiltonian spectra with respect to symmetries, spectral gaps, and eigenstate properties. We find that the structure of the entanglement Hamiltonian associated with the ground state is helpful to discover various spectral properties of the full system. RT acknowledges support from a Feodor Lynen Fellowship of the Humboldt Foundation.
Quantum Finance Hamiltonian for Coupon Bond European and Barrier Options
Chaudhuri, Sanjay
Quantum Finance Hamiltonian for Coupon Bond European and Barrier Options Belal E. Baaquie RMI are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward-2963 Fax: (65) 6777-6126 Email: phybeb@nus.edu.sg #12;Quantum Finance Hamiltonian for Coupon Bond European
A mathematical theory for deterministic quantum mechanics
Gerard't Hooft
2007-01-01
Classical, i.e. deterministic theories underlying quantum mechanics are considered, and it is shown how an apparent quantum mechanical Hamiltonian can be defined in such theories, being the operator that generates evolution in time. It includes various types of interactions. An explanation must be found for the fact that, in the real world, this Hamiltonian is bounded from below. The mechanism
PT -symmetric Hamiltonians and their application in quantum information
NASA Astrophysics Data System (ADS)
Croke, Sarah
2015-05-01
We discuss the prospect of PT -symmetric Hamiltonians finding applications in quantum information science, and conclude that such evolution is unlikely to provide any benefit over existing techniques. Although it has been known for some time that PT -symmetric quantum theory, when viewed as a unitary theory, is exactly equivalent to standard quantum mechanics, proposals continue to be put forward for schemes in which PT -symmetric quantum theory can outperform standard quantum theory. The most recent of these is the suggestion to use PT -symmetric Hamiltonians to perform an exponentially fast database search, a task known to be impossible with a quantum computer. Further, such a scheme has been shown to apparently produce effects in conflict with fundamental information-theoretic principles, such as the impossibility of superluminal information transfer, and the invariance of entanglement under local operations. In this paper we propose three inequivalent experimental implementations of PT -symmetric Hamiltonians, with careful attention to the resources required to realize each such evolution. Such an operational approach allows us to resolve these apparent conflicts, and evaluate fully schemes proposed in the literature for faster time evolution and state discrimination.
Geometry of adiabatic Hamiltonians for two-level quantum systems
NASA Astrophysics Data System (ADS)
Lehto, J. M. S.; Suominen, K.-A.
2015-06-01
We present the formulation of the problem of the coherent dynamics of quantum mechanical two-level systems in the adiabatic region in terms of the differential geometry of plane curves. We show that there is a natural plane curve corresponding to the Hamiltonian of the system for which the geometrical quantities have a simple physical interpretation. In particular, the curvature of the curve has the role of the nonadiabatic coupling.
Evolution under polynomial Hamiltonians in quantum and optical phase spaces
NASA Astrophysics Data System (ADS)
Rivera, A. L.; Atakishiyev, N. M.; Chumakov, S. M.; Wolf, K. B.
1997-02-01
We analyze the difference between classical and quantum nonlinear dynamics by computing the time evolution of the Wigner functions for the simplest polynomial Hamiltonians of fourth degree in coordinate and momentum. This class of Hamiltonians contains examples which are important in wave and quantum optics. The Hamiltonians under study describe the third-order aberrations to the paraxial approximation and the nonlinear Kerr medium. Special attention is given to the quantum analog of the conservation of the volume element in classical phase space.
Uncertainty relation for non-Hamiltonian quantum systems
Tarasov, Vasily E. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)] [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)
2013-01-15
General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.
NSDL National Science Digital Library
De Raedt, Hans
This website contains a number of descriptions of quantum mechanical phenomena, using 3D animations to illustrate the physics. The goal is to introduce basic concepts and phenomena using simulations rather than complex mathematics. The time-dependence of quantum systems is a focus of this material.
Determinism Beneath Quantum Mechanics
Gerard't Hooft
Contrary to common belief, it is not difficult to construct deterministic\\u000amodels where stochastic behavior is correctly described by quantum mechanical\\u000aamplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What\\u000ais difficult however is to obtain a Hamiltonian that is bounded from below, and\\u000awhose ground state is a vacuum that exhibits complicated vacuum fluctuations,\\u000aas in the real world.
A Quantum Algorithm for the Hamiltonian NAND Tree
E. Farhi; J. Goldstone; S. Gutmann
2007-02-22
We give a quantum algorithm for the binary NAND tree problem in the Hamiltonian oracle model. The algorithm uses a continuous time quantum walk with a run time proportional to sqrt N. We also show a lower bound of sqrt N for the NAND tree problem in the Hamiltonian oracle model.
PT quantum mechanics - Recent results
Bender, Carl M. [Physics Department, Washington University, St. Louis, MO 63130 (United States)
2012-09-26
Most quantum physicists believe that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under matrix transposition and complex conjugation) to be sure that the energy eigenvalues are real and that time evolution is unitary. However, the non-Dirac-hermitian Hamiltonian H p{sup 2}+ix{sup 3} has a real positive discrete spectrum and generates unitary time evolution and defines a fully consistent and physical quantum theory. Evidently, Dirac Hermiticity is too restrictive. While H = p{sup 2}+ix{sup 3} is not Dirac Hermitian, it is PT symmetric (invariant under combined space reflection P and time reversal T). Another PT-symmetric Hamiltonian whose energy levels are real, positive and discrete is H = p{sup 2}-x{sup 4}, which contains an upside-down potential. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics and quantum field theory are extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past two years some of these properties have been verified in laboratory experiments. Here, we first discuss PT-symmetric Hamiltonians at a simple intuitive level and explain why the energy levels of such Hamiltonians may be real, positive, and discrete. Second, we describe a recent experiment in which the PT phase transition was observed. Third, we briefly mention that PT-symmetric theories can be useful at a fundamental level. While the double-scaling limit of an O(N)-symmetric g{phi}{sup 4} quantum field theory appears to be inconsistent because the critical value of g is negative, this limit is in fact not inconsistent because the critical theory is PT symmetric.
Entanglement Hamiltonian of the quantum Néel state
NASA Astrophysics Data System (ADS)
Poilblanc, Didier
2014-10-01
2D projected entangled pair states (PEPS) provide a unique framework giving access to detailed entanglement features of correlated (spin or electronic) systems. For a bi-partitioned quantum system, it has been argued that the entanglement spectrum (ES) is in a one-to-one correspondence with the physical edge spectrum on the cut and that the structure of the corresponding entanglement Hamiltonian (EH) reflects closely bulk properties (finite correlation length, criticality, topological order, etc). However, entanglement properties of systems with spontaneously broken continuous symmetry are still not fully understood. The spin-1/2 square lattice Heisenberg antiferromagnet provides a simple example showing spontaneous breaking of SU(2) symmetry down to U(1). The ground state can be viewed as a ‘quantum Néel state’ where the classical (Néel) staggered magnetization is reduced by quantum fluctuations. Here I consider the (critical) resonating valence bond (RVB) state doped with spinons to describe such a state; this enables the use of the associated PEPS representation (with virtual bond dimension D = 3) to compute the EH and the ES for a partition of an (infinite) cylinder. In particular, I find that the EH is (almost exactly) a chain of a dilute mixture of heavy (? spins) and light (? spins) hardcore bosons, where light particles are subject to long-range hoppings. The corresponding ES shows drastic differences with the typical ES obtained previously for ground states with restored SU(2)-symmetry (on finite systems).
An Alternative Adiabatic Quantum Algorithm for the Hamiltonian Cycle Problem
NASA Astrophysics Data System (ADS)
Zhang, Da-Jian; Tong, Dian-Min; Lu, Yao; Long, Gui-Lu
2015-05-01
We put forward an alternative quantum algorithm for finding Hamiltonian cycles in any N-vertex graph based on adiabatic quantum computing. With a von Neumann measurement on the final state, one may determine whether there is a Hamiltonian cycle in the graph and pick out a cycle if there is any. Although the proposed algorithm provides a quadratic speedup, it gives an alternative algorithm based on adiabatic quantum computation, which is of interest because of its inherent robustness.
Time and a physical Hamiltonian for quantum gravity.
Husain, Viqar; Paw?owski, Tomasz
2012-04-01
We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. PMID:22540782
Simplifying quantum double Hamiltonians using perturbative gadgets
Robert Koenig
2009-01-01
Perturbative gadgets were originally introduced to generate effective k-local interactions in the low-energy sector of a 2-local Hamiltonian. Extending this idea, we present gadgets which are specifically suited for realizing Hamiltonians exhibiting non-abelian anyonic excitations. At the core of our construction is a perturbative analysis of a widely used hopping-term Hamiltonian. We show that in the low-energy limit, this Hamiltonian
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 5 problems LAST NAME FIRST NAME #12 with the effective electron mass at the band edges. #12;Applied quantum mechanics 3 (c) Write a computer program
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 8 problems LAST NAME FIRST NAME #12;Applied quantum mechanics 3 (b) If the electron is in a semiconductor and has an effective mass m * 0.07 m
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 1 problems LAST NAME FIRST NAME #12 happens to the beat frequency if the airplane moves in an arc? #12;Applied quantum mechanics 3 Problem 1
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 10 problems LAST NAME FIRST NAME #12 ( ) L/( )= L/ #12;Applied quantum mechanics 3 (d) Use the results of (b) an (c) to draw the electron
Quantum Mechanics II (Undergraduate)
Nickrent, Daniel L.
Quantum Mechanics II (Undergraduate) Applications of Quantum Mechanics Spring, 2014 Physics 440 TEXTBOOK: Introduction to Quantum Mechanics (Second Edition), by David J. Griffiths, and QUNET's wikibook to apply quantum mechanics to some fundamental and important problems such as: better understanding
Supersymmetric q-deformed quantum mechanics
Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
2012-06-27
A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.
The ubiquity of the symplectic hamiltonian equations in mechanics
P. Balseiro; M. de Leon; J. C. Marrero; D. Martin de Diego
2008-11-26
In this paper, we derive a "hamiltonian formalism" for a wide class of mechanical systems, including classical hamiltonian systems, nonholonomic systems, some classes of servomechanism... This construction strongly relies in the geometry characterizing the different systems. In particular, we obtain that the class of the so-called algebroids covers a great variety of mechanical systems. Finally, as the main result, a hamiltonian symplectic realization of systems defined on algebroids is obtained.
2T Physics and Quantum Mechanics
W. Chagas-Filho
2008-02-20
We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit described by the same Hamiltonian. One of these formulations is used as a basis for a complementation of the usual quantum mechanics when in the presence of gravity.
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 6 problems LAST NAME FIRST NAME #12 --- and that for a Poisson distribution of such photons #12; 1 2 n ---------------- Applied quantum mechanics 3 (c) Apply conditions is the quantum mechanical result m t 2 2 d d x xd d V x = the same Newton's second law in which
Gapped spin Hamiltonian motivated by quantum teleportation
Ari Mizel
2014-10-07
We construct a Hamiltonian whose ground state encodes a time-independent emulation of quan- tum teleportation. We calculate properties of the Hamiltonian, using exact diagonalization and a mean-field theory, and argue that it has a gap. The system exhibits an illuminating relationship to the well-known AKLT (Affleck, Lieb, Kennedy and Tasaki) model.
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 6 problems LAST NAME FIRST NAME #12 of the system. (b) Find . (c) Find and show that . Under what conditions is the quantum mechanical result( ) td d A t( ) t A td d A /= A B i 2 --- A^ B^,[ ] A^ B^ Et 2 --- n n 1 2 --- #12;Applied quantum
Bender, Carl M; DeKieviet, Maarten; Klevansky, S. P.
2013-01-01
-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter–antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics. PMID:23509390
Fiber Hamiltonians in the non-relativistic quantum electrodynamics
Fumio Hiroshima
2006-07-11
A translation invariant Hamiltonian $H$ in the nonrelativistic quantum electrodynamics is studied. This Hamiltonian is decomposed with respect to the total momentum $\\tot$: $$H=\\int_{\\BR} ^\\oplus \\fri(P) dP,$$ where the self-adjoint fiber Hamiltonian $\\fri(P)$ is defined for arbitrary values of coupling constants. It is discussed a relationship between rotation invariance of $H(P)$ and polarization vectors, and functional integral representations of $n$ point Euclidean Green functions of $H(P)$ is given. From these, some applications concerning with degeneracy of ground states, ground state energy and expectation values of suitable observables with respect to ground states are given.
An additive Hamiltonian plus Landauer's Principle yields quantum theory
Chris Fields
2015-03-27
It is shown that no-signalling, a quantum of action, unitarity, detailed balance, Bell's theorem, the Hilbert-space representation of physical states and the Born rule all follow from the assumption of an additive Hamiltonian together with Landauer's principle. Common statements of the "classical limit" of quantum theory, as well as common assumptions made by "interpretations" of quantum theory, contradict additivity, Landauer's principle, or both.
Gaussian States for Quantum Systems with Linear Constraints and Quadratic Hamiltonians
O. Yu. Shvedov
2008-12-25
Different constructions for Hilbert state space for constrained systems are investigated. Properties of Gaussian states analogous to quantum mechanical Gaussian wave functions are studied. Their evolution for quadratic Hamiltonian case are discussed. A notion of Maslov complex germ is introduced for systems with linear constraints.
Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
Bellucci, Stefano [INFN-Laboratori Nazionali di Frascati, P.O. Box 13, I-00044 (Italy); Nersessian, Armen [Yerevan State University, Alex Manoogian St., 1, Yerevan, 375025 (Armenia); Artsakh State University, Stepanakert and Yerevan Physics Institute, Yerevan (Armenia); Yeranyan, Armen [Yerevan State University, Alex Manoogian St., 1, Yerevan, 375025 (Armenia)
2006-09-15
We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out.
Introduction: quantum resonances Classical and quantum mechanics
Ramond, Thierry
: quantum resonances Classical and quantum mechanics Microlocal analysis Resonances associated;..... . .... . .... . ..... . .... . .... . .... . ..... . .... . .... . .... . ..... . .... . .... . .... . ..... . .... . ..... . .... . .... . Introduction: quantum resonances Classical and quantum mechanics Microlocal analysis Resonances associated with homoclinic orbits Outline Introduction: quantum resonances Classical and quantum mechanics Microlocal
Chaos in Bohmian quantum mechanics
NASA Astrophysics Data System (ADS)
Efthymiopoulos, C.; Contopoulos, G.
2006-02-01
This paper presents a number of numerical investigations of orbits in the de Broglie-Bohm version of quantum mechanics. We first clarify how the notion of chaos should be implemented in the case of Bohmian orbits. Then, we investigate the Bohmian orbits in three different characteristic quantum systems: (a) superposition of three stationary states in the Hamiltonian of two uncoupled harmonic oscillators with incommensurable frequencies, (b) wave packets in a Hénon-Heiles-type Hamiltonian and (c) a modified two-slit experiment. In these examples, we identify regular or chaotic orbits and also orbits exhibiting a temporarily regular and then chaotic behaviour. Then, we focus on a numerical investigation of the Bohm-Vigier (Bohm and Vigier 1954 Phys. Rev. 26 208) theory, that an arbitrary initial particle distribution P should asymptotically tend to |?|2, by considering the role of chaotic mixing in causing irregularity of Madelung's flow, a necessary condition for P to tend to |?|2. We find that the degree of chaos of a particular system correlates with the speed of convergence of P to |?|2. In the case of wave-packet dynamics, our numerical data show that the time of convergence scales exponentially with the inverse of the effective perturbation from the harmonic oscillator Hamiltonian. The latter result can be viewed as a quantum analogue of Nekhoroshev's (Nekhoroshev 1977 Russ. Math. Surveys 32 1) theorem of exponential stability in classical nonlinear Hamiltonian dynamics.
Can Quantum Mechanics Heal Classical Singularities?
NASA Astrophysics Data System (ADS)
Helliwell, T. M.; Konkowski, D. A.
2008-09-01
We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. We show that a large subset of classically singular spacetimes is nevertheless nonsingular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint so the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities.
Hamiltonian mechanics and divergence-free fields
Boozer, A.H.
1986-08-01
The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space.
Continuous decomposition of quantum measurements via Hamiltonian feedback
Jan Florjanczyk; Todd A. Brun
2015-04-15
We characterize the set of generalized quantum measurements that can be decomposed into a continuous measurement process using a stream of probe qubits and a tunable interaction Hamilto- nian. Each probe in the stream interacts weakly with the target quantum system, then is measured projectively in a standard basis. This measurement result is used in a closed feedback loop to tune the interaction Hamiltonian for the next probe. The resulting evolution is a stochastic process with the structure of a one-dimensional random walk. To maintain this structure, and require that at long times the measurement outcomes be independent of the path, the allowed interaction Hamil- tonians must lie in a restricted set, such that the Hamiltonian terms on the target system form a finite dimensional Jordan algebra. This algebraic structure of the interaction Hamiltonians yields a large class of generalized measurements that can be continuously performed by our scheme, and we fully describe this set.
Bohmian mechanics contradicts quantum mechanics
Neumaier, Arnold
Bohmian mechanics contradicts quantum mechanics Arnold Neumaier Institut fur Mathematik, Universit://solon.cma.univie.ac.at/#24;neum/ Abstract. It is shown that, for a harmonic oscillator in the ground state, Bohmian mechanics and quantum mechanics predict values of opposite sign for certain time correlations. The discrepancy can
Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics
Radu Miron
2012-03-19
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus applied to the integral of action and these can be studied by using the methods of Lagrangian or Hamiltonian geometries. More general, the notions of higher order Lagrange or Hamilton spaces have been introduced and developed by the present author. The applications led to the notions of Lagrangian or Hamiltonian Analytical Mechanics of higher order. For short, in this text we aim to solve some difficult problems: The problem of geometrization of classical non conservative mechanical systems; The foundations of geometrical theory of new mechanics: Finslerian, Lagrangian and Hamiltonian;To determine the evolution equations of the classical mechanical systems for whose external forces depend on the higher order accelerations. My colleagues Professors M. Anastasiei, I. Bucataru, I. Mihai, K. Stepanovici made important remarks and suggestions and Mrs. Carmen Savin prepared an excellent print-form of the hand-written text. Many thanks to all of them.
Quantum Mechanics Measurements, Mutually
Gruner, Daniel S.
Quantum Mechanics Measurements, Mutually Unbiased Bases and Finite Geometry Or why six is the first) #12;Quantum Mechanics for Dummies Finite dimensional quantum states are represented by trace one,1 -icS1,1[ ] #12;Quantum systems evolve and are measured. The evolution of a quantum system using
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 5 problems LAST NAME FIRST NAME #12 + --------------------------------------------- k = t 10/= t 1= Ek 2t kxL( ) 2t 2kxL( )cos+cos= t 10/= t 1= t 0.2= #12;Applied quantum mechanics 3 (c) Write a computer program to plot the electron density of states for a square lat- tice
Nikolai Laskin
2000-01-01
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Lévy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Lévy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and
A. L. Stewart; G. Scolarici; L. Solombrino
1963-01-01
We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two alternative descriptions of a quantum
Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians
NASA Astrophysics Data System (ADS)
Ma, Fengjie; Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry
2015-06-01
We present a combination of a downfolding many-body approach with auxiliary-field quantum Monte Carlo (AFQMC) calculations for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to dial, in principle, between the simplest model and the original Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated using frozen orbitals constructed adaptively from the solid environment. The computational cost of the many-body calculation is dramatically reduced without sacrificing accuracy. Excellent accuracy is achieved for a range of solids, including semiconductors, ionic insulators, and metals. We apply the method to calculate the equation of state of cubic BN under ultrahigh pressure, and determine the spin gap in NiO, a challenging prototypical material with strong electron correlation effects.
Quantum Mechanical Search and Harmonic Perturbation
Jiang, J H R; Wu, C E; Chiou, Dah-Wei; Jiang, Jie-Hong R.; Wu, Cheng-En
2007-01-01
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some important technology advances, such as masers, lasers, nuclear magnetic resonance, etc., originated from it. Here we add quantum computation to this list with a theoretical demonstration. Based on harmonic perturbation, a quantum mechanical algorithm is devised to search the ground state of a given Hamiltonian. The intrinsic complexity of the algorithm is continuous and parametric in both time T and energy E. More precisely, the probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is optimal. As harmonic perturbation provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers.
Quantum Mechanical Search and Harmonic Perturbation
Jie-Hong R. Jiang; Dah-Wei Chiou; Cheng-En Wu
2007-09-14
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some important technology advances, such as masers, lasers, nuclear magnetic resonance, etc., originated from it. Here we add quantum computation to this list with a theoretical demonstration. Based on harmonic perturbation, a quantum mechanical algorithm is devised to search the ground state of a given Hamiltonian. The intrinsic complexity of the algorithm is continuous and parametric in both time T and energy E. More precisely, the probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is optimal. As harmonic perturbation provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers.
Quantum Mechanics + Open Systems
Steinhoff, Heinz-Jürgen
Quantum Mechanics + Open Systems = Thermodynamics ? Jochen Gemmer T¨ubingen, 09.02.2006 #12., World Scientific) #12;Fundamental Law or Emergent Description? Quantum Mechanics i t = (- 2 2m + V or Emergent Description? Quantum Mechanics i t = (- 2 2m + V ) "Heisenberg Cut" Classical Mechanics: m d2
Newton algorithm for Hamiltonian characterization in quantum control
M. Ndong; J. Salomon; D. Sugny
2014-06-30
We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank-Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown parameters are obtained in some cases. We discuss the numerical limits of the algorithm in terms of basin of convergence and non uniqueness of the solution.
Quantum integrability and nonintegrability of Hamiltonian systems with two degrees of freedom
NASA Astrophysics Data System (ADS)
Stepanov, Vyacheslav V.
The subject of the four manuscripts which make up this dissertation is the concept of integrability in quantum mechanical systems with two degrees of freedom, including the relation between quantum integrability and classical integrability in such systems. In the first manuscript, I consider a two-spin model both classically and quantum mechanically. In the six-dimensional parameter space of this model, classical integrability is satisfied on a five-dimensional hypersurface, and level crossings occur on four-dimensional manifolds that are completely embedded in the integrability hypersurface except for some lower-dimensional sub-manifolds. Under mild assumptions, the classical integrability condition can be reconstructed from a purely quantum mechanical study of level degeneracies in finite-dimensional invariant blocks of the Hamiltonian matrix. In the second manuscript, I analyze the functional dependence ?=HQ ?1,? 2 of the Hamiltonian operator on the action operators for an integrable quantum system, and I compare it with the corresponding functional relationship H (p1, q1; p2, q 2) = HC(J1, J2) in the classical limit of that system. It is demonstrated that the functional dependence is not the same quantum mechanically and (semi-)classically. The former is shown to converge toward the latter in some asymptotic regime associated with the classical limit, but the convergence may be non-uniform. This analysis is carried out for an integrable one- parameter two-spin model. Additional results presented for the (integrable) circular billiard model exhibit similar quantum corrections to the predictions of semiclassical quantization. In the third and the fourth manuscripts, I investigate the relations between symmetry, integrability, and the assignment of quantum numbers to eigenstates for two-spin and spin-boson models. I calculate quantum invariants in the form of expectation values for selected operators and monitor their dependence on the Hamiltonian parameters along loops within, without, and across the integrability region in parameter space. I find clear-cut signatures of integrability and nonintegrability in the observed traces of quantum invariants evaluated in invariant Hilbert subspaces. The results support the notion that quantum integrability depends on the existence of action operators as constituent elements of the Hamiltonian.
Quantum integrals of motion for variable quadratic Hamiltonians
Cordero-Soto, Ricardo, E-mail: ricardojavier81@gmail.co [Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States); Suazo, Erwin, E-mail: erwin.suazo@upr.ed [Department of Mathematical Sciences, University of Puerto Rico, Mayaquez, call box 9000, PR 00681-9000 (Puerto Rico); Suslov, Sergei K., E-mail: sks@asu.ed [School of Mathematical and Statistical Sciences and Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States)
2010-09-15
We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.
Chapin, Kimberly R.
1997-01-01
The role of time in quantum mechanics has been and is still very controversial. The purpose of this paper was to explore the historical interpretation of time in quantum mechanics, to determine the current status of this ...
Introduction to Quantum Mechanics
Eduardo J. S. Villaseñor
2008-04-23
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.
NASA Astrophysics Data System (ADS)
Laskin, Nikolai
2000-06-01
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the non-relativistic fractional quantum-mechanical particle has been found, and the Levy wave packet has been introduced into quantum mechanics. We have derived a free particle quantum-mechanical propagator using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been established. We also discuss the relationships between fractional and the well-known Feynman path integrals approaches to quantum mechanics.
Kowalevski top in quantum mechanics
Matsuyama, A., E-mail: spamatu@ipc.shizuoka.ac.jp
2013-09-15
The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra. -- Highlights: •Quantum spectra of the Kowalevski top are calculated. •Semiclassical quantization is carried out by the EBK formulation. •Quantum states are labeled by the semiclassical integer quantum numbers. •Multiplicity of the classical torus makes the spectra nearly degenerate. •Symmetries, quantum numbers and near-degenerate spectra are closely related.
Probabilistic Approach to Teaching the Principles of Quantum Mechanics
ERIC Educational Resources Information Center
Santos, Emilio
1976-01-01
Approaches the representation of quantum mechanics through Hilbert space postulates. Demonstrates that if the representation is to be accurate, an evolution operator of the form of a Hamiltonian must be used. (CP)
Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries
Jennifer L. Dodd; Michael A. Nielsen; Michael J. Bremner; Robert T. Thew
2001-07-27
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit Hamiltonian and local unitaries. It follows that universal quantum computation can be performed using any entangling interaction and local unitary operations.
Extended SUSY quantum mechanics, intertwining operators and coherent states
F. Bagarello
2009-04-01
We propose an extension of {\\em supersymmetric quantum mechanics} which produces a family of isospectral hamiltonians. Our procedure slightly extends the idea of intertwining operators. Several examples of the construction are given. Further, we show how to build up vector coherent states of the Gazeau-Klauder type associated to our hamiltonians.
Fractals and quantum mechanics
NASA Astrophysics Data System (ADS)
Laskin, Nick
2000-12-01
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Lévy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Lévy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrödinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical particle has been established, and the Lévy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a free particle quantum-mechanical kernel using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a free particle in a square infinite potential well, the fractional "Bohr atom" and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics.
Fractals and quantum mechanics.
Laskin, Nick
2000-12-01
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical particle has been established, and the Levy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a free particle quantum-mechanical kernel using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a free particle in a square infinite potential well, the fractional "Bohr atom" and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics. (c) 2000 American Institute of Physics. PMID:12779428
Statistical mechanics based on fractional classical and quantum mechanics
Korichi, Z.; Meftah, M. T., E-mail: mewalid@yahoo.com [Physics Department, LRPPS Laboratory, Ouargla University, Ouargla 30000 (Algeria)
2014-03-15
The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.
NSDL National Science Digital Library
Mabuchi, Hideo
This web site contains resources for a comprehensive quantum mechanics course designed for graduate and advanced undergraduate students at Cal Tech. The course has been revised to include quantum information science, and prepares students for a course in quantum computation. Lecture notes, a syllabus, homework problems with solutions, and exam solutions are available.
Chapin, Kimberly R.
1997-01-01
to describe the quantum mechanical system The first, matrix mechanics, was presented by Heisenberg [31-33] in 1925. The second, wave mechanics, was presented by Schrodinger [34-37] a year later. In 1926, Schrodmger [38] demonstrated the equivalence... can jump &om one state to another. The result is a discontinuous variation in time (i. e. the tune atom) [42]. Throughout the development of quantum mechanics, this atomistic view of time surfaces again and again, For example, In 1925, J. J...
Introduction to Quantum Mechanics
NSDL National Science Digital Library
The Concord Consortium
2011-12-12
The microscopic world is full of phenomena very different from what we see in everyday life. Some of those phenomena can only be explained using quantum mechanics. This activity introduces basic quantum mechanics concepts about electrons that are essential to understanding modern and future technology, especially nanotechnology. Start by exploring probability distribution, then discover the behavior of electrons with a series of simulations.
Geometrization of Quantum Mechanics
J. F. Carinena; J. Clemente-Gallardo; G. Marmo
2007-03-23
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.
Okazaki, Tadashi
2015-01-01
We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N = 16 and N = 12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2) and SU(1,1|6) quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi-Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N = 8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.
Covariant quantum mechanics and quantum symmetries
JanyÂ?ka, Josef
Covariant quantum mechanics and quantum symmetries Josef JanyÅ¸ska 1 , Marco Modugno 2 , Dirk Saller: quantum mechanics, classical mechanics, general relativity, infinitesimal symmetries. 2000 MSC: 81P99, 81Q Introduction 2 2 Covariant quantum mechanics 5 2.1 Classical background
Longhi, Stefano, E-mail: stefano.longhi@fisi.polimi.it
2014-06-15
Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H{sup -hat} (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H{sup -hat} (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for the Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization.
Laskin
2000-09-01
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Levy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and statistical mechanics have been developed via our fractional path integral approach. A fractional generalization of the Schrodinger equation has been found. A relationship between the energy and the momentum of the nonrelativistic quantum-mechanical particle has been established. The equation for the fractional plane wave function has been obtained. We have derived a free particle quantum-mechanical kernel using Fox's H function. A fractional generalization of the Heisenberg uncertainty relation has been established. Fractional statistical mechanics has been developed via the path integral approach. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in terms of the Fox's H function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics. PMID:11088808
Quantum Mechanics Without Observers
W. H. Sulis
2013-03-03
The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process theory and utilizing methods from combinatorial games, interpolation theory and complex systems theory results in a novel realist version of quantum mechanics incorporating quasi-local, nondeterministic hidden variables that are compatible with the no-hidden variable theorems and relativistic invariance, and reproduce the standard results of quantum mechanics to a high degree of accuracy without invoking observers.
Kapustin, Anton [California Institute of Technology, Pasadena, California 91125 (United States)] [California Institute of Technology, Pasadena, California 91125 (United States)
2013-06-15
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
NASA Astrophysics Data System (ADS)
Fischer, Werner; Leschke, Hajo; Müller, Peter
1995-05-01
The capabilities of the functional-analytic and of the functional-integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics. Differences are worked out by taking the one-dimensional hydrogen atom as an example, that is, a point mass on the Euclidean line subjected to the inverse-distance potential. This particular choice is made with the intent to clarify a long-lasting discussion about its spectral properties. In fact, for the four-parameter family of possible Hamiltonians the corresponding energy-dependent Green functions are derived in closed form. The multiplicity of Hamiltonians should be kept in mind when modeling certain experimental situations as, for instance, in quantum wires.
Quantum-Merlin-Arthur-complete problems for stoquastic Hamiltonians and Markov matrices
Jordan, Stephen P.; Gosset, David; Love, Peter J. [Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 6-304, Cambridge, Massachusetts 02139 (United States); Department of Physics, Haverford College, 370 Lancaster Avenue, Haverford, Pennsylvania 19041, USA, and Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States)
2010-03-15
We show that finding the lowest eigenvalue of a 3-local symmetric stochastic matrix is Quantum-Merlin-Arthur-complete (QMA-complete). We also show that finding the highest energy of a stoquastic Hamiltonian is QMA-complete and that adiabatic quantum computation using certain excited states of a stoquastic Hamiltonian is universal. We also show that adiabatic evolution in the ground state of a stochastic frustration-free Hamiltonian is universal. Our results give a QMA-complete problem arising in the classical setting of Markov chains and adiabatically universal Hamiltonians that arise in many physical systems.
Imprints of the Quantum World in Classical Mechanics
Maurice A. de Gosson; Basil J. Hiley
2011-01-01
The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed.\\u000a We show that the Schrödinger equation for a nonrelativistic spinless particle is a classical equation which is equivalent\\u000a to Hamilton’s equations. Our discussion is quite general, and incorporates time-dependent systems. This gives us the opportunity\\u000a of discussing the group of Hamiltonian canonical
Ontology and Quantum Mechanics
N. D. Hari Dass
2014-06-19
The issue of ontology in quantum mechanics, or equivalently the issue of the reality of the wave function is critically examined within standard quantum theory. It is argued that though no strict ontology is possible within quantum theory, ingenious measurement schemes may still make the notion of a \\emph{FAPP Ontology} i.e ontology for all practical purposes (a phrase coined by John Bell), meaningful and useful.
Non-Markovian quantum Brownian motion: a non-Hamiltonian approach
A. O. Bolivar
2015-05-26
We generalize the classical theory of Brownian motion so as to reckon with non-Markovian effects on both Klein-Kramers and Smoluchowski equations. For a free particle and a harmonic oscillator, it is shown that such non-Markovian effects account for the differentiability of the Brownian trajectories as well as the breakdown of the energy equipartition of statistical mechanics at short times in some physical situations. This non-Markovian approach is also extended to look at anomalous diffusion. Next, we bring in the dynamical-quantization method for investigating open quantum systems, which does consist in quantizing the classical Brownian motion starting directly from our non-Markovian Klein-Kramers and Smoluchowski equations, without alluding to any model Hamiltonian. Accordingly, quantizing our non-Markovian Klein-Kramers in phase space gives rise to a non-Markovian quantum master equation in configuration space, whereas quantizing our non-Markovian Smoluchowski equation in configuration space leads to a non-Markovian quantum Smoluchowski equation in phase space. In addition, it is worth noticing that non-Markovian quantum Brownian motion takes place in presence of a generic environment (e.g. a non-thermal quantum fluid). As far as the special case of a heat bath comprising of quantum harmonic oscillators is concerned, a non-Markovian Caldeira-Leggett master equation and a thermal quantum Smoluchowski equation are derived and extended to bosonic and fermionic heat baths valid for all temperatures.
W G Unruh
2006-01-01
Quantum mechanics is one of the most successful theoretical structures in all of science. Developed between 1925-26 to explain the optical spectrum of atoms, the theory over the succeeding 80 years has been extended, first to quantum field theories, gauge field theories, and now even string theory. It is used every day by thousands of physicists to calculate physical phenomena
Principle of Least Action in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Kobe, Donald H.
2004-10-01
We show that Hamilton's Principle of Least (or Extremum) Action for a complex scalar field to give the Schroedinger equation is equivalent to a commonly used time-dependent variational principle used in quantum mechanics with a Lagrangian density involving the wave function and the Hamiltonian operator. The method is applied to a many-boson system to derive a time-dependent Gross-Pitaevski equation.
Supersymmetry in quantum mechanics
Avinash Khare
1997-01-01
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical\\u000a problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable. In\\u000a this lecture I review the theoretical formulation of supersymmetric quantum mechanics and discuss many of its applications.\\u000a I show that the well-known exactly solvable
QUANTUM MECHANICS II Physics 342
Rosner, Jonathan L.
QUANTUM MECHANICS II Physics 342 KPTC 103 9:00 Â 10:20 a.m. 1 Tues., Thurs. Â Winter Quarter 2011 quantum mechanics at the graduate level. The text for Quantum Mechanics II will be J. J. Sakurai and Jim Napolitano, Modern Quantum Mechanics, Second Edition (Addison-Wesley, San Francisco, 2011). For supplemental
A Quantum Mechanical Travelling Salesman
Ravindra N. Rao
2011-08-23
A quantum simulation of a travelling salesman is described. A vector space for a graph is defined together with a sequence of operators which transform a special initial state into a superposition states representing Hamiltonian tours. The quantum amplitude for any tour is a function of the classical cost of travelling along the edges in that tour. Tours with the largest quantum amplitude may be different than those with the smallest classically-computed cost.
Adaptive Perturbation Theory I: Quantum Mechanics
Weinstein, Marvin; /SLAC
2005-10-19
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be treatable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, H, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. This paper introduces the method in the context of the pure anharmonic oscillator and then goes on to apply it to the case of tunneling between both symmetric and asymmetric minima. It concludes with an introduction to the extension of these methods to the discussion of a quantum field theory. A more complete discussion of this issue will be given in the second paper in this series, and it will show how to use the method of adaptive perturbation theory to non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.
Quantum State Restoration and Single-Copy Tomography for Ground States of Hamiltonians
Farhi, Edward
Given a single copy of an unknown quantum state, the no-cloning theorem limits the amount of information that can be extracted from it. Given a gapped Hamiltonian, in most situations it is impractical to compute properties ...
Quantum-Merlin-Arthur-complete problems for stoquastic Hamiltonians and Markov matrices
Gosset, David Nicholas
We show that finding the lowest eigenvalue of a 3-local symmetric stochastic matrix is Quantum-Merlin-Arthur-complete (QMA-complete). We also show that finding the highest energy of a stoquastic Hamiltonian is QMA-complete ...
Fun with supersymmetric quantum mechanics
Freedman, B.; Cooper, F.
1984-04-01
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup ..cap alpha../ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index ..delta.. which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if ..delta.. is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate ..delta.. for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references.
NSDL National Science Digital Library
Zollman, Dean
The Kansas State University Visual Quantum Mechanics project is developing instructional materials about quantum physics for high school and college students. Instructional units and/or courses are being created for high school and college non-science students, pre-medical and biology students, and science and engineering majors. Each set of the teaching-learning materials integrates interactive visualizations with inexpensive materials and written documents in an activity-based environment.
CALL FOR PAPERS: Special issue on Pseudo Hermitian Hamiltonians in Quantum Physics
Andreas Fring; Hugh F. Jones; Miloslav Znojil
2007-01-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to the subject of Pseudo Hermitian Hamiltonians in Quantum Physics as featured in the conference '6th International Workshop on Pseudo Hermitian Hamiltonians in Quantum Physics', City University London, UK, July 16--18 2007 (http:\\/\\/www.staff.city.ac.uk\\/~fring\\/PT\\/). Invited speakers at that meeting as well as
Symplectic Topology and Geometric Quantum Mechanics
NASA Astrophysics Data System (ADS)
Sanborn, Barbara
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
Werner Fischer; Hajo Leschke; Peter Müller
1995-01-01
The capabilities of the functional-analytic and of the functional-integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics. Differences are worked out by taking the one-dimensional hydrogen atom as an example, that is, a point mass on the Euclidean line subjected to the inverse-distance potential. This
W. Chagas-Filho
2009-05-11
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position or in the momentum representation. As a way to support this complementation, starting from the action that describes conformal gravity in the world-line formalism, we show that there are duality transformations that relate the dynamics in the presence of position dependent vector and tensor fields to the dynamics in the presence of momentum dependent vector and tensor fields.
The Global versus Local Hamiltonian Description of Quantum Input-Output Theory
John E. Gough
2014-09-24
The aim of this paper is to derive the global Hamiltonian form for a quantum system and bath, or more generally a quantum network with multiple quantum input field connections, based on the local descriptions. We give a new simple argument which shows that the global Hamiltonian for a single Markov component arises as the singular perturbation of the free translation operator. We show that the Fermi analogue takes an equivalent form provided the parity of the coefficients is correctly specified. This allows us to immediately extend the theory of quantum feedback networks to Fermi systems.
QUANTUM MECHANICS I Physics 341
Rosner, Jonathan L.
QUANTUM MECHANICS I Physics 341 KPTC 103 9:00 Â 10:20 a.m. 1 Tues., Thurs. Â Fall Quarter 1999 mechanics at the graduate level. The text for Quantum mechanics I and II will be J. J. Sakurai and Jim Napolitano, Modern Quantum Mechanics, Second Edition (Addison- Wesley, 2011). We will cover the first three
From Quantum Mechanics to Thermodynamics?
Steinhoff, Heinz-Jürgen
From Quantum Mechanics to Thermodynamics? Dresden, 22.11.2004 Jochen Gemmer Universit¨at Osnabr Description? Quantum Mechanics i¯h t = (- ¯h2 2m + V ) Classical Mechanics: m d2 dt2 x = - V Thermodynamics: dU = TdS - pdV dS dt > 0 #12;Fundamental Law or Emergent Description? Quantum Mechanics i
Quantum Mechanics in Phase Space
Ali Mohammad Nassimi
2008-06-11
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
Biorthogonal quantum mechanics
NASA Astrophysics Data System (ADS)
Brody, Dorje C.
2014-01-01
The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called ‘biorthogonal quantum mechanics’, is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems.
Argyris Nicolaidis
2012-11-09
We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics.
Interpretation of quantum mechanics
Roland Omnès
1987-01-01
New axioms are proposed for the interpretation of quantum mechanics. They rest on a kind of calculus allowing to select meaningful physical statements and giving rules to check a given physical reasoning containing implications. Measurement theory is reformulated. Laboratoire associé au Centre National de la Recherche Scientifique.
Supersymmetry and quantum mechanics
Fred Cooper; Avinash Khare; Uday Sukhatme
1995-01-01
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of
Path integral in energy representation in quantum mechanics
P. Putrov
2007-08-30
In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it is much more better defined than the usual functional integral. We investigate this representation from various directions and compare such approach to quantum mechanics with the standard ones.
Correct quantum chemistry in a minimal basis from effective Hamiltonians
Watson, Thomas J
2015-01-01
We describe how to create ab-initio effective Hamiltonians that qualitatively describe correct chemistry even when used with a minimal basis. The Hamiltonians are obtained by folding correlation down from a large parent basis into a small, or minimal, target basis, using the machinery of canonical transformations. We demonstrate the quality of these effective Hamiltonians to correctly capture a wide range of excited states in water, nitrogen, and ethylene, and to describe ground and excited state bond-breaking in nitrogen and the chromium dimer, all in small or minimal basis sets.
On Randomness in Quantum Mechanics
Alberto C. de la Torre
2007-07-19
The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.
Epigenetics: Biology's Quantum Mechanics
Jorgensen, Richard A.
2011-01-01
The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene – the molecular biological view and the epigenetic view – are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider. PMID:22639577
Quantum error suppression with commuting Hamiltonians: Two-local is too local
Iman Marvian; Daniel A. Lidar
2014-10-30
We consider error suppression schemes in which quantum information is encoded into the ground subspace of a Hamiltonian comprising a sum of commuting terms. Since such Hamiltonians are gapped they are considered natural candidates for protection of quantum information and topological or adiabatic quantum computation. However, we prove that they cannot be used to this end in the 2-local case. By making the favorable assumption that the gap is infinite we show that single-site perturbations can generate a degeneracy splitting in the ground subspace of this type of Hamiltonians which is of the same order as the magnitude of the perturbation, and is independent of the number of interacting sites and their Hilbert space dimensions, just as in the absence of the protecting Hamiltonian. This splitting results in decoherence of the ground subspace, and we demonstrate that for natural noise models the coherence time is proportional to the inverse of the degeneracy splitting. Our proof involves a new version of the no-hiding theorem which shows that quantum information cannot be approximately hidden in the correlations between two quantum systems, and should be of independent interest. The main reason that 2-local commuting Hamiltonians cannot be used for quantum error suppression is that their ground subspaces have only short-range (two-body) entanglement.
Glenn Eric Johnson
2014-12-21
The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the Feynman series for Compton scattering. To have a semi-norm, photon states are constrained to transverse polarizations and for Compton scattering, the constructed cross section deviates at large momentum exchanges from the cross section prediction of the Feynman rules. Discussion includes the incompatibility of canonical quantization with the constructed interacting fields, and the role of interpretations of quantum mechanics in realizing QFT.
Probabilistic Interpretation of Quantum Mechanics
Brigitte Falkenburg; Peter Mittelstaedt
The probabilistic interpretation of quantum mechanics is based on Born's 1926 papers and von Neumann's formal account of quantum\\u000a mechanics in ? Hilbert space. According to Max Born (1882–1970), the quantum mechanical ? wave function ? does not have any\\u000a direct physical meaning, whereas its square ???2 is a probability [1] ? Born rule, probability in quantum mechanics. According to
Almost Periodic Orbits and Stability for Quantum Time-Dependent Hamiltonians
Cesar R. de Oliveira; Mariza S. Simsen
2007-11-05
We study almost periodic orbits of quantum systems and prove that for periodic time-dependent Hamiltonians an orbit is almost periodic if, and only if, it is precompact. In the case of quasiperiodic time-dependence we present an example of a precompact orbit that is not almost periodic. Finally we discuss some simple conditions assuring dynamical stability for nonautonomous quantum system.
Quantum Mechanics and Representation Theory Columbia University
Woit, Peter
Quantum Mechanics and Representation Theory Peter Woit Columbia University Texas Tech, November 21 2013 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 1 / 30 #12;Does Anyone Understand Quantum Mechanics? "No One Understands Quantum Mechanics" "I think
Euclidean Relativistic Quantum Mechanics
Philip Kopp; Wayne Polyzou
2013-01-28
We discuss a formulation of exactly Poincar\\'e invariant quantum mechanics where the input is model Euclidean Green functions or their generating functional. We discuss the structure of the models, the construction of the Hilbert space, the construction and transformation properties of single-particle states, and the construction of GeV scale transition matrix elements. A simple model is utilized to demonstrate the feasibility of this approach.
Relativity and quantum mechanics
Hüseyin Yilmaz
1982-01-01
Conditions under which quantum mechanics can be made compatible with the curved space-time of gravitation theories is investigated. A postulate is imposed in the formv=vg wherev is the kinematical Hamilton-Jacobi (geometric optic limit) velocity andvg is the group velocity of the waves. This imposes a severe condition on the possible coordinates in which the Schrödinger form (the coordinate realization) of
Principles of Fractional Quantum Mechanics
Nick Laskin
2010-09-28
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum mechanics, hermiticity of the Hamilton operator, parity conservation law and the current density. Applications of fractional quantum mechanics cover dynamics of a free particle, new representation for a free particle quantum mechanical kernel, infinite potential well, bound state in {\\delta}-potential well, linear potential, fractional Bohr atom and fractional oscillator. We also review fundamentals of the L\\'evy path integral approach to fractional statistical mechanics.
Marcus Gaul; Carlo Rovelli
2001-03-08
We study a generalized version of the Hamiltonian constraint operator in nonperturbative loop quantum gravity. The generalization is based on admitting arbitrary irreducible SU(2) representations in the regularization of the operator, in contrast to the original definition where only the fundamental representation is taken. This leads to a quantization ambiguity and to a family of operators with the same classical limit. We calculate the action of the Euclidean part of the generalized Hamiltonian constraint on trivalent states, using the graphical notation of Temperley-Lieb recoupling theory. We discuss the relation between this generalization of the Hamiltonian constraint and crossing symmetry.
The structure of supersymmetry in ${\\cal PT}$ symmetric quantum mechanics
D. Bazeia; Ashok Das; L. Greenwood; L. Losano
2009-03-17
The structure of supersymmetry is analyzed systematically in ${\\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\\cal PT}$ symmetric quantum mechanical theories. We show that there is a richer structure present in these theories compared to the conventional theories associated with Hermitian Hamiltonians. We bring out various properties associated with these supersymmetric systems and generalize such quantum mechanical theories to higher dimensions as well as to the case of one dimensional shape invariant potentials.
Taming the zoo of supersymmetric quantum mechanical models
Smilga, A V
2013-01-01
We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii) similarity transformation of the complex supercharges. We conjecture that it is true for any SQM model.
Taming the zoo of supersymmetric quantum mechanical models
A. V. Smilga
2013-05-30
We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii) similarity transformation of the complex supercharges. We conjecture that it is true for any SQM model.
Abstract: Quantum mechanics provides a
Shahriar, Selim
Abstract: Quantum mechanics provides a mechanism for absolutely secure communication between remote parties. For distances greater than 100 kilometers direct quantum communication via optical fiber is not viable, due to fiber losses, and intermediate storage of the quantum information along the trans- mission
Bohmian quantum mechanics with quantum trajectories
NASA Astrophysics Data System (ADS)
Jeong, Yeuncheol
The quantum trajectory method in the hydrodynamical formulation of Madelung-Bohm-Takabayasi quantum mechanics is an example of showing the cognitive importance of scientific illustrations and metaphors, especially, in this case, in computational quantum chemistry and electrical engineering. The method involves several numerical schemes of solving a set of hydrodynamical equations of motion for probability density fluids, based on the propagation of those probability density trajectories. The quantum trajectory method gives rise to, for example, an authentic quantum electron transport theory of motion to, among others, classically-minded applied scientists who probably have less of a commitment to traditional quantum mechanics. They were not the usual audience of quantum mechanics and simply choose to use a non-Copenhagen type interpretation to their advantage. Thus, the metaphysical issues physicists had a trouble with are not the main concern of the scientists. With the advantages of a visual and illustrative trajectory, the quantum theory of motion by Bohm effectively bridges quantum and classical physics, especially, in the mesoscale domain. Without having an abrupt shift in actions and beliefs from the classical to the quantum world, scientists and engineers are able to enjoy human cognitive capacities extended into the quantum mechanical domain.
Octonic relativistic quantum mechanics
V. L. Mironov; S. V. Mironov
2008-04-22
In this paper we represent the generalization of relativistic quantum mechanics on the base of eght-component values "octons", generating associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the eight-component octonic wave function, obtained from the Einshtein relation for energy and momentum, describes particles with spin of 1/2. It is established that the octonic wave function of a particle in the state with defined spin projection has the specific spatial structure in the form of octonic oscillator with two spatial polarizations: longitudinal linear and transversal circular. The relations between bispinor and octonic descriptions of relativistic particles are established. We propose the eight-component spinors, which are octonic generalisation of two-component Pauli spinors and four-component Dirac bispinors. It is shown that proposed eight-component spinors separate the states with different spin projection, different particle-antiparticle state as well as different polarization of the octonic oscillator. We demonstrate that in the frames of octonic relativistic quantum mechanics the second-order equation for octonic wave function can be reformulated in the form of the system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special type of wave functions the second-order equation can be reduced to the single first-order equation, which is analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not create quantum fields.
Topics in Representation Theory: Hamiltonian Mechanics and Symplectic
Woit, Peter
equations, known as Hamilton's equations dpi dt = - H qi dqi dt = H pi and there is an obvious is the equations for a gradient flow in 2n dimensions dpi dt = - f pi dqi dt = - f qi 1 #12;These equations dqi In this case, starting with a Hamiltonian function H, one produces a vector field XH as follows H
Gravitomagnetism in quantum mechanics
Adler, Ronald J.; Chen Pisin [Gravity Probe B, Hansen Laboratory for Experimental Physics, Stanford University, Stanford California 94309 (United States); Leung Center for Cosmology and Particle Astrophysics and Department of Physics and Graduate Institute of Astrophysics, National Taiwan University, Taipei, Taiwan 10617 and Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States)
2010-07-15
We give a systematic treatment of the quantum mechanics of a spin zero particle in a combined electromagnetic field and a weak gravitational field that is produced by a slow moving matter source. The analysis is based on the Klein-Gordon equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The Klein-Gordon equation is recast into Schroedinger equation form, which we then analyze in the nonrelativistic limit. We include a discussion of some rather general observable physical effects implied by the Schroedinger equation form, concentrating on gravitomagnetism. Of particular interest is the interaction of the orbital angular momentum of the particle with the gravitomagnetic field.
Diffusion-Schrödinger Quantum Mechanics
NASA Astrophysics Data System (ADS)
Lasukov, V. V.; Lasukova, T. V.; Lasukova, O. V.; Novoselov, V. V.
2014-08-01
A quantum solution of a nonlinear differential equation of diffusion type with a potential term has been found. Diffusion-Schrödinger quantum mechanics can find wide application in quantum biology, biological electronics, synthetic biology, nanomedicine, the quantum theory of consciousness, cosmology, and other fields of science and technology. One consequence of the macroscopic nature of diffusion-Schrödinger quantum mechanics is the possibility of generation of hard photons. The dust plasma in the Universe can generate cosmic rays with ultra-relativistic energies in a galactic magnetic field via a diffusion mechanism.
Advanced Concepts in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Esposito, Giampiero; Marmo, Giuseppe; Miele, Gennaro; Sudarshan, George
2014-11-01
Preface; 1. Introduction: the need for a quantum theory; 2. Experimental foundations of quantum theory; 3. Waves and particles; 4. Schrödinger picture, Heisenberg picture and probabilistic aspects; 5. Integrating the equations of motion; 6. Elementary applications: 1-dimensional problems; 7. Elementary applications: multidimensional problems; 8. Coherent states and related formalism; 9. Introduction to spin; 10. Symmetries in quantum mechanics; 11. Approximation methods; 12. Modern pictures of quantum mechanics; 13. Formulations of quantum mechanics and their physical implications; 14. Exam problems; Glossary of geometric concepts; References; Index.
Gamification of Quantum Mechanics Teaching
Ole Eggers Bjælde; Mads Kock Pedersen; Jacob Sherson
2015-06-26
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
Gamification of Quantum Mechanics Teaching
Bjælde, Ole Eggers; Sherson, Jacob
2015-01-01
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
NASA Astrophysics Data System (ADS)
Jones, Robert
2011-03-01
I do not agree with mind-body dualism. Today the consensus view is that thought and mind is a combination of processes like memory, generalization, comparison, deduction, organization, induction, classification, feature detection, analogy, etc. performed by computational machinery. (R. Jones, Trans. of the Kansas Acad. Sci., vol. 109, # 3/4, 2006 and www.robert-w-jones.com, philosopher, theory of thought) But I believe that quantum mechanics is a more plausible dualist theory of reality. The quantum mechanical wave function is nonphysical, it exists in a 3N space (for an N body system) not in (x,y,z,t) 4-space, and does not possess physical properties. But real physical things like energy (which do exist in our 4-space world) influence the wave function and the wave function, in its turn, influences real physical things, like where a particle can be found in 4-space. The coupling between the spirit-like wave function and things found in the real (4-space) world (like energy) is via mathematical equations like the Schrodinger equation and Born normalization.
Brown, K R; Clark, R J; Brown, Kenneth R.; Chuang, Isaac L.; Clark, Robert J.
2006-01-01
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm to find the low-lying spectrum of a Hamiltonian. While the number of elementary quantum gates does scale polynomially with the size of the system, it increases inversely to the desired error bound $\\epsilon$. Making such simulations robust to decoherence using fault-tolerance constructs requires an additional factor of $1/ \\epsilon$ gates. These constraints are illustrated by using a three qubit nuclear magnetic resonance system to simulate a pairing Hamiltonian, following the algorithm proposed by Wu, Byrd, and Lidar.
ccsd-00008676,version1-13Sep2005 Quadratic Quantum Hamiltonians revisited
Boyer, Edmond
is a survey concerning exact useful formulas for time dependent Schr¨odinger equations with quadratic quadratic Schr¨odinger equation and Gaus- sian Coherent States. It is well known and clearccsd-00008676,version1-13Sep2005 Quadratic Quantum Hamiltonians revisited Monique Combescure IPNL
Koch, Christiane
from a normal mode analysis combined with a weak systembath coupling assumption.2 If the bath is only is closely related to a normal mode decomposi- tion. Once this is done the spectral density function iDissipative quantum dynamics with the surrogate Hamiltonian approach. A comparison between spin
Realization of a quantum Hamiltonian Boolean logic gate on the Si(001):H surface.
Kolmer, Marek; Zuzak, Rafal; Dridi, Ghassen; Godlewski, Szymon; Joachim, Christian; Szymonski, Marek
2015-08-01
The design and construction of the first prototypical QHC (Quantum Hamiltonian Computing) atomic scale Boolean logic gate is reported using scanning tunnelling microscope (STM) tip-induced atom manipulation on an Si(001):H surface. The NOR/OR gate truth table was confirmed by dI/dU STS (Scanning Tunnelling Spectroscopy) tracking how the surface states of the QHC quantum circuit on the Si(001):H surface are shifted according to the input logical status. PMID:26144212
Equivalence between Quantum Mechanics and PT Symmetric Quantum Mechanics
David Girardelli; Eduardo M. Zavanin; Marcelo M. Guzzo
2015-02-24
In this paper we develop a discussion about PT Symmetric Quantum Mechanics, working with basics elements of this theory. In a simple case of two body system, we developed the Quantum Brachistochrone problem. Comparing the results obtained through the PT Symmetric Quantum Mechanics with that ones obtained using the standard formalism, we conclude that this new approach is not able to reveal any new effect.
Quantum Leap Quantum Mechanics' Killer App
Bigelow, Stephen
Quantum Leap Quantum Mechanics' Killer App Q&A with Craig Hawker Director of the Materials Research in the nation Thomson Reuters ranked Materials research at UCSB as second in the world in terms of research. Q&A with Craig Hawker LEAP The Materials Research Laboratory is the only Wes
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics. PMID:23509390
Tensorial description of quantum mechanics
J. Clemente-Gallardo; G. Marmo
2013-02-01
Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a covariant formulation of quantum mechanics under the full diffeomorphism group.
Invariance in adelic quantum mechanics
Branko Dragovich
2006-12-07
Adelic quantum mechanics is form invariant under an interchange of real and p-adic number fields as well as rings of p-adic integers. We also show that in adelic quantum mechanics Feynman's path integrals for quadratic actions with rational coefficients are invariant under changes of their entries within nonzero rational numbers.
The Generation of Quantum Hamiltonian Evolution from A Pseudo-Measurement Process
Matthew F. Brown
2014-03-13
Here we shall consider the idea that the Hamiltonian evolution of a quantum system is generated by sequential observations of the system by a `pseudo-apparatus'. This representation of Hamiltonian dynamics, originally discovered by Belavkin, is a canonical dilation of the Schroedinger equation that reveals a Minkowski space structure outside of the context of Special Relativity. In particular, this formalism gives rise to the notion of a Boosted Schroedinger equation referred to a dilated time increment which is the manifestation of a Lorentz transform in the Minkowski space of the apparatus.
Hamiltonian cosmological perturbation theory with loop quantum gravity corrections
NASA Astrophysics Data System (ADS)
Bojowald, Martin; Kagan, Mikhail; Singh, Parampreet; Hernández, Hector H.; Skirzewski, Aureliano
2006-12-01
Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out. Nevertheless, the treatment is more systematic when correction terms of canonical quantum gravity are to be included. This is done throughout the paper for one example of characteristic modifications expected from loop quantum gravity.
Hamiltonian approach to the dynamics of Ehrenfest expectation values and Gaussian quantum states
Bonet-Luz, Esther
2015-01-01
The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical operators are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest's theorem is shown to be Lie-Poisson for a semidirect-product Lie group, named the `Ehrenfest group'. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie-Poisson structure associated to a semidirect-product subgroup of the Ehrenfest group, which is called the Jacobi group. This structure produces new energy-conserving terms in a class of Gaussian moment models (previously appeared in the chemical physics literature) that suffer from lack of energy conservation ...
A Study about the Supersymmetry in the context of Quantum Mechanics
Fabricio Marques
2011-11-04
In this work we present an introduction to Supersymmetry in the context of 1-dimensional Quantum Mechanics. For that purpose we develop the concept of hamiltonians factorization using the simple harmonic oscillator as an example, we introduce the supersymmetric oscilator and, next, we generalize these concepts to introduce the fundamentals of Supersymmetric Quantum Mechanics. We also discuss useful tools to solve problems in Quantum Mechanics which are intrinsecally related to Supersymmetry as hierarchy of hamiltonians and shape invariance. We present two approximation methods which will be specially useful: the well known Variational Method and the Logarithmic Perturbation Theory, the latter being closely related to the concepts of superpotentials and hierarchy of hamiltonians. Finally, we present problems related to superpotentials which are monomials in even powers of the x coordinate multiplied by the sign function epsilon(x), which seems to be a new class of problems in Supersymmetric Quantum Mechanics.
Quantum Mechanics 1 for graduate students
Course 606 Quantum Mechanics 1 for graduate students Fall 2010 Instructor Valery Pokrovsky 1 electromagnetic field. Gauge invariance. Landau levels. 7. Semiclassical approximation. 8. Quantum mechanics. Scattering. The main textbook is E. Merzbacher, Quantum Mechanics, third edition, Wiley. Additional
Quantum Mechanics as Classical Physics
Charles Sebens
2015-04-02
Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.
V. P. Belavkin; O. Melsheimer
2005-12-22
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles" which admit a continual counting observation. This model allows to watch a quantum trajectory in a photodetector or in a cloud chamber by spontaneous localisations of the momentums of the scattered photons or bubbles. Thus, the continuous reduction and spontaneous localization theory is obtained from a Hamiltonian singular interaction as a result of quantum filtering, i.e., a sequential time continuous conditioning of an input quantum process by the output measurement data. We show that in the case of indistinguishable particles or atoms the a posteriori dynamics is mixing, giving rise to an irreversible Boltzmann-type reduction equation. The latter coincides with the nonstochastic Schroedinger equation only in the mean field approximation, whereas the central limit yelds Gaussian mixing fluctuations described by a quantum state reduction equation of diffusive type.
Spectral Properties of a Magnetic Quantum Hamiltonian on a Strip
Philippe Briet; Georgi Raikov; Eric Soccorsi
2007-11-24
We consider a 2D Schroedinger operator H0 with constant magnetic field, on a strip of finite width. The spectrum of H0 is absolutely continuous, and contains a discrete set of thresholds. We perturb H0 by an electric potential V which decays in a suitable sense at infinity, and study the spectral properties of the perturbed operator H = H0 + V . First, we establish a Mourre estimate, and as a corollary prove that the singular continuous spectrum of H is empty, and any compact subset of the complement of the threshold set may contain at most a finite set of eigenvalues of H, each of them having a finite multiplicity. Next, we introduce the Krein spectral shift function (SSF) for the operator pair (H,H0). We show that this SSF is bounded on any compact subset of the complement of the threshold set, and is continuous away from the threshold set and the eigenvalues of H. The main results of the article concern the asymptotic behaviour of the SSF at the thresholds, which is described in terms of the SSF for a pair of effective Hamiltonians.
Decoherence in quantum mechanics and quantum cosmology
NASA Technical Reports Server (NTRS)
Hartle, James B.
1992-01-01
A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.
Phase Space Quantum Mechanics - Direct
S. Nasiri; Y. Sobouti; F. Taati
2006-05-15
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of non commuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.
Phase space quantum mechanics - Direct
Nasiri, S.; Sobouti, Y.; Taati, F. [Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of) and Department of Physics, Zanjan University, Zanjan (Iran); Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of); Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of) and Department of Physics, University of Kurdistan, D-78457 Sanadaj (Iran)
2006-09-15
Conventional approach to quantum mechanics in phase space (q,p), is to take the operator based quantum mechanics of Schroedinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.
An approach to nonstandard quantum mechanics
Andreas Raab
2006-12-27
We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to non-relativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the M{\\o}ller wave operators and the S-Matrix.
Scattering Relativity in Quantum Mechanics
Richard Shurtleff
2011-08-09
Transforming from one reference frame to another yields an equivalent physical description. If quantum fields are transformed one way and quantum states transformed a different way then the physics changes. We show how to use the resulting changed physical description to obtain the equations of motion of charged, massive particles in electromagnetic and gravitational fields. The derivation is based entirely on special relativity and quantum mechanics.
Quantum mechanics from classical statistics
Wetterich, C. [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)], E-mail: c.wetterich@thphys.uni-heidelberg.de
2010-04-15
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.
Progress in Supersymmetric Quantum Mechanics
2003-01-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General dedicated to the subject of Supersymmetric Quantum Mechanics as featured in the International Conference in Supersymmetric Quantum Mechanics (PSQM03), 15--19 July 2003, University of Valladolid, Spain (http:\\/\\/metodos.fam.cie.uva.es\\/~susy_qm_03\\/). Participants at that meeting, as well as other researchers working in this area or in
Event Horizons, Quantum Mechanics, and the Semiclassical Stability of de Sitter Space
Jeffrey Alan Isaacson
1991-01-01
Quantum effects in the presence of an event horizon are examined in two contexts: first-quantized particle mechanics and quantum field theory in curved space-time. First, the inertial motion of a fermion in Minkowski space is analyzed from the standpoint of a uniformly accelerated observer. The Dirac Hamiltonian of the freely falling particle is derived and used to determine the extent
Morrison, Philip J.,
Cite as: P.J. Morrison, ``Hamiltonian Fluid Mechanics", in Encyclopedia of Mathematical Physics, vol. 2, (Elsevier, Amsterdam, 2006) p. 593. #12;H Hamiltonian Fluid Dynamics P J Morrison, University, that was termed noncanonical Hamilto- nian form in the fluid mechanics context by P Morrison and J Greene (1980
Bush, John W. M.
Some two centuries before the quantum revolution, Newton (1) suggested that corpuscles of light generate waves in an aethereal medium like skipping stones generate waves in water, with their motion then being affected by ...
Chem 793 Quantum Mechanics I Chemistry 793
Chem 793 Quantum Mechanics I Chemistry 793 Quantum Mechanics I Fall 2000 Course outline 1 formulation. · Constants of the motion. 2. Probability in classical and quantum mechanics · Probability University #12;Chem 793 Quantum Mechanics I 7. Separable problems in 2D and 3D · Direct product functions
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics, 2009 #12;Quantum Mechanics: Measurement and Uncertainty Thursday, May 7, 2009 #12;Puzzle: The Stern it. Quantum mechanics understanding: the particle exists in a state without definite position
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics) New Particles anti-particles (combining special relativity and quantum mechanics pions (mediator/momentum/mass discrepancy must fit inside the quantum mechanical uncertainty p, E E2 - p2 c2 = 0 Thursday, May 7, 2009 #12
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Strings and the Strong Force Thursday, May 7, 2009 #12;Review of Quantum Mechanics In general, particles Planck's constant determines the scale where quantum mechanical effects become important Thursday, May 7
Brown, Kenneth R; Clark, Robert J; Chuang, Isaac L
2006-08-01
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm proposed by Wu, Byrd, and Lidar [Phys. Rev. Lett. 89, 057904 (2002).10.1103/PhysRevLett.89.057904] to find the low-lying spectrum of a pairing Hamiltonian. While the number of elementary quantum gates required scales polynomially with the size of the system, it increases inversely to the desired error bound E. Making such simulations robust to decoherence using fault tolerance requires an additional factor of approximately 1/E gates. These constraints, along with the effects of control errors, are illustrated using a three qubit NMR system. PMID:17026087
Modeling Quantum Mechanical Observers via Neural-Glial Networks
NASA Astrophysics Data System (ADS)
Konishi, Eiji
2012-07-01
We investigate the theory of observers in the quantum mechanical world by using a novel model of the human brain which incorporates the glial network into the Hopfield model of the neural network. Our model is based on a microscopic construction of a quantum Hamiltonian of the synaptic junctions. Using the Eguchi-Kawai large N reduction, we show that, when the number of neurons and astrocytes is exponentially large, the degrees of freedom (d.o.f) of the dynamics of the neural and glial networks can be completely removed and, consequently, that the retention time of the superposition of the wavefunctions in the brain is as long as that of the microscopic quantum system of pre-synaptics sites. Based on this model, the classical information entropy of the neural-glial network is introduced. Using this quantity, we propose a criterion for the brain to be a quantum mechanical observer.
Relations between multi-resolution analysis and quantum mechanics
F. Bagarello
2009-04-01
We discuss a procedure to construct multi-resolution analyses (MRA) of $\\Lc^2(\\R)$ starting from a given {\\em seed} function $h(s)$ which should satisfy some conditions. Our method, originally related to the quantum mechanical hamiltonian of the fractional quantum Hall effect (FQHE), is shown to be model independent. The role of a canonical map between certain canonically conjugate operators is discussed. This clarifies our previous procedure and makes much easier most of the original formulas, producing a convenient framework to produce examples of MRA.
What quantum computers may tell us about quantum mechanics
Monroe, Christopher
17 What quantum computers may tell us about quantum mechanics Christopher R. Monroe University of Michigan, Ann Arbor Quantum mechanics occupies a unique position in the history of science. It has sur successes of quantum mechanics, its foundations are often questioned, owing to the glaring difficulties
Quantum Mechanics and Determinism
Gerard't Hooft
2001-01-01
It is shown how to map the quantum states of a system of free scalar\\u000aparticles one-to-one onto the states of a completely deterministic model. It is\\u000aa classical field theory with a large (global) gauge group. The mapping is now\\u000aalso applied to free Maxwell fields. Lorentz invariance is demonstrated.
NSDL National Science Digital Library
Galvez, Enrique
This web site, authored by Enrique Galvez and Charles Holbrow of Colgate University, outlines a project to develop undergraduate physics labs that investigate quantum interference and entanglement with photons. The labs are designed for simplicity and low cost. A description of the lab set up, background information, and an article on the project are provided.
Are nonlinear discrete cellular automata compatible with quantum mechanics?
Hans-Thomas Elze
2015-05-14
We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises "Hamiltonian CA" with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The dynamics is linear, quite similar to unitary evolution described by the Schroedinger equation. This has been essential in our construction of an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental discreteness scale. Based on Shannon's sampling theory, it leads, for example, to a one-to-one relation between quantum mechanical and CA conservation laws. The important issue of linearity of the theory is examined here by incorporating higher-order nonlinearities into the underlying action. These produce inconsistent nonlocal (in time) effects when trying to describe continuously such nonlinear CA. Therefore, in the present framework, only linear CA and local quantum mechanical dynamics are compatible.
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics with constant velocity with respect to each other (These are inertial reference frames) Newton's Laws (mechanics
New Type of Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories
Stefan Teufel; Roderich Tumulka
2015-05-19
We propose a novel type of Hamiltonians for quantum field theories. They are mathematically well-defined (and in particular, ultraviolet finite) without any ultraviolet cut-off such as smearing out the particles over a nonzero radius; rather, the particles are assigned radius zero. We describe explicit examples of such Hamiltonians. Their definition, which is best expressed in the particle-position representation of the wave function, involves a novel type of boundary condition on the wave function, which we call an interior-boundary condition. The relevant configuration space is one of a variable number of particles, and the relevant boundary consists of the configurations with two or more particles at the same location. The interior-boundary condition relates the value (or derivative) of the wave function at a boundary point to the value of the wave function at an interior point (here, in a sector of configuration space corresponding to a lesser number of particles).
New Type of Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories
Teufel, Stefan
2015-01-01
We propose a novel type of Hamiltonians for quantum field theories. They are mathematically well-defined (and in particular, ultraviolet finite) without any ultraviolet cut-off such as smearing out the particles over a nonzero radius; rather, the particles are assigned radius zero. We describe explicit examples of such Hamiltonians. Their definition, which is best expressed in the particle-position representation of the wave function, involves a novel type of boundary condition on the wave function, which we call an interior-boundary condition. The relevant configuration space is one of a variable number of particles, and the relevant boundary consists of the configurations with two or more particles at the same location. The interior-boundary condition relates the value (or derivative) of the wave function at a boundary point to the value of the wave function at an interior point (here, in a sector of configuration space corresponding to a lesser number of particles).
Quantum Mechanics (QM) Measurement Package
NSDL National Science Digital Library
Belloni, Mario
This set of tutorial worksheets, based on the OSP Quantum Mechanics Simulations, help students explore the effects of position, momentum, and energy measurements on quantum state wavepackets. The probabilistic change in the wavefunction upon measurements and the time propagation of the states are illustrated. Similar worksheets are available for measurements of single and superpositions of energy eigenstates. The worksheets can be run online or downloaded as a pdf (attached).
Quantum Mechanics: Sum Over Paths
NSDL National Science Digital Library
Taylor, Edwin F.
Created by Edwin F. Taylor a former professor at the Department of Physics at the Massachusetts Institute of Technology, this material describes methods of presenting quantum mechanics using the path-integral formulation. Included are links to a paper and presentation outlining the method, software to simulate the path integrals, and student workbook materials. This course has been used for introducing quantum physics to high school teachers.
ccsd00002942, ON SUPERSYMMETRIC QUANTUM MECHANICS
ccsdÂ00002942, version 1 Â 25 Sep 2004 ON SUPERSYMMETRIC QUANTUM MECHANICS M.R. KIBLER Institut de Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl supersymmetric Quantum Mechanics corresponds to k = 2. A connection between fractional supersymmetric Quantum
Histories Approach to Quantum Mechanics
Tulsi Dass
2005-01-27
These lecture notes cover the important developments in histories approach to quantum mechanics with overall content and emphasis somewhat different from other reviews and books on the subject.The idea of Houtappel, Van Dam and Wigner of employing objects based on primitive concepts of physical theories is discussed in some detail and the fact that histories are such objects is emphasized. Application of histories formalism to the problem of understanding the quasiclassical domain is treated in some detail. Other topics discussed include generalized histories-based quantum mechanics and its application to the quantum mechanics of space-time,generalization of the notion of time sequences employing partial semigroups,quasitemporal structures, history projection operator (HPO) formalism, the algebraic scheme of Isham and Linden, an axiomatic scheme for quasitemporal histories-based theories and symmetries and conservation laws in histories-based theories.
Wüthrich, Christian
THE OBJECTIVE INDEFINITENESS INTERPRETATION OF QUANTUM MECHANICS: Partition logic, logical information theory, and quantum mechanics David Ellerman University of California at Riverside www ago that quantum mechanics was not compatible with Boolean logic, then the natural thing to do would
Hans Cruz; Dieter Schuch; Octavio Castaños; Oscar Rosas-Ortiz
2015-05-11
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.
Arash Kh. Sichani; Igor G. Vladimirov; Ian R. Petersen
2015-03-07
This paper is concerned with open quantum systems whose dynamic variables satisfy canonical commutation relations and are governed by quantum stochastic differential equations. The latter are driven by quantum Wiener processes which represent external boson fields. The system-field coupling operators are linear functions of the system variables. The Hamiltonian consists of a nominal quadratic function of the system variables and an uncertain perturbation which is represented in a Weyl quantization form. Assuming that the nominal linear quantum system is stable, we develop sufficient conditions on the perturbation of the Hamiltonian which guarantee robust mean square stability of the perturbed system. Examples are given to illustrate these results for a class of Hamiltonian perturbations in the form of trigonometric polynomials of the system variables.
Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics
NASA Astrophysics Data System (ADS)
Ohzeki, Masayuki
2013-09-01
In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called quantum annealing. The most typical instance is quantum adiabatic computation based on the adiabatic theorem. The quantum adiabatic computation as discussed in the other chapter, unfortunately, has a crucial bottleneck for a part of the optimization problems. We here introduce several recent trials to overcome such a weakpoint by use of developments in statistical mechanics. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.
Quantum mechanical force field for water with explicit electronic polarization
Han, Jaebeom; Mazack, Michael J. M.; Zhang, Peng; Truhlar, Donald G.; Gao, Jiali [Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street, SE, Minneapolis, Minnesota 55455-0431 (United States)] [Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street, SE, Minneapolis, Minnesota 55455-0431 (United States)
2013-08-07
A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 10{sup 6} self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across biological ion channels through membranes.
Quantum mechanical force field for water with explicit electronic polarization.
Han, Jaebeom; Mazack, Michael J M; Zhang, Peng; Truhlar, Donald G; Gao, Jiali
2013-08-01
A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 10(6) self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across biological ion channels through membranes. PMID:23927266
Hamiltonian approach to the dynamics of Ehrenfest expectation values and Gaussian quantum states
Esther Bonet-Luz; Cesare Tronci
2015-07-09
The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical operators are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest's theorem is shown to be Lie-Poisson for a semidirect-product Lie group, named the `Ehrenfest group'. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie-Poisson structure associated to a semidirect-product subgroup of the Ehrenfest group, which is called the Jacobi group. This structure produces new energy-conserving terms in a class of Gaussian moment models (previously appeared in the chemical physics literature) that suffer from lack of energy conservation in the general case.
He, Lewei; Wang, Wen-Ge
2014-02-01
We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is shown that, under an initial condition composed of sufficiently many energy eigenstates of the total system, such a basis is given by the eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of large Hilbert space of the environment. Here, the renormalized self-Hamiltonian is given by the unperturbed self-Hamiltonian plus a certain average of the interaction Hamiltonian over the environmental degrees of freedom. Numerical simulations performed in two models, both with the kicked rotor as the environment, give results consistent with the above analytical predictions. PMID:25353440
Svetoslav S. Ivanov; Michael Johanning; Christof Wunderlich
2015-03-30
We propose a simplified mathematical construction of the quantum Fourier transform which is suited for systems described by Ising-type Hamiltonians. By contrast to the standard scheme, which prescribes concatenated sequences of control phase gates, our implementation is based on one-qubit gates and a free evolution process. We show a realization of our method with homogeneous microwave driven ion traps in a magnetic field with gradient. In this setup our implementation presents a series of microwave $\\pi$ or $\\pi/2$ pulses applied at certain times.
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Mechanical Particle Physics General Relativistic Quantum Gravity increasing speed decreasing size increasing Extra Dimensions Strings and the Strong Force Thursday, June 4, 2009 #12;The Higgs Mechanism Summary
A Transfer Hamiltonian Model for Devices Based on Quantum Dot Arrays
Illera, S.; Prades, J. D.; Cirera, A.; Cornet, A.
2015-01-01
We present a model of electron transport through a random distribution of interacting quantum dots embedded in a dielectric matrix to simulate realistic devices. The method underlying the model depends only on fundamental parameters of the system and it is based on the Transfer Hamiltonian approach. A set of noncoherent rate equations can be written and the interaction between the quantum dots and between the quantum dots and the electrodes is introduced by transition rates and capacitive couplings. A realistic modelization of the capacitive couplings, the transmission coefficients, the electron/hole tunneling currents, and the density of states of each quantum dot have been taken into account. The effects of the local potential are computed within the self-consistent field regime. While the description of the theoretical framework is kept as general as possible, two specific prototypical devices, an arbitrary array of quantum dots embedded in a matrix insulator and a transistor device based on quantum dots, are used to illustrate the kind of unique insight that numerical simulations based on the theory are able to provide. PMID:25879055
Remarks on osmosis, quantum mechanics, and gravity
Robert Carroll
2011-04-03
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
Remarks on osmosis, quantum mechanics, and gravity
Carroll, Robert
2011-01-01
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
NASA Astrophysics Data System (ADS)
Sakmann, Kaspar; Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S.
2010-07-01
The quantum dynamics of one-dimensional bosonic Josephson junctions with attractive and repulsive interparticle interactions is studied by using the Bose-Hubbard model and by numerically exact computations of the full many-body Hamiltonian. A symmetry present in the Bose-Hubbard Hamiltonian dictates an equivalence between the evolution in time of the survival probability and the fragmentation of attractive and repulsive Josephson junctions with attractive and repulsive interactions of equal magnitude. The full many-body Hamiltonian does not possess this symmetry and, consequently, the dynamics of the attractive and repulsive junctions are different.
The quantum field theory interpretation of quantum mechanics
Alberto C. de la Torre
2015-03-02
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
Quantum tunneling process and Zambrini's Euclidean quantum mechanics
Mari Jibu; Kunio Yasue
1992-01-01
By adopting Zambrini's new Euclidean quantum mechanics, a theoretical procedure to describe the ill-defined problem of quantum tunneling processes studied recently in quantum cosmology is proposed. It is shown that the tunneling process from the vacuum state to a semi-classical state can be analyzed a priori in consrast with the conventional Copenhagen interpretation of quantum mechanics.
Quantum tunneling process and Zambrini's Euclidean quantum mechanics
NASA Astrophysics Data System (ADS)
Jibu, Mari; Yasue, Kunio
1992-11-01
By adopting Zambrini's new Euclidean quantum mechanics, a theoretical procedure to describe the ill-defined problem of quantum tunneling processes studied recently in quantum cosmology is proposed. It is shown that the tunneling process from the vacuum state to a semi-classical state can be analyzed a priori in consrast with the conventional Copenhagen interpretation of quantum mechanics.
Quantum mechanics and brain uncertainty.
Macgregor, Ronald J
2006-09-01
This paper argues that molecular governing structures (such as receptors, gating molecules, or ionic channels) which operate pervasively in the brain, often with small number particle systems (as, for example, at the surfaces of membranes, synaptic clefts, or macromolecules), may plausibly be vehicles for the transmutation of quantum mechanical fluctuations to normal-level neural signaling. PMID:17125159
Quantum Mechanics and Leggett's Inequalities
NASA Astrophysics Data System (ADS)
Socolovsky, M.
2009-12-01
We show that when the proper description of the behaviour of individual photons or spin {{1}over{2}} particles in a spherically symmetric entangled pair is done through the use of the density matrix, the Leggett’s inequality is not violated by quantum mechanics.
Time, Quantum Mechanics, and Probability
Simon Saunders
2001-11-07
A "geometric" intepretation of probability is proposed, modelled on the treatment of tense in 4-dimensional spacetime. It is applied to Everett's approach to quantum mechanics, as formulated in terms of consistent histories. Standard objections to Everett's approach, based on the difficulties of interpreting probability in its terms, are considered in detail, but found to be wanting.
Non-exponential decay in Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Giacosa, Francesco
2014-10-01
We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by using relativistic Lagrangians. In particular, the case in which two decay channels are present is analyzed: the ratio of decay probability densities, which is a constant equal to the ratio of decay widths in the exponential limit, shows in general sizable fluctuations which persist also at long times.
Delay Time in Quaternionic Quantum Mechanics
Stefano De Leo; Gisele Ducati
2012-04-11
In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex quantum mechanics.
Star Products for Relativistic Quantum Mechanics
P. Henselder
2007-05-24
The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.
Quantum Mechanics Revisited Jean Claude Dutailly
Boyer, Edmond
Quantum Mechanics Revisited Jean Claude Dutailly Paris (France) August 20, 2014 Abstract The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general a new theoretical foundation. ii) The quantum mechanics (QM) which is presented in all the books
Quantum Mechanics for Mathematicians: Introduction and Overview
Woit, Peter
Quantum Mechanics for Mathematicians: Introduction and Overview Peter Woit Department Richard Feynman goes "I think it is safe to say that no one understands quantum mechanics."[1 was contrasting quantum mechanics with the theory of general relativity, a supposedly equally hard to understand
On a realistic interpretation of quantum mechanics
Neumaier, Arnold
On a realistic interpretation of quantum mechanics Arnold Neumaier Institut fur Mathematik respecting the indeter- ministic nature of quantum mechanics, allows to speak of de#12;nite values for all], there are at least two levels of inter- preting quantum mechanics: the statistical interpretation in the narrower
First Day Handout Phys 430: Quantum Mechanics
Nickrent, Daniel L.
First Day Handout Phys 430: Quantum Mechanics (Dated: 18 August 2014) Meeting times: MWF 1:00-1:50 Room: Neckers 410 Text: "Introduction to Quantum Mechanics," 2nd Edition, by D. Griffiths. Instructor Interpretation (e) The Uncertainty Principle (f) Dirac Notation 4. Chapter 4: Quantum Mechanics in Three
On the interpretation of quantum mechanics
V. A. Fock
1957-01-01
After a brief discussion of the reasons for the complete failure of a deterministic interpretation of quantum mechanics (§ 1)Niels Bohr's ideas on quantum mechanics are exposed. The importance of Bohr's idea on the necessity of combining the quantum-mechanical description of atomic objects with a classical description of the instruments is stressed (§ 2).It is pointed out, however, that the
Visualizing quantum mechanics in phase space
Heiko Bauke; Noya Ruth Itzhak
2011-01-11
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner function formalism resembles the mathematical language of classical mechanics of non-interacting particles. Thus, it allows a more direct comparison between classical and quantum dynamical features.
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Particle Interaction Summary quantum mechanics and special relativity together imply the existence of anti-particles forces are mediated
129 Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
129 Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion
221B Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion
221B Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We, similarly to the Newton's equation of motion in mechanics. The initial condtions to solve the Newton
Quantum Mechanics: Structures, Axioms and Paradoxes
Aerts, Diederik
Quantum Mechanics: Structures, Axioms and Paradoxes Diederik Aerts Center Leo Apostel, Brussels present an analysis of quantum mechanics and its problems and para- doxes taking into account the results a genuine incomplete- ness of standard quantum mechanics, however not an incompleteness that means
A Criterion for Holism in Quantum Mechanics
Seevinck, Michiel
A Criterion for Holism in Quantum Mechanics M.P Seevinck E-mail: M.P.Seevinck@phys.uu.nl Utrecht University, The Netherlands, August 2003. 1 #12; Motivation · The question whether or not quantum mechanics is it that makes quantum mechanics a holistic theory (if so), and other physical theories not (if so). · I propose
Entanglement and Disentanglement in Relativistic Quantum Mechanics
Stanford, Kyle
Entanglement and Disentanglement in Relativistic Quantum Mechanics Jeffrey A. Barrett August 16, 2014 Abstract A satisfactory formulation of relativistic quantum mechanics re- quires that one be able in relativistic quantum mechanics must ultimately depend on the details of one's strategy for addressing
QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT
Stanford, Kyle
QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT Abstract. The quantum measurement problem has led mechanics, a strong variety of mind-body dualism provides a natural criterion for when collapses occur, and in a no-collapse formulation of quantum mechanics, a strong variety of dualism provides a way to account
Probability in modal interpretations of quantum mechanics
Seevinck, Michiel
Probability in modal interpretations of quantum mechanics Dennis Dieks Institute for the History interpretations have the ambition to construe quantum mechanics as an ob- jective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix
Improving student understanding of quantum mechanics
NASA Astrophysics Data System (ADS)
Singh, Chandralekha
2015-04-01
Learning quantum mechanics is challenging for many students. We are investigating the difficulties that upper-level students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) and tools for peer-instruction. Many of the QuILTs employ computer simulations to help students visualize and develop better intuition about quantum phenomena. We will discuss the common students' difficulties and research-based tools we are developing to bridge the gap between quantitative and conceptual aspects of quantum mechanics and help students develop a solid grasp of quantum concepts. Support from the National Science Foundation is gratefully acknowledged.
Nielsen, Steven O.
The Postulates of Quantum Mechanics (from Quantum Mechanics by Claude Cohen-Tannoudji, Bernard Diu, and Franck Lalo¨e) Introduction The postulates of quantum mechanics are the theory. Their physical content to the following questions: (i) How is the state of a quantum mechanical system at a given time described
Paradoxical Reflection in Quantum Mechanics
Pedro L. Garrido; Sheldon Goldstein; Jani Lukkarinen; Roderich Tumulka
2011-05-03
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This phenomenon is suggested by non-normalizable solutions to the time-independent Schroedinger equation, and we present evidence, numerical and mathematical, that it is also indeed predicted by the time-dependent Schroedinger equation. Furthermore, this paradoxical reflection effect suggests, and we confirm mathematically, that a quantum particle can be trapped for a long time (though not forever) in a region surrounded by downward potential steps, that is, on a plateau.
Quantum mechanics and the psyche
NASA Astrophysics Data System (ADS)
Galli Carminati, G.; Martin, F.
2008-07-01
In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.
Lagrangian Densities and Principle of Least Action in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Kobe, Donald H.
2006-03-01
A Lagrangian density in terms of the wave function and its first derivatives can be used to derive the Schroedinger equation. From this Lagrangian density, we derive an equivalent one involving the Hamiltonian with second derivatives of the wave function that is commonly used in quantum mechanics. Using Hamilton's Principle of Least Action, we obtain the time-dependent Schroedinger equation by varying with respect to the wave function. For a time-independent Hamiltonian and a stationary-state trial wave function, the Principle of Least Action gives the usual Rayleigh-Ritz energy variational principle. Using a Hartree product trial wave function for a many-boson system, we apply the Principle of Least Action to obtain the time-dependent Gross-Pitaevski equation, a nonlinear Schroedinger equation that describes a Bose condensate.
The Transactional Interpretation of Quantum Mechanics and Quantum Nonlocality
John G. Cramer
2015-02-28
Quantum nonlocality is discussed as an aspect of the quantum formalism that is seriously in need of interpretation. The Transactional Interpretation of quantum mechanics, which describes quantum processes as transactional "handshakes" between retarded $\\psi$ waves and advanced $\\psi*$ waves, is discussed. Examples of the use of the Transactional Interpretation in resolving quantum paradoxes and in understanding the counter-intuitive aspects of the formalism, particularly quantum nonlocality, are provided.
The Mechanism of Quantum Computation
NASA Astrophysics Data System (ADS)
Castagnoli, Giuseppe
2008-08-01
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine whose coordinates are submitted to a nonfunctional relation representing all the problem constraints; moving an input part, reversibly and nondeterministically produces a solution through a many body interaction. The machine can be considered the many body generalization of another perfect machine, the bouncing ball model of reversible computation. The mathematical description of the machine’s motion, as it is, is applicable to quantum problem solving, an extension of the quantum algorithms that comprises the physical representation of the interdependence between the problem and the solution. The configuration space of the classical machine is replaced by the phase space of the quantum machine. The relation between the coordinates of the machine parts now applies to the populations of the reduced density operators of the parts of the computer register throughout state vector reduction. Thus, reduction produces the solution of the problem under a nonfunctional relation representing the problem-solution interdependence. At the light of this finding, the quantum speed up turns out to be “precognition” of the solution, namely the reduction of the initial ignorance of the solution due to backdating, to before running the algorithm, a part of the state vector reduction on the solution (a time-symmetric part in the case of unstructured problems); as such, it is bounded by state vector reduction through an entropic inequality. The computation mechanism under discussion might also explain the wholeness appearing in the introspective analysis of perception.
Supersymmetric Quantum Mechanics with Reflections
S. Post; L. Vinet; A. Zhedanov
2011-08-09
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wave functions of extended Scarf I potentials with different parameters are presented.
Complementarity in Categorical Quantum Mechanics
NASA Astrophysics Data System (ADS)
Heunen, Chris
2012-07-01
We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a `point-free' definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.
Quantum Field Theory for Mathematicians: Hamiltonian Mechanics and Symplectic
Woit, Peter
equations, known as Hamilton's equations dpi dt = - H qi dqi dt = H pi There is an obvious generalization moving on an arbitrary man- ifold M. For the special case N = Rn , = n i=1 pi dqi and the symplectic form is 0 = n i=1 dpi dqi Â· KÂ¨ahler manifolds. Special cases here include the sphere S2 = CP1 (with
Probability Distributions and Hilbert Spaces: Quantum and Classical Systems
V. I. Man'ko; G. Marmo
1999-03-04
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular class of linear Hamiltonian systems.
Effective equations for the quantum pendulum from momentous quantum mechanics
Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)
2012-08-24
In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Exploration of similarities between classical wave mechanics and quantum mechanics
Kim Fook Lee
2002-01-01
This dissertation explores classical analogs of one particle wave mechanics and multiparticle quantum entanglement by using classical wave optics. We develop classical measurement techniques to simulate one particle wave mechanics and quantum entanglement for up to four particles. Classical simulation of multi-particle entanglement is useful for quantum information processing (QIP) because much of the QIP does not require collapse and
Effective quantum-memory Hamiltonian from local two-body interactions
NASA Astrophysics Data System (ADS)
Hutter, Adrian; Pedrocchi, Fabio L.; Wootton, James R.; Loss, Daniel
2014-07-01
In Phys. Rev. A 88, 062313 (2013), 10.1103/PhysRevA.88.062313 we proposed and studied a model for a self-correcting quantum memory in which the energetic cost for introducing a defect in the memory grows without bounds as a function of system size. This positive behavior is due to attractive long-range interactions mediated by a bosonic field to which the memory is coupled. The crucial ingredients for the implementation of such a memory are the physical realization of the bosonic field as well as local five-body interactions between the stabilizer operators of the memory and the bosonic field. Here, we show that both of these ingredients appear in a low-energy effective theory of a Hamiltonian that involves only two-body interactions between neighboring spins. In particular, we consider the low-energy, long-wavelength excitations of an ordered Heisenberg ferromagnet (magnons) as a realization of the bosonic field. Furthermore, we present perturbative gadgets for generating the required five-spin operators. Our Hamiltonian involving only local two-body interactions is thus expected to exhibit self-correcting properties as long as the noise affecting it is in the regime where the effective low-energy description remains valid.
Quantum mechanical light harvesting mechanisms in photosynthesis
NASA Astrophysics Data System (ADS)
Scholes, Gregory
2012-02-01
More than 10 million billion photons of light strike a leaf each second. Incredibly, almost every red-coloured photon is captured by chlorophyll pigments and initiates steps to plant growth. Last year we reported that marine algae use quantum mechanics in order to optimize photosynthesis [1], a process essential to its survival. These and other insights from the natural world promise to revolutionize our ability to harness the power of the sun. In a recent review [2] we described the principles learned from studies of various natural antenna complexes and suggested how to utilize that knowledge to shape future technologies. We forecast the need to develop ways to direct and regulate excitation energy flow using molecular organizations that facilitate feedback and control--not easy given that the energy is only stored for a billionth of a second. In this presentation I will describe new results that explain the observation and meaning of quantum-coherent energy transfer. [4pt] [1] Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer, and Gregory D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature 463, 644-648 (2010).[0pt] [2] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro and Rienk van Grondelle, ``Lessons from nature about solar light harvesting'' Nature Chem. 3, 763-774 (2011).
Levitated Quantum Nano-Magneto-Mechanical Systems
Mauro Cirio; Jason Twamley; Gavin K. Brennen; Gerard J. Milburn
2011-01-01
Quantum nanomechanical sysems have attracted much attention as they provide new macroscopic platforms for the study of quantum mechanics but may also have applications in ultra-sensitive sensing, high precision measurements and in quantum computing. In this work we study the control and cooling of a quantum nanomechanical system which is magnetically levitated via the Meissner effect. Supercurrents in nano-sized superconducting
D. L. Mathine; S. Krishnan Myjak; G.N. Maracas
1995-01-01
A new technique for solving the BenDaniel-Duke Hamiltonian using a Fourier series method is discussed. This method Fourier transforms the effective mass and potential profiles to calculate the eigenenergies and probability densities in transform space. Numerical solutions of the eigenenergies of a rectangular quantum well are compared to the finite difference, finite element, and transfer matrix methods. The eigenenergies of
Quantum registers based on single NV + n 13C centers in diamond: I. The spin Hamiltonian method
A. P. Nizovtsev; S. Ya. Kilin; V. A. Pushkarchuk; A. L. Pushkarchuk; S. A. Kuten
2010-01-01
Details of the application of the spin Hamiltonian method for studying spin characteristics of a quantum register that includes an electron spin S = 1 of a single NV center in the ground electronic state and nuclear spins I = 1\\/2 of several isotopic atoms 13C located at different lattice sites near the vacancy of the NV center. Two methods
Quantum mechanical effects from deformation theory
Much, A. [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)
2014-02-15
We consider deformations of quantum mechanical operators by using the novel construction tool of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a role. Furthermore, a quantum plane can be defined by using the deformation techniques. This in turn gives an experimentally verifiable effect.
Teaching Quantum Mechanics on an Introductory Level.
ERIC Educational Resources Information Center
Muller, Rainer; Wiesner, Hartmut
2002-01-01
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
Quantum Mechanical Observers and Time Reparametrization Symmetry
Eiji Konishi
2012-12-20
We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their non-unitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.
Quantum Mechanical Observers and Time Reparametrization Symmetry
NASA Astrophysics Data System (ADS)
Konishi, Eiji
2012-07-01
We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their nonunitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.
Orthodox Quantum Mechanics Free from Paradoxes
Rodrigo Medina
2005-08-02
A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The classical paradoxes of quantum mechanics are analyzed and their origin is found to be the fictitious properties that are usually attributed to quantum-mechanical states. The hypothesis that any mixed state can always be considered as an incoherent superposition of pure states is found to contradict quantum mechanics. A solution of EPR paradox is proposed. It is shown that entanglement of quantum states is compatible with realism and locality of events, but implies non-local encoding of information.
Ab-Initio Hamiltonian Approach to Light Nuclei And to Quantum Field Theory
Vary, J.P.; /Iowa State U.; Honkanen, H.; /Iowa State U.; Li, Jun; /Iowa State U.; Maris, P.; /Iowa State U.; Shirokov, A.M.; /SINP, Moscow; Brodsky, S.J.; /SLAC /Stanford U., Phys. Dept.; Harindranath, A.; /Saha Inst.; de Teramond, G.F.; /Costa Rica U.; Ng, E.G.; /LBL, Berkeley; Yang, C.; /LBL, Berkeley; Sosonkina, M.; /Ames Lab
2012-06-22
Nuclear structure physics is on the threshold of confronting several long-standing problems such as the origin of shell structure from basic nucleon-nucleon and three-nucleon interactions. At the same time those interactions are being developed with increasing contact to QCD, the underlying theory of the strong interactions, using effective field theory. The motivation is clear - QCD offers the promise of great predictive power spanning phenomena on multiple scales from quarks and gluons to nuclear structure. However, new tools that involve non-perturbative methods are required to build bridges from one scale to the next. We present an overview of recent theoretical and computational progress with a Hamiltonian approach to build these bridges and provide illustrative results for the nuclear structure of light nuclei and quantum field theory.
Quantum Mechanics Joachim Burgdorfer and Stefan Rotter
Rotter, Stefan
1 1 Quantum Mechanics Joachim BurgdÂ¨orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution 29 1.8.3 Resonances 30 1.9 Semiclassical Mechanics 31 1.9.1 The WKB Approximation 31 1.9.2 The EBK
BOOK REVIEWS: Quantum Mechanics: Fundamentals
NASA Astrophysics Data System (ADS)
Whitaker, A.
2004-02-01
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried’s well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantum mechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell’s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried’s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried’s book. Gottfried had devoted a chapter of his book to these matters, titled ‘The Measurement Process and the Statistical Interpretation of Quantum Mechanics’. Gottfried considered the von Neumann or Dirac ‘collapse of state-vector’ (or ‘reduction postulate’ or ‘projection postulate’) was unsatisfactory, as he argued that it led inevitably to the requirement to include ‘consciousness’ in the theory. He replaced this by a more mathematically and conceptually sophisticated treatment in which, following measurement, the density matrix of the correlated measured and measuring systems, rho, is replaced by hat rho, in which the interference terms from rho have been removed. rho represents a pure state, and hat rho a mixture, but Gottfried argued that they are ‘indistinguishable’, and that we may make our replacement, ‘safe in the knowledge that the error will never be found’. Now our combined state is represented as a mixture, it is intuitive, Gottfried argued, to interpret it in a probabilistic way, |cm|2 being the probability of obtaining the mth measurement result. Bell liked Gottfried’s treatment little more than the cruder ‘collapse’ idea of von Neumann, and when, shortly before Bell’s death, his polemical article ‘Against measurement’ was published in the August 1990 issue of Physics World (pages 33-40), his targets included, not only Landau and Lifshitz’s classic Quantum Mechanics, pilloried for its advocacy of old-fashioned collapse, and a paper by van Kampen in Physica, but also Gottfried’s approach. Bell regarded his replacement of rho by hat rho as a ‘butchering’ of the density matrix, and considered, in any case, that even the butchered density matrix should represent co-existence of different terms, not a set of probabilities. Gottfried has replied to Bell ( Physics World, October 1991, pages 34-40; Nature 405, 533-36 (2000)). He has also become a major commentator on Bell’s work, for example editing the section on quantum foundations in the World Scientific edition of Bell’s collected works. Thus it is exceedingly interesting to disco
NASA Astrophysics Data System (ADS)
Jafari, Abolfazl
2014-10-01
We present a systematic study of the noncommutative interaction of gravitational waves with matter at the quantum mechanical level in the long wavelength and small velocity limit. In particular, the noncommutative quantum dynamics of the Landau's problem is employed to measure the transmission amplitudes in terms of the Riemann's tensor elements by a gravitational wave in linearized approximation. It turns out that the Hamiltonian of the charged particles derived based on DeWitt's approach is valid by the deformed electromagnetic fields.
Treating time travel quantum mechanically
NASA Astrophysics Data System (ADS)
Allen, John-Mark A.
2014-10-01
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilizing the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their nonlinearity and time-travel paradoxes. In particular, the "equivalent circuit model"—which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory—is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of alternate theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features—such as time-travel paradoxes, the ability to distinguish nonorthogonal states with certainty, and the ability to clone or delete arbitrary pure states—that are present with D-CTCs and P-CTCs. The problems with nonlinear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
Treating Time Travel Quantum Mechanically
John-Mark A. Allen
2014-10-10
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their non-linearity and time travel paradoxes. In particular, the "equivalent circuit model"---which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory---is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of new theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features---such as time travel paradoxes, the ability to distinguish non-orthogonal states with certainty, and the ability to clone or delete arbitrary pure states---that are present with D-CTCs and P-CTCs. The problems with non-linear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
The Linguistic Interpretation of Quantum Mechanics
Ishikawa, Shiro
2012-01-01
About twenty years ago, we proposed the mathematical formulation of Heisenberg's uncertainty principle, and further, we concluded that Heisenberg's uncertainty principle and EPR-paradox are not contradictory. This is true, however we now think that we should have argued about it under a certain firm interpretation of quantum mechanics. Recently we proposed the linguistic quantum interpretation (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy). In fact, we can consider that traditional philosophies have progressed toward quantum philosophy. In this paper, we first review the linguistic quantum interpretation, and further, clarify the relation between EPR-paradox and Heisenberg's uncertainty...
Errors and paradoxes in quantum mechanics
D. Rohrlich
2007-08-28
Errors and paradoxes in quantum mechanics, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear
The Konigsberg Interpretation Of Quantum Mechanics?
Horner, Jack K.
THE KÖNIGSBERG INTERPRETATION OF QUANTUM MECHANICS? Jack K. Horner It is surely a truism that the science and philos ophy of an age influence one another; and this century has been no exception: the rise of quantum theory in particular... against this criterion to show that the rejoinder must, if cogent, assume B. 1. The EPR argument. The object of the EPR argu ment Ts to show that the quantum theory fails to describe "completely" certain quantum-mechanical events. Provided...
Stability of pure states in quantum mechanics
Zloshchastiev, Konstantin G
2015-01-01
We demonstrate that quantum fluctuations can cause, under certain conditions, the instability of pure states. The degree and type of such instability are controlled by the environment-induced anti-Hermitian parts of Hamiltonians. This is drastically different from the Hermitian case where both the purity's value and pure states are preserved during time evolution. The instability of pure states is not preassigned in the evolution equation but arises as the emergent phenomenon in its solutions. In order to illustrate the different types of instability that may occur, we consider some exactly solvable two-state models which can be used in a theory of open quantum-optical and spin systems.
Stability of pure states in quantum mechanics
Konstantin G. Zloshchastiev
2015-05-13
We demonstrate that quantum fluctuations can cause, under certain conditions, the instability of pure states. The degree and type of such instability are controlled by the environment-induced anti-Hermitian parts of Hamiltonians. This is drastically different from the Hermitian case where both the purity's value and pure states are preserved during time evolution. The instability of pure states is not preassigned in the evolution equation but arises as the emergent phenomenon in its solutions. In order to illustrate the different types of instability that may occur, we consider some exactly solvable two-state models which can be used in a theory of open quantum-optical and spin systems.
Quantum Mechanics Dung-Hai Lee
Murayama, Hitoshi
Quantum Mechanics Dung-Hai Lee Summer 2000 #12;Contents 1 A brief reminder of linear Algebra 3 1 mechanics as Feynman path inte- grals in imaginary time . . . . . . . . . . . . . . . . . . . 47 3.14 From classical to quantum mechanics . . . . . . . . . . . 47 3.14.1 Route I
A Criterion for Holism in Quantum Mechanics
Seevinck, Michiel
A Criterion for Holism in Quantum Mechanics M.P Seevinck Utrecht University, The Netherlands, June 2003. 1 #12; Motivation · The question whether or not quantum mechanics (QM) gives rise to some mechanics a holistic theory (if so), and other physical theories not (if so). · I propose an operational
A Criterion for Holism in Quantum Mechanics
Seevinck, Michiel
A Criterion for Holism in Quantum Mechanics # M.P Seevinck # # Utrecht University, The Netherlands, June 2003. # 1 #12; # Motivation # . The question whether or not quantum mechanics (QM) gives rise mechanics a holistic theory (if so), and other physical theories not (if so). . I propose an operational
Quantum mechanics as a complete physical theory
D. A. Slavnov
2002-11-10
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that allow constructing a renewed mathematical scheme of quantum mechanics. This scheme involves the standard mathematical formalism of quantum mechanics. Simultaneously, it contains a mathematical object that adequately describes a single experiment. We give an example of the application of the proposed scheme.
Principles of a 2nd Quantum Mechanics
Mioara Mugur-Schächter
2014-10-23
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this representation as a reference-and-imbedding-structure, the foundations of an intelligible reconstruction of the Hilbert-Dirac formulation of Quantum Mechanics is developed. Inside this reconstruction the measurement problem as well as the other major problems raised by the quantum mechanical formalism, dissolve.
Bohmian particle trajectories contradict quantum mechanics
Michael Zirpel
2009-03-23
The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to avoid contradictions with quantum mechanics. There are correlations between particle positions at different times which cannot be reproduced with real particle trajectories. A simple rearrangement of an experimental test of the Bell-CHSH inequality demonstrates this.
Quantum Mechanics and Closed Timelike Curves
Florin Moldoveanu
2007-04-23
General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal region of space-time are investigated. If the correspondence principle is true, then all generalizations of quantum mechanics on acausal manifolds are not renormalizable. Therefore quantum mechanics can only be defined on global hyperbolic manifolds and all general relativity solutions exhibiting time travel are unphysical.
Non-Hermitian Hamiltonians and supersymmetric quantum Quentin Duret and Francois Gieres
Paris-Sud XI, Université de
quantum mechanics. PACS: 03.65.Ca, 03.65.Fd Key words: Non-Hermitian operators with real spectrum, PT such that H and H act in the same way and such that the domains of definition of H and H coincide. Somewhat biology, . . . - see the cited papers for precise refer- ences. In our presentation of the described
Deformation of supersymmetric and conformal quantum mechanics through affine transformations
NASA Technical Reports Server (NTRS)
Spiridonov, Vyacheslav
1993-01-01
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.
Bravyi, Sergey; DiVincenzo, David P; Loss, Daniel; Terhal, Barbara M
2008-08-15
We show how to map a given n-qubit target Hamiltonian with bounded-strength k-body interactions onto a simulator Hamiltonian with two-body interactions, such that the ground-state energy of the target and the simulator Hamiltonians are the same up to an extensive error O(epsilon n) for arbitrary small epsilon. The strength of the interactions in the simulator Hamiltonian depends on epsilon and k but does not depend on n. We accomplish this reduction using a new way of deriving an effective low-energy Hamiltonian which relies on the Schrieffer-Wolff transformation of many-body physics. PMID:18764519
Emergent Quantum Mechanics and Emergent Symmetries
Gerard't Hooft; Gerard t
2007-01-01
Quantum mechanics is ‘emergent’ if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such theories allow for a natural explanation of the existence of gauge equivalence classes (gauge orbits), including the equivalence classes
Kindergarten Quantum Mechanics: Lecture Notes
NASA Astrophysics Data System (ADS)
Coecke, Bob
2006-01-01
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in [3, 4]) which subsumes my Logic of Entanglement [11]. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes [12, 13]. In a last section we provide some pointers to the body of technical literature on the subject.
The auxiliary field method in quantum mechanics
Bernard Silvestre-Brac; Claude Semay; Fabien Buisseret
2012-06-20
The auxiliary field method is a new technique to obtain closed formulae for the solutions of eigenequations in quantum mechanics. The idea is to replace a Hamiltonian $H$ for which analytical solutions are not known by another one $\\tilde H$, including one or more auxiliary fields. For instance, a potential $V(r)$ not solvable is replaced by another one $P(r)$ more familiar, or a semirelativistic kinetic part is replaced by an equivalent nonrelativistic one. The approximation comes from the replacement of the auxiliary fields by pure real constants. The approximant solutions for $H$, eigenvalues and eigenfunctions, are then obtained by the solutions of $\\tilde H$ in which the auxiliary parameters are eliminated by an extremization procedure for the eigenenergies. If $H=T(\\bm p)+V(r)$ and if $P(r)$ is a power law, the approximate eigenvalues can be written $T(p_0)+V(r_0)$, where the mean impulsion $p_0$ is a function of the mean distance $r_0$ and where $r_0$ is determined by an equation which is linked to the generalized virial theorem. The general properties of the method are studied and the connections with the envelope theory presented. This method is first applied to nonrelativistic and semirelativistic two-body systems, with a great variety of potentials. Closed formulae are produced for energies, eigenstates, various observables and critical constants, with sometimes a very good accuracy. The method is then used to solve nonrelativistic and semirelativistic many-body systems with one-body and two-body interactions. For such cases, analytical solutions can only be obtained for systems of identical particles, but several systems of interest for atomic and hadronic physics are studied. General results concerning the many-body critical constants are presented, as well as duality relations existing between approximate and exact eigenvalues.
Thermodynamic integration from classical to quantum mechanics
Habershon, Scott [Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS (United Kingdom); Manolopoulos, David E. [Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ (United Kingdom)
2011-12-14
We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.
Tests of CPT and Quantum Mechanics: experiment
NASA Astrophysics Data System (ADS)
Ambrosino, F.; Antonelli, A.; Antonelli, M.; Bacci, C.; Barva, M.; Beltrame, P.; Bencivenni, G.; Bertolucci, S.; Bini, C.; Bloise, C.; Bocchetta, S.; Bocci, V.; Bossi, F.; Bowring, D.; Branchini, P.; Bulychjov, S. A.; Caloi, R.; Campana, P.; Capon, G.; Capussela, T.; Carboni, G.; Ceradini, F.; Cervelli, F.; Chi, S.; Chiefari, G.; Ciambrone, P.; Conetti, S.; De Lucia, E.; De Santis, A.; De Simone, P.; De Zorzi, G.; Dell'Agnello, S.; Denig, A.; Di Domenico, A.; Di Donato, C.; Di Falco, S.; Di Micco, B.; Doria, A.; Dreucci, M.; Farilla, A.; Felici, G.; Ferrari, A.; Ferrer, M. L.; Finocchiaro, G.; Fiore, S.; Forti, C.; Franzini, P.; Gatti, C.; Gauzzi, P.; Giovannella, S.; Gorini, E.; Graziani, E.; Incagli, M.; Kluge, W.; Kulikov, V.; Lacava, F.; Lanfranchi, G.; Lee-Franzini, J.; Leone, D.; Martemianov, M.; Martini, M.; Massarotti, P.; Matsyuk, M.; Mei, W.; Meola, S.; Messi, R.; Miscetti, S.; Moulson, M.; Müller, S.; Murtas, F.; Napolitano, M.; Nguyen, F.; Palutan, M.; Pasqualucci, E.; Passalacqua, L.; Passeri, A.; Patera, V.; Perfetto, F.; Pontecorvo, L.; Primavera, M.; Santangelo, P.; Santovetti, E.; Saracino, G.; Schamberger, R. D.; Sciascia, B.; Sciubba, A.; Scuri, F.; Sfiligoi, I.; Sibidanov, A.; Spadaro, T.; Spiriti, E.; Tabidze, M.; Testa, M.; Tortora, L.; Valente, P.; Valeriani, B.; Venanzoni, G.; Veneziano, S.; Ventura, A.; Ventura, S.; Versaci, R.; Villella, I.; Xu, G.; KLOE Collaboration
2007-05-01
Neutral kaons provide one of the systems most sensitive to quantum mechanics and CPT violation. Models predicting quantum mechanics violation, also related to CPT violation, have been tested at the CPLEAR and KLOE experiments. In this report results of CPLEAR obtained by studying the time evolution of single and two entangled kaons are reviewed. New or improved limits on decoherence and CPT violation parameters have been obtained by KLOE studying the quantum interference in the channel ??KK?????. No deviations from the expectations of quantum mechanics and CPT symmetry have been observed.
Experimental status of quaternionic quantum mechanics
S. P. Brumby; G. C. Joshi
1996-01-01
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic effects in
Quantum mechanics on a real Hilbert space
Jan Myrheim
1999-01-01
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics, keeping the same set of physical states, but admitting more general observables. The standard time reversal operator involves complex conjugation, in
On the quantum mechanics of supermembranes
Bernard de Wit; J. Hoppe; H. Nicolai
1988-01-01
We study the quantum-mechanical properties of a supermembrane and examine the nature of its ground state. A supersymmetric gauge theory of area-preserving transformations provides a convenient framework for this study. The supermembrane can be viewed as a limiting case of a class of models in supersymmetric quantum mechanics. Its mass does not depend on the zero modes and vanishes only
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Friday, June 19, 2009 #12;String Theory Origins We introduced string theory as a possible solution to our
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification that is naturally solved by string theory Strings vibrating in a variety of ways give rise to particles of different
Quantum mechanics in complex systems
NASA Astrophysics Data System (ADS)
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown. These nodes are spaced far enough from each other to minimized the electronic repulsion of the electrons, while still providing adequate enough attraction so as to bind the excess elections into orbitals. We have found that even with relativistic considerations these species are stably bound within the field. It was also found that performing the dimensional scaling calculations for systems within the confines of laser fields to be a much simpler and more cost-effective method than the supporting D=3 SCF method. The dimensional scaling method is general and can be extended to include relativistic corrections to describe the stability of simple molecular systems in super-intense laser fields. Chapter 3, we delineate the model, and aspects therein, of inelastic electron tunneling and map this model to the protein environment. G protein-coupled receptors (GPCRs) constitute a large family of receptors that sense molecules outside of a cell and activate signal transduction pathways inside the cell. Modeling how an agonist activates such a receptor is important for understanding a wide variety of physiological processes and it is of tremendous value for pharmacology and drug design. Inelastic electron tunneling spectroscopy (IETS) has been proposed as the mechanism by which olfactory GPCRs are activated by an encapsulated agonist. In this note we apply this notion to GPCRs within the mammalian nervous system using ab initio quantum chemical modeling. We found that non-endogenous agonists of the serotonin receptor share a singular IET spectral aspect both amongst each other and with the serotonin molecule: a peak that scales in intensity with the known agonist activities. We propose an experiential validation of this model by utilizing lysergic acid dimethylamide (DAM-57), an ergot derivative, and its isotopologues in which hydrogen atoms are replaced by deuterium. If validated our theory may provide new avenues for guided drug design and better in silico prediction of efficacies. Our final chapter, explores methods which may be explored to assist in the early instructio
An entropic picture of emergent quantum mechanics
D. Acosta; P. Fernandez de Cordoba; J. M. Isidro; J. L. G. Santander
2011-09-20
Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on space. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant h from Boltzmann's constant k.
Quantum registers based on single NV + n 13 C centers in diamond: I. The spin Hamiltonian method
A. P. Nizovtsev; S. Ya. Kilin; V. A. Pushkarchuk; A. L. Pushkarchuk; S. A. Kuten’
2010-01-01
Details of the application of the spin Hamiltonian method for studying spin characteristics of a quantum register that includes\\u000a an electron spin S = 1 of a single NV center in the ground electronic state and nuclear spins I = 1\\/2 of several isotopic atoms 13C located at different lattice sites near the vacancy of the NV center. Two methods
Quantum Mechanical Models Of The Fermi Shuttle
Sternberg, James [University of Tennessee, Department of Physics and Astronomy, Knoxville TN 37996 (United States)
2011-06-01
The Fermi shuttle is a mechanism in which high energy electrons are produced in an atomic collision by multiple collisions with a target and a projectile atom. It is normally explained purely classically in terms of the electron's orbits prescribed in the collision. Common calculations to predict the Fermi shuttle use semi-classical methods, but these methods still rely on classical orbits. In reality such collisions belong to the realm of quantum mechanics, however. In this paper we discuss several purely quantum mechanical calculations which can produce the Fermi shuttle. Being quantum mechanical in nature, these calculations produce these features by wave interference, rather than by classical orbits.
Time-averaged quantum dynamics and the validity of the effective Hamiltonian model
Gamel, Omar; James, Daniel F. V. [Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7 (Canada)
2010-11-15
We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the general equation to harmonic Hamiltonians, we confirm a previous formula for the effective Hamiltonian together with a additional decoherence term which should, in general, be included and whose vanishing provides the criteria for validity of the effective Hamiltonian approach. Finally, we apply the theory to examples of the ac Stark shift and three-level Raman transitions, recovering a decoherence effect in the latter.
Quantum-mechanical description of Lense-Thirring effect for relativistic scalar particles
Alexander J. Silenko
2014-08-10
Exact expression for the Foldy-Wouthuysen Hamiltonian of scalar particles is used for a quantum-mechanical description of the relativistic Lense-Thirring effect. The exact evolution of the angular momentum operator in the Kerr field approximated by a spatially isotropic metric is found. The quantum-mechanical description of the full Lense-Thirring effect based on the Laplace-Runge-Lenz vector is given in the nonrelativistic and weak-field approximation. Relativistic quantum-mechanical equations for the velocity and acceleration operators are obtained. The equation for the acceleration defines the Coriolis-like and centrifugal-like accelerations and presents the quantum-mechanical description of the frame-dragging effect.
Polymer Quantum Mechanics and its Continuum Limit
Alejandro Corichi; Tatjana Vukasinac; Jose A. Zapata
2007-08-22
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle and a simple cosmological model.
Superconformal Quantum Mechanics from M2-branes
Tadashi Okazaki
2015-03-12
We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a number of exotic and enlightening properties which do not occur in higher dimensional field theories. We see that superfield and superspace formalism is available for $\\mathcal{N}\\le 8$ superconformal mechanical models. We then discuss the M2-branes with a focus on the world-volume descriptions of the multiple M2-branes which are superconformal three-dimensional Chern-Simons matter theories. Finally we argue that the two topics are connected in M-theoretical construction by considering the multiple M2-branes wrapped around a compact Riemann surface and study the emerging IR quantum mechanics. We establish that the resulting quantum mechanics realizes a set of novel $\\mathcal{N}\\ge 8$ superconformal quantum mechanical models which have not been reached so far. Also we discuss possible applications of the superconformal quantum mechanics to mathematical physics.
NON-COMMUTATIVE SPHERES AND NUMERICAL QUANTUM MECHANICS
Arveson, William
NON-COMMUTATIVE SPHERES AND NUMERICAL QUANTUM MECHANICS basic issues that arise when one attempts to mo* *del quantum mechanical systems on a computer, quantum mechanics. Contributed to the proceedings of a NATO conference on operator algebras, ma
Suppressing Chaos of Warship Power System Based on the Quantum Mechanics Theory
NASA Astrophysics Data System (ADS)
Cong, Xinrong; Li, Longsuo
2014-08-01
Chaos control of marine power system is investigated by adding the Gaussian white noise to the system. The top Lyapunov exponent is computed to detect whether the classical system chaos or not, also the phase portraits are plotted to further verify the obtained results. The classical control of chaos and its quantum counterpart of the marine power system are investigated. The Hamiltonian of the controlled system is given to analyze the quantum counterpart of the classical system, which is based on the quantum mechanics theory.
Asplund, Erik; Kluener, Thorsten [Institut fuer Reine und Angewandte Chemie, Carl von Ossietzky Universitaet Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany)
2012-03-28
In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ({Dirac_h}/2{pi})=m{sub e}=e=a{sub 0}= 1, have been used unless otherwise stated.
Construction of the metric and equivalent Hermitian Hamiltonian via SUSY transformation operators
Shamshutdinova, V. V., E-mail: shvv@phys.tsu.ru [Tomsk State University (Russian Federation)
2012-10-15
The metric operator, which is the basic ingredient for studying a quantum system described by a pseudo-Hermitian Hamiltonian, provides the necessary means for obtaining an equivalent description of the system using a Hermitian Hamiltonian. In the framework of supersymmetric quantum mechanics, we propose a method of constructing the metric operator and to obtain the Hermitian Hamiltonian equivalent to the given pseudo-Hermitian.
OPTI 570A-Quantum Mechanics Course Description
Arizona, University of
OPTI 570A- Quantum Mechanics Course Description: This is a one-semester course designed to provide students with a solid understanding of quantum mechanics formalism, techniques, and important example physics, quantum optics, relativistic quantum mechanics and other advanced quantum mechanics topics
Dorit Aharonov; Umesh Vazirani
2012-06-16
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regime by extending the usual scientific paradigm to include {\\it interactive experiments}.
Aalok Pandya
2008-09-08
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.
Causal structure in categorical quantum mechanics
NASA Astrophysics Data System (ADS)
Lal, Raymond Ashwin
Categorical quantum mechanics is a way of formalising the structural features of quantum theory using category theory. It uses compound systems as the primitive notion, which is formalised by using symmetric monoidal categories. This leads to an elegant formalism for describing quantum protocols such as quantum teleportation. In particular, categorical quantum mechanics provides a graphical calculus that exposes the information flow of such protocols in an intuitive way. However, the graphical calculus also reveals surprising features of these protocols; for example, in the quantum teleportation protocol, information appears to flow `backwards-in-time'. This leads to question of how causal structure can be described within categorical quantum mechanics, and how this might lead to insight regarding the structural compatibility between quantum theory and relativity. This thesis is concerned with the project of formalising causal structure in categorical quantum mechanics. We begin by studying an abstract view of Bell-type experiments, as described by `no-signalling boxes', and we show that under time-reversal no-signalling boxes generically become signalling. This conflicts with the underlying symmetry of relativistic causal structure. This leads us to consider the framework of categorical quantum mechanics from the perspective of relativistic causal structure. We derive the properties that a symmetric monoidal category must satisfy in order to describe systems in such a background causal structure. We use these properties to define a new type of category, and this provides a formal framework for describing protocols in spacetime. We explore this new structure, showing how it leads to an understanding of the counter-intuitive information flow of protocols in categorical quantum mechanics. We then find that the formal properties of our new structure are naturally related to axioms for reconstructing quantum theory, and we show how a reconstruction scheme based on purification can be formalised using the structures of categorical quantum mechanics. Finally, we discuss the philosophical aspects of using category theory to describe fundamental physics. We consider a recent argument that category-theoretic formulations of physics, such as categorical quantum mechanics, can be used to support a variant of structural realism. We argue against this claim. The work of this thesis suggests instead that the philosophy of categorical quantum mechanics is subtler than either operationalism or realism.
NASA Astrophysics Data System (ADS)
Quesne, C.
2010-02-01
In a recent communication paper by Tremblay et al (2009 J. Phys. A: Math. Theor. 42 205206), it has been conjectured that for any integer value of k, some novel exactly solvable and integrable quantum Hamiltonian Hk on a plane is superintegrable and that the additional integral of motion is a 2kth-order differential operator Y2k. Here we demonstrate the conjecture for the infinite family of Hamiltonians Hk with odd k >= 3, whose first member corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination of the centre-of-mass motion. Our approach is based on the construction of some D2k-extended and invariant Hamiltonian {\\cal H}_k, which can be interpreted as a modified boson oscillator Hamiltonian. The latter is then shown to possess a D2k-invariant integral of motion {\\cal Y}_{2k}, from which Y2k can be obtained by projection in the D2k identity representation space.
NASA Astrophysics Data System (ADS)
Zhong, Wan-Xie; Ouyang, Hua-Jiang
1992-12-01
A fundamental theory is used to analyze anisotropic plane stress problems. First, we construct the generalized variational principle for the entire Hamiltonian system, and obtain the Hamiltonian differential operator matrix; then eigenproblem is solved. Finally, the process of obtaining analytical solutions and semianalytical solutions for anisotropic plane stress problems on a rectangular area is presented.
Four-dimensional understanding of quantum mechanics
Jarek Duda
2009-10-14
In this paper I will try to convince that quantum mechanics does not have to lead to indeterminism, but is just a natural consequence of four-dimensional nature of our world - that for example particles shouldn't be imagined as 'moving points' in space, but as their trajectories in the spacetime like in optimizing action formulation of Lagrangian mechanics. There will be analyzed simplified model - Boltzmann distribution among trajectories occurs to give quantum mechanic like behavior - for example electron moving in proton's potential would make some concrete trajectory which average exactly to the probability distribution of the quantum mechanical ground state. We will use this model to build intuition about quantum mechanics and discuss its generalizations to get some effective approximation of physics. We will see that topological excitations of the simplest model obtained this way already creates known from physics particle structure, their decay modes and electromagnetic/gravitational interactions between them.
Is quantum field theory a generalization of quantum mechanics?
A. V. Stoyanovsky
2009-01-01
We construct a mathematical model analogous to quantum field theory, but without the notion of vacuum and without measurable physical quantities. This model is a direct mathematical generalization of scattering theory in quantum mechanics to path integrals with multidimensional trajectories (whose mathematical interpretation has been given in a previous paper). In this model the normal ordering of operators in the
Chem 7940 Quantum Mechanics II Spring 2010 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2010 Chemistry 7940 Quantum Mechanics II Spring 2010 Mechanics in Chemistry (Dover reprint). [8] D. J. Tannor, Introduction to Quantum Mechanics: a Time. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940 Quantum Mechanics II Spring 2013 Mechanics in Chemistry (Dover reprint). [6] P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
Visual Quantum Mechanics: Online Interactive Programs
NSDL National Science Digital Library
The Visual Quantum Mechanics project, from the Physics Education Group of Kansas State University's Department of Physics, develops innovative ways to "introduce quantum physics to high school and college students who do not have a background in modern physics or higher level math." Funded by the National Science Foundation, this resource for educators provides interactive computer visualizations and animations that introduce quantum mechanics. The interactive programs (which require Shockwave) include a spectroscopy lab suite, a probability illustrator, an energy band creator, quantum tunneling, a color creator (a Java version is also available), a wave function sketcher, a wave packet explorer, an energy diagram explorer, a diffraction suite, and a hydrogen spectroscopy program. These online demonstrations should prove to be excellent visual, hands-on teaching aids when introducing concepts involving quantum mechanics. Users can download Shockwave at the site.
Spin-flavor oscillations of Dirac neutrinos described by relativistic quantum mechanics
Dvornikov, M. S., E-mail: maxdvo@izmiran.ru [Russian Academy of Sciences, Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radiowave Propagation (Russian Federation)
2012-02-15
Spin-flavor oscillations of Dirac neutrinos in matter and a magnetic field are studied using the method of relativistic quantum mechanics. Using the exact solution of the wave equation for a massive neutrino, taking into account external fields, the effective Hamiltonian governing neutrino spin-flavor oscillations is derived. Then the The consistency of our approach with the commonly used quantum mechanical method is demonstrated. The obtained correction to the usual effective Hamiltonian results in the appearance of the new resonance in neutrino oscillations. Applications to spin-flavor neutrino oscillations in an expanding envelope of a supernova are discussed. In particular, transitions between right-polarized electron neutrinos and additional sterile neutrinos are studied for realistic background matter and magnetic field distributions. The influence of other factors such as the longitudinal magnetic field, the matter polarization, and the non-standard contributions to the neutrino effective potential, is also analyzed.
On Wigner functions and a damped star product in dissipative phase-space quantum mechanics
Belchev, B. [Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive West, Lethbridge, Alta., T1K 3M4 (Canada)], E-mail: borislav.belchev@uleth.ca; Walton, M.A. [Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive West, Lethbridge, Alta., T1K 3M4 (Canada)], E-mail: walton@uleth.ca
2009-03-15
Dito and Turrubiates recently introduced an interesting model of the dissipative quantum mechanics of a damped harmonic oscillator in phase space. Its key ingredient is a non-Hermitian deformation of the Moyal star product with the damping constant as deformation parameter. We compare the Dito-Turrubiates scheme with phase-space quantum mechanics (or deformation quantization) based on other star products, and extend it to incorporate Wigner functions. The deformed (or damped) star product is related to a complex Hamiltonian, and so necessitates a modified equation of motion involving complex conjugation. We find that with this change the Wigner function satisfies the classical equation of motion. This seems appropriate since non-dissipative systems with quadratic Hamiltonians share this property.
Playing Games with Quantum Mechanics
Simon J. D. Phoenix; Faisal Shah Khan
2012-02-22
We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence. We call such games playable. By focusing on the notion of playability for games we can more clearly see the distinction between classical and quantum games and tackle the thorny issue of what it means to quantize a game. The approach we take can more properly be thought of as gaming the quantum rather than quantizing a game and we find that in this perspective we can think of a complete quantum game, for a given set of preferences, as representing a single family of quantum games with many different playable versions. The versions of Quantum Prisoners Dilemma presented in the literature can therefore be thought of specific instances of the single family of Quantum Prisoner's Dilemma with respect to a particular measurement. The conditions for equilibrium are given for playable quantum games both in terms of expected outcomes and a geometric approach. We discuss how any quantum game can be simulated with a classical game played with classical coins as far as the strategy selections and expected outcomes are concerned.
Quantum mechanics and the generalized uncertainty principle
NASA Astrophysics Data System (ADS)
Bang, Jang Young; Berger, Micheal S.
2006-12-01
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
Local quantum mechanics with finite Planck mass
M Kozlowski; J. Marciak -Kozlowska; M. pelc
2007-04-20
In this paper the motion of quantum particles with initial mass m is investigated. The quantum mechanics equation is formulated and solved. It is shown that the wave function contains the component which is depended on the gravitation fine structure constant
The Compton effect: Transition to quantum mechanics
R. H. Stuewer
2000-01-01
The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite
Quantum Mechanics and the Generalized Uncertainty Principle
Jang Young Bang; Micheal S. Berger
2006-11-30
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
Quantum Mechanics and Multiply Connected Spaces
B. G. Sidharth
2006-05-16
t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of the fact that Quantum Theory is actually a theory in multiply connected space while Classical Theory operates in simply connected space.
Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist
Castro, P. G. [DM/ICE/UFJF, Campus Universitario, cep 36036-330, Juiz de Fora (Brazil); Kullock, R.; Toppan, F. [TEO/CBPF, Rua Dr. Xavier Sigaud 150, cep 22290-180, Rio de Janeiro (Brazil)
2011-06-15
Nonrelativistic quantum mechanics and conformal quantum mechanics are deformed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called 'unfolded formalism' discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the universal enveloping algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed two-particle Hamiltonian, is composed of bosonic particles.
SUSY approach to Pauli Hamiltonians with an axial symmetry
NASA Astrophysics Data System (ADS)
Ioffe, M. V.; Kuru, S.; Negro, J.; Nieto, L. M.
2006-06-01
A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second-order symmetries is considered. After separation of variables, the one-dimensional matrix Hamiltonian is analysed from the point of view of supersymmetric quantum mechanics. Attention is paid to the discrete symmetries of the Hamiltonian and also to the Hamiltonian hierarchies generated by intertwining operators. The spectrum is studied by means of the associated matrix shape invariance. The relation between the intertwining operators and the second-order symmetries is established, and the full set of ladder operators that complete the dynamical algebra is constructed.
Student Difficulties in Learning Quantum Mechanics.
ERIC Educational Resources Information Center
Johnston, I. D.; Crawford, K.; Fletcher, P. R.
1998-01-01
Reports on a preliminary project that uses a phenomenographic approach to explore the ways in which a small number of fundamental ideas are conceptualized by students who are judged to have mastered quantum mechanics material. (DDR)
A quantum mechanical investigation of silsesquioxane cages
Earley, C.W. [Univ. of Missouri, Kansas City, MO (United States)
1994-09-01
A quantum mechanical investigation of molecular silsesquioxane cages determined that molecules containing (Si-O-){sub 3} rings were more unstable than those with larger rings. 49 refs., 2 figs., 4 tabs.
Scattering in conformally invariant quantum mechanics
Oksak, A.I.
1986-08-01
The S matrix conformally invariant quantum mechanics is determined by the multiple valuedness of the representation of the conformal group (i.e., by the operator that realizes conformal rotation through angle 2..pi..).
Beyond Quantum Mechanics and General Relativity
Andrea Gregori
2010-02-24
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
Quantum mechanical streamlines. I - Square potential barrier
NASA Technical Reports Server (NTRS)
Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.
1974-01-01
Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.
Remarks on Quantum Mechanics Norbert Dragon
Dragon, Norbert
Remarks on Quantum Mechanics Norbert Dragon #12;Intended as completion, repetition and comment once: //www.itp.uni-hannover.de/~dragon. I am grateful for feedback concerning errors, including type slips
Is quantum field theory a generalization of quantum mechanics?
A. V. Stoyanovsky
2009-09-10
We construct a mathematical model analogous to quantum field theory, but without the notion of vacuum and without measurable physical quantities. This model is a direct mathematical generalization of scattering theory in quantum mechanics to path integrals with multidimensional trajectories (whose mathematical interpretation has been given in a previous paper). In this model the normal ordering of operators in the Fock space is replaced by the Weyl-Moyal algebra. This model shows to be useful in proof of various results in quantum field theory: one first proves these results in the mathematical model and then "translates" them into the usual language of quantum field theory by more or less "ugly" procedures.
Aalok Pandya
2009-01-19
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of probability in Quantum Mechanics and its interpretations. We give yet another interpretation to the notion of Faraday lines and loops as the locus of probability flow. Also, the possibilities of visualization of spectra of area operators by means of classical geometric forms and conventional Quantum Mechanics are explored.
Experimental status of quaternionic quantum mechanics
Brumby, S P
1996-01-01
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic effects in correlated multi-particle systems. We set out how such experiments might distinguish between the several quaternionic models proposed in the literature.
Experimental status of quaternionic quantum mechanics
S. P. Brumby; G. C. Joshi
1996-10-08
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic effects in correlated multi-particle systems. We set out how such experiments might distinguish between the several quaternionic models proposed in the literature.
Epistemic cognition: issues in learning quantum mechanics
NASA Astrophysics Data System (ADS)
Oliver, Keith; Bao, Lei
2001-10-01
Epistemology is the branch of philosophy concerned with the nature and justification of knowledge. Epistemic cognition is thinking about the general methodologies and epistemological/philosophical views about learning. Quantum mechanics is the branch of physics that involves a fundamental uncertainty and that is being continuously developed and argued both theoretically and practically. We will illustrate the potential opportunity quantum mechanics presents us in discussing epistemic issues with our students and in exploring the nature of student epistemology.
Some mutant forms of quantum mechanics
NASA Astrophysics Data System (ADS)
Takeuchi, Tatsu; Chang, Lay Nam; Lewis, Zachary; Minic, Djordje
2012-12-01
We construct a 'mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative 'mutation' is also suggested.
Quantum mechanics in de Sitter space
Subir Ghosh; Salvatore Mignemi
2011-01-25
We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however of the order of the ratio between the length scale of the quantum mechanical system and the de Sitter radius, and therefore exceedingly small. Nevertheless, the existence of effects due to the large scale curvature of spacetime in atomic experiments has a theoretical relevance.
CLNS 96/1399 Peculiarities of Quantum Mechanics
CLNS 96/1399 Peculiarities of Quantum Mechanics: Origins and Meaning Yuri F. Orlov Floyd R. Newman, specifically quantum, features of quantum mechanics --- quan tum nonlocality, indeterminism, interference are quantum observables themselves and are represented in quantum mechanics by density matrices of pure states
Theoretical Chemistry I Quantum Mechanics 16 October 2008
Pfeifer, Holger
Theoretical Chemistry I Quantum Mechanics Axel Groß 16 October 2008 #12;#12;Preface Theoretical Chemistry 1 Quantum Mechanics Prof. Dr. Axel Groß Phone: 5022819 Room No.: O25/342 Email: axel of Quantum Mechanics 3. Quantum Dynamics 4. Angular Momentum 5. Approximation Methods 6. Symmetry in Quantum
On a New Form of Quantum Mechanics (II)
N. Gorobey; A. Lukyanenko; I. Lukyanenko
2009-12-16
The correspondence of a new form of quantum mechanics based on a quantum version of the action principle, which was proposed earlier [arXiv:0807.3508], with the ordinary quantum mechanics is established. New potentialities of the quantum action principle in the interpretation of quantum mechanics are considered.
N=4 Supersymmetric Quantum Mechanics with Magnetic Monopole
Soon-Tae Hong; Joohan Lee; Tae Hoon Lee; Phillial Oh
2005-07-20
We propose an N=4 supersymmetric quantum mechanics of a charged particle on a sphere in the background of Dirac magnetic monopole and study the system using the CP(1) model approach. We explicitly calculate the symmetry algebra taking the operator ordering ambiguity into consideration. We find that it is given by the superalgebra SU(1|2)x SU(2). We show that the Hamiltonian can be written in terms of the Casimir invariant of SU(2). Using this relation and the lower bound for angular momentm we obtain the energy spectrum. We then examine the ground energy sector to find that the N=4 supersymmetry is spontaneously broken to N=2 for certain values of the monopole charge.
Mechanical systems in the quantum regime
Menno Poot; Herre S. J. van der Zant
2011-10-12
Mechanical systems are ideal candidates for studying quantumbehavior of macroscopic objects. To this end, a mechanical resonator has to be cooled to its ground state and its position has to be measured with great accuracy. Currently, various routes to reach these goals are being explored. In this review, we discuss different techniques for sensitive position detection and we give an overview of the cooling techniques that are being employed. The latter include sideband cooling and active feedback cooling. The basic concepts that are important when measuring on mechanical systems with high accuracy and/or at very low temperatures, such as thermal and quantum noise, linear response theory, and backaction, are explained. From this, the quantum limit on linear position detection is obtained and the sensitivities that have been achieved in recent opto and nanoelectromechanical experiments are compared to this limit. The mechanical resonators that are used in the experiments range from meter-sized gravitational wave detectors to nanomechanical systems that can only be read out using mesoscopic devices such as single-electron transistors or superconducting quantum interference devices. A special class of nanomechanical systems are bottom-up fabricated carbon-based devices, which have very high frequencies and yet a large zero-point motion, making them ideal for reaching the quantum regime. The mechanics of some of the different mechanical systems at the nanoscale is studied. We conclude this review with an outlook of how state-of-the-art mechanical resonators can be improved to study quantum {\\it mechanics}.
The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum Mechanics
P. Garbaczewski; J. R. Klauder; R. Olkiewicz
1995-05-09
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schr\\"{o}dinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feyman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard "free" case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schr\\"{o}dinger problem, the "free noise" can also be extended to any infinitely divisible probability law, as covered by the L\\'{e}vy-Khintchine formula. Since the relativistic Hamiltonians $|\
Carlos Mochon
2007-04-14
Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of these shortest paths leads to lower bounds of the original unitary oracle problem. A number of example Hamiltonian oracles are studied in this paper, including oracle interrogation and the problem of computing the XOR of the hidden bits. Both of these problems are related to the study of geodesics on spheres with non-round metrics. For the case of two hidden bits a complete description of the geodesics is given. For n hidden bits a simple lower bound is proven that shows the problems require a query time proportional to n, even in the continuum limit. Finally, the problem of continuous Grover search is reexamined leading to a modest improvement to the protocol of Farhi and Gutmann.
Quantum Information Theory and the Foundations of Quantum Mechanics
Christopher Gordon Timpson
2004-12-08
This thesis is a contribution to the debate on the implications of quantum information theory for the foundations of quantum mechanics. In Part 1, the logical and conceptual status of various notions of information is assessed. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings `information' functions as an abstract noun, hence does not refer to a particular or substance (the worth of this point is illustrated in application to quantum teleportation). The claim that `Information is Physical' is assessed and argued to face a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. The reflections of Bruckner and Zeilinger (2001) and Deutsch and Hayden (2000) on the nature of information in quantum mechanics are critically assessed and some results presented on the characterization of entanglement in the Deutsch-Hayden formalism. Some philosophical aspects of quantum computation are discussed and general morals drawn concerning the nature of quantum information theory. In Part II, following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger's (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, Bub and Halvorson (2003) is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.
Jingwen Chen; Willie J. G. M. Peijnenburg; Liansheng Wang
1998-01-01
Based on the descriptors computed by the PM3 hamiltonian and the application of factor analysis and multiple regression analysis, several Quantitative Structure-Property Relationship (QSPR) equations for disappearance quantum yields of 45 substituted halogen compounds were obtained. After the exclusion of the outliers, the remaining two QSPR equations can be used to predict disappearance quantum yields for compounds with similar structure.
Testing foundations of quantum mechanics with photons
NASA Astrophysics Data System (ADS)
Shadbolt, Peter; Mathews, Jonathan C. F.; Laing, Anthony; O'Brien, Jeremy L.
2014-04-01
Quantum mechanics continues to predict effects at odds with a classical understanding of nature. Experiments with light at the single-photon level have historically been at the forefront of fundamental tests of quantum theory and the current developments in photonic technologies enable the exploration of new directions. Here we review recent photonic experiments to test two important themes in quantum mechanics: wave-particle duality, which is central to complementarity and delayed-choice experiments; and Bell nonlocality, where the latest theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different experiments.
Quantum mechanics: Passage through chaos
Daniel A. Steck
2009-01-01
A quantum system can undergo tunnelling even without a barrier to tunnel through. The latest experiments visualize this process in exquisite detail, completely reconstructing the state of the evolving system.
Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series
Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series: From Quantum Mechanics one component at a time. · Planck's constant determines the scale at which quantum mechanical effects could get rid of quantum mechanical effects The "wavelength" of particles given by h mv would all
Chem 7940 Quantum Mechanics II Spring 2011 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2011 Chemistry 7940 Quantum Mechanics II Spring 2011 in Chemistry (Dover reprint). [8] D. J. Tannor, Introduction to Quantum Mechanics: a Time-Dependent Perspective. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
Chem 7940 Quantum Mechanics II Spring 2012 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2012 Chemistry 7940 Quantum Mechanics II Spring 2012 Theory (Dover reprint). [6] G.C. Schatz and M.A. Ratner, Quantum Mechanics in Chemistry (Dover reprint. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
The Möbius Symmetry of Quantum Mechanics
Alon E. Faraggi; Marco Matone
2015-02-16
The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under $D$--dimensional M\\"obius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global M\\"obius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the M\\"obius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.
Probability in modal interpretations of quantum mechanics
Dennis Dieks
2007-03-02
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from introducing new structure by hand. In this paper we explain how this programme can be made concrete. In particular, we show that the Born probability rule, and sets of definite-valued observables to which the Born probabilities pertain, can be uniquely defined from the quantum state and Hilbert space structure. We discuss the status of probability in modal interpretations, and to this end we make a comparison with many-worlds alternatives. An overall point that we stress is that the modal ideas define a general framework and research programme rather than one definite and finished interpretation.
Zheng Wang; Peter Goldsmith; Jason Gu
2009-01-01
We consider the control of Port-Controlled Hamiltonian (PCH) systems, which are a generalization of Euler-Lagrange Systems. A new matching equation for PCH systems is developed so that interconnection damping assignment passivity-based control (IDA-PBC) can be extended to the regulation of some underactuated PCH systems whosekinetic energy must be modified. A simple underactuated mechanical system (the inertial wheel pendulum) is used
New approach to nonperturbative quantum mechanics with minimal length uncertainty
NASA Astrophysics Data System (ADS)
Pedram, Pouria
2012-01-01
The existence of a minimal measurable length is a common feature of various approaches to quantum gravity such as string theory, loop quantum gravity, and black-hole physics. In this scenario, all commutation relations are modified and the Heisenberg uncertainty principle is changed to the so-called Generalized (Gravitational) Uncertainty Principle (GUP). Here, we present a one-dimensional nonperturbative approach to quantum mechanics with minimal length uncertainty relation which implies X=x to all orders and P=p+(1)/(3)?p3 to first order of GUP parameter ?, where X and P are the generalized position and momentum operators and [x,p]=i?. We show that this formalism is an equivalent representation of the seminal proposal by Kempf, Mangano, and Mann and predicts the same physics. However, this proposal reveals many significant aspects of the generalized uncertainty principle in a simple and comprehensive form and the existence of a maximal canonical momentum is manifest through this representation. The problems of the free particle and the harmonic oscillator are exactly solved in this GUP framework and the effects of GUP on the thermodynamics of these systems are also presented. Although X, P, and the Hamiltonian of the harmonic oscillator all are formally self-adjoint, the careful study of the domains of these operators shows that only the momentum operator remains self-adjoint in the presence of the minimal length uncertainty. We finally discuss the difficulties with the definition of potentials with infinitely sharp boundaries.
Quantum mechanics: last stop for reductionism
Gabriele Carcassi
2012-03-16
The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a complex vector space, used in quantum mechanics.
Adrian Faigon
2007-11-01
Mechanics can be founded on a principle relating the uncertainty delta-q in the trajectory of an observable particle to its motion relative to the observer. From this principle, p.delta-q=const., p being the q-conjugated momentum, mechanical laws are derived and the meaning of the Lagrangian and Hamiltonian functions are discussed. The connection between the presented principle and Hamilton's Least Action Principle is examined. Wave mechanics and Schrodinger equation appear without additional assumptions by choosing the representation for delta-q in the case the motion is not trajectory describable. The Cramer-Rao inequality serves that purpose. For a particle hidden from direct observation, the position uncertainty determined by the enclosing boundaries leads to thermodynamics in a straightforward extension of the presented formalism. The introduction of uncertainty in classical mechanics formulation enables the translation of mechanical laws into the wide ranging conceptual framework of information theory. The boundaries between classical mechanics, thermodynamics and quantum mechanics are defined in terms of informational changes associated with the system evolution. As a direct application of the proposed formulation upper bounds for the rate of information transfer are derived.
Foster, Mark P.
11 1 Introduction to quantum mechanics Quantum mechanics is the basic tool needed to describe, understand and devise NMR experiments. Fortunately for NMR spectroscopists, the quantum mechanics of nuclear mathematical concepts frequently encountered in quantum mechanics and NMR. 0DWKHPDWLFDO FRQFHSWV 1.1.1 Complex
Quantum Lyapunov Control Based on the Average Value of an Imaginary Mechanical Quantity
Shuang Cong; Fangfang Meng; Sen Kuang
2013-05-17
The convergence of closed quantum systems in the degenerate cases to the desired target state by using the quantum Lyapunov control based on the average value of an imaginary mechanical quantity is studied. On the basis of the existing methods which can only ensure the single-control Hamiltonian systems converge toward a set, we design the control laws to make the multi-control Hamiltonian systems converge to the desired target state. The convergence of the control system is proved, and the convergence to the desired target state is analyzed. How to make these conditions of convergence to the target state to be satisfied is proved or analyzed. Finally, numerical simulations for a three level system in the degenrate case transfering form an initial eigenstate to a target superposition state are studied to verify the effectiveness of the proposed control method.
Local Currents for a Deformed Algebra of Quantum Mechanics with a Fundamental Length Scale
Gerald A. Goldin; Sarben Sarkar
2006-01-31
We explore some explicit representations of a certain stable deformed algebra of quantum mechanics, considered by R. Vilela Mendes, having a fundamental length scale. The relation of the irreducible representations of the deformed algebra to those of the (limiting) Heisenberg algebra is discussed, and we construct the generalized harmonic oscillator Hamiltonian in this framework. To obtain local currents for this algebra, we extend the usual nonrelativistic local current algebra of vector fields and the corresponding group of diffeomorphisms, modeling the quantum configuration space as a commutative spatial manifold with one additional dimension.
NASA Astrophysics Data System (ADS)
Illera, S.; Prades, J. D.; Cirera, A.
2015-05-01
The role of different charge transport mechanisms in Si / Si O 2 structures has been studied. A theoretical model based on the Transfer Hamiltonian Formalism has been developed to explain experimental current trends in terms of three different elastic tunneling processes: (1) trap assisted tunneling; (2) transport through an intermediate quantum dot; and (3) direct tunneling between leads. In general, at low fields carrier transport is dominated by the quantum dots whereas, for moderate and high fields, transport through deep traps inherent to the SiO2 is the most relevant process. Besides, current trends in Si / Si O 2 superlattice structure have been properly reproduced.
Intrusion Detection with Quantum Mechanics: A Photonic Quantum Fence
Humble, Travis S [ORNL; Bennink, Ryan S [ORNL; Grice, Warren P [ORNL; Owens, Israel J [Los Alamos National Laboratory (LANL)
2008-01-01
We describe the use of quantum-mechanically entangled photons for sensing intrusions across a physical perimeter. Our approach to intrusion detection uses the no-cloning principle of quantum information science as protection against an intruder s ability to spoof a sensor receiver using a classical intercept-resend attack. We explore the bounds on detection using quantum detection and estimation theory, and we experimentally demonstrate the underlying principle of entanglement-based detection using the visibility derived from polarization-correlation measurements.
Operational measurements in quantum mechanics
NASA Astrophysics Data System (ADS)
Kocha?ski, Piotr; Wódkiewicz, Krzysztof
1997-10-01
The operational approach to quantum measurements is formulated in terms of a phase space propensity and the corresponding positive operator-valued measure. This general approach is illustrated by an operational measurement of the position and momentum of a particle, and by an operational Malus measurement of spin phases.
Quantum mechanism of Biological Search
Younghun Kwon
2006-05-09
We wish to suggest an algorithm for biological search including DNA search. Our argument supposes that biological search be performed by quantum search.If we assume this, we can naturally answer the following long lasting puzzles such that "Why does DNA use the helix structure?" and "How can the evolution in biological system occur?".
ERIC Educational Resources Information Center
Oss, Stefano; Rosi, Tommaso
2015-01-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many…
Levitated Quantum Nano-Magneto-Mechanical Systems
NASA Astrophysics Data System (ADS)
Cirio, Mauro; Twamley, Jason; Brennen, Gavin K.; Milburn, Gerard J.
2011-03-01
Quantum nanomechanical sysems have attracted much attention as they provide new macroscopic platforms for the study of quantum mechanics but may also have applications in ultra-sensitive sensing, high precision measurements and in quantum computing. In this work we study the control and cooling of a quantum nanomechanical system which is magnetically levitated via the Meissner effect. Supercurrents in nano-sized superconducting loops give rise to a motional restoring force (trap), when placed in an highly inhomogenous magnetic field and can yield complete trapping of all translational and rotational motions of the levitated nano-object with motional oscillation frequencies ? ~ 10 - 100 MHz. As the supercurrents experience little damping this system will possess unprecendented motional quality factors, with Qmotion ~109 -1013 , and motional superposition states may remain coherent for days. We describe how to execute sideband cooling through inductive coupling to a nearby flux qubit, cooling the mechanical motion close to the ground state.
Nonrelativistic Quantum Mechanics with Fundamental Environment
NASA Astrophysics Data System (ADS)
Gevorkyan, Ashot S.
2011-03-01
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ? R { ?}, where R 3 and R { ?} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.
Creation mechanism of quantum accelerator modes
NASA Astrophysics Data System (ADS)
Ahmadi, P.; Behinaein, G.; Ramareddy, V.; Summy, G. S.
2009-11-01
We investigate the creation mechanism of quantum accelerator modes which are attributed to the existence of the stability islands in an underlying pseudoclassical phase space of the quantum delta-kicked accelerator. Quantum accelerator modes can be created by exposing a Bose-Einstein condensate to a pulsed standing light wave. We show that constructive interference between momentum states populated by the pulsed light determines the stability island’s existence in the underlying pseudoclassical phase space. We generalize this interference model to incorporate higher-order accelerator modes, showing that they are generated if the rephasing occurs after multiple pulses. The model is extended to predict the momentum structure of the quantum accelerator modes close to higher-order quantum resonances. These predictions are in good agreement with our experimental observations.
Coherent states in noncommutative quantum mechanics
J Ben Geloun; F G Scholtz
2009-01-21
Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position uncertainty relation, obey a Poisson distribution and possess a flat geometry. Using the natural isometry between the quantum Hilbert space of Hilbert Schmidt operators and the tensor product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.
Coherent states in noncommutative quantum mechanics
Ben Geloun, J. [National Institute for Theoretical Physics, Private Bag X1, Matieland 7602 (South Africa); International Chair of Mathematical Physics and Applications (ICMPA-UNESCO Chair) 072 B.P. 50 Cotonou (Benin); Departement de Mathematiques et Informatique, Faculte des Sciences et Techniques, Universite Cheikh Anta Diop (Senegal); Scholtz, F. G. [National Institute for Theoretical Physics, Private Bag X1, Matieland 7602 (South Africa)
2009-04-15
Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position uncertainty relation, obey a Poisson distribution, and possess a flat geometry. Using the natural isometry between the quantum Hilbert space of Hilbert-Schmidt operators and the tensor product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.
Green's Functions and Their Applications to Quantum Mechanics
Morrow, James A.
Green's Functions and Their Applications to Quantum Mechanics Jeff Schueler June 2, 2011 Contents 1 Green's Functions in Quantum Mechanics and Many-body Theory 8 3.1 Time Independent Green's Fuctions, specifically in how they apply to quantum mechan- ics. I plan to introduce some of the fundamentals of quantum
CLNS 96/1443 Peculiarities of Quantum Mechanics
CLNS 96/1443 REVISED Peculiarities of Quantum Mechanics: Origins and Meaning 1 Yuri F. Orlov Floyd The most peculiar, specifically quantum, features of quantum mechanics --- quan tum nonlocality mechanics 1 This paper, to be presented to the Nordic Symposium on Basic Problems in Quantum Physics, June
Emergent Quantum Mechanics and Emergent Symmetries
Hooft, Gerard 't [Institute for Theoretical Physics Utrecht University and Spinoza Institute Postbox 80.195 3508 TD Utrecht (Netherlands)
2007-11-20
Quantum mechanics is 'emergent' if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such theories allow for a natural explanation of the existence of gauge equivalence classes (gauge orbits), including the equivalence classes generated by general coordinate transformations. Thus, local gauge symmetries and general coordinate invariance could be emergent symmetries, and this might lead to new alleys towards understanding the flatness problem of the Universe.
Optimal guidance law in quantum mechanics
Yang, Ciann-Dong, E-mail: cdyang@mail.ncku.edu.tw; Cheng, Lieh-Lieh, E-mail: leo8101@hotmail.com
2013-11-15
Following de Broglie’s idea of a pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by the Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle’s motion is just the wavefunction ?(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for ?(t,x), from which quantum operators emerge naturally. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function ?{sup ?}?. -- Highlights: •Treating quantum mechanics as a pursuit-evasion game. •Reveal an interesting analogy between guided flight motion and guided quantum motion. •Solve optimal quantum guidance problem by dynamic programming. •Gives a formal proof of de Broglie–Bohm’s idea of a pilot wave. •The optimal pilot wave is shown to be a wavefunction solved from Schrödinger equation.
Improving students' understanding of quantum mechanics
NASA Astrophysics Data System (ADS)
Singh, Chandralekha
2011-03-01
Learning quantum mechanics is especially challenging, in part due to the abstract nature of the subject. We have been conducting investigations of the difficulties that students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) as well as tools for peer-instruction. The goal of QuILTs and peer-instruction tools is to actively engage students in the learning process and to help them build links between the formalism and the conceptual aspects of quantum physics without compromising the technical content. They focus on helping students integrate qualitative and quantitative understanding, confront and resolve their misconceptions and difficulties, and discriminate between concepts that are often confused. In this talk, I will give examples from my research in physics education of how students' prior knowledge relevant for quantum mechanics can be assessed, and how learning tools can be designed to help students develop a robust knowledge structure and critical thinking skills. Supported by the National Science Foundation.
Multichannel framework for singular quantum mechanics
Camblong, Horacio E., E-mail: camblong@usfca.edu [Department of Physics and Astronomy, University of San Francisco, San Francisco, CA 94117-1080 (United States); Epele, Luis N., E-mail: epele@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Fanchiotti, Huner, E-mail: huner@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina)] [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); García Canal, Carlos A., E-mail: garcia@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Ordóñez, Carlos R., E-mail: ordonez@uh.edu [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States)
2014-01-15
A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.
The statistical origins of quantum mechanics
U. Klein
2011-03-08
It is shown that Schroedinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle mechanics by replacing all observables by statistical averages. The second is a local conservation law of probability with a probability current which takes the form of a gradient. The third is a principle of maximal disorder as realized by the requirement of minimal Fisher information. The rule for calculating expectation values is obtained from a fourth postulate, the requirement of energy conservation in the mean. The fact that all these basic relations of quantum theory may be derived from premises which are statistical in character is interpreted as a strong argument in favor of the statistical interpretation of quantum mechanics. The structures of quantum theory and classical statistical theories are compared and some fundamental differences are identified.
Probability in the Many-Worlds Interpretation of Quantum Mechanics
Vaidman, Lev
of standard quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence
The Quantum Mechanics of Hyperion
Nathan Wiebe; L. E. Ballentine
2005-03-21
This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as hbar^{2/3} for chaotic states, and as hbar^2 for non-chaotic states, leading to negligible QC differences for a macroscopic object like Hyperion. The quantum probability distributions do not approach their classical limit smoothly, having an extremely fine oscillatory structure superimposed on the smooth classical background. For a macroscopic object, this oscillatory structure is too fine to be resolved by any realistic measurement. Either a small amount of smoothing (due to the finite resolution of the apparatus) or a very small amount of environmental decoherence is sufficient ensure the classical limit. Under decoherence, the QC differences in the probability distributions scale as (hbar^2/D)^{1/6}, where D is the momentum diffusion parameter. We conclude that decoherence is not essential to explain the classical behavior of macroscopic bodies.
Fractional quantum mechanics and Lévy path integrals
NASA Astrophysics Data System (ADS)
Laskin, Nikolai
2000-04-01
A new extension of a fractality concept in quantum physics has been developed. The path integrals over the Lévy paths are defined and fractional quantum and statistical mechanics have been developed via new fractional path integrals approach. A fractional generalization of the Schrödinger equation has been found. The new relation between the energy and the momentum of non-relativistic fractional quantum-mechanical particle has been established. We have derived a free particle quantum-mechanical kernel using Fox's H-function. The equation for the fractional plane wave function has been obtained. As a physical application of the developed fQM we have proposed a new fractional approach to the QCD problem of quarkonium. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in term of the Fox's H-function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics.
Quantum mechanics on a real Hilbert space
Jan Myrheim
1999-05-11
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics, keeping the same set of physical states, but admitting more general observables. The standard time reversal operator involves complex conjugation, in this sense it goes beyond the complex theory and may serve as an example to motivate the generalization. Another example is unconventional canonical quantization such that the harmonic oscillator of angular frequency $\\omega$ has any given finite or infinite set of discrete energy eigenvalues, limited below by $\\hbar\\omega/2$.
Quantum mechanics on a real Hilbert space
Myrheim, Jan
1999-01-01
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics, keeping the same set of physical states, but admitting more general observables. The standard time reversal operator involves complex conjugation, in this sense it goes beyond the complex theory and may serve as an example to motivate the generalization. Another example is unconventional canonical quantization such that the harmonic oscillator of angular frequency $\\omega$ has any given finite or infinite set of discrete energy eigenvalues, limited below by $\\hbar\\omega/2$.
Space and time from quantum mechanics
Chew, G.F.
1992-09-16
Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over collapse of the quantum-mechanical state vector when measurement is performed. Additionally, pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.
Space and time from quantum mechanics
NASA Astrophysics Data System (ADS)
Chew, G. F.
1992-09-01
Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over the collapse of the quantum-mechanical state vector when measurement is performed. Additionally, the pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as a coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.
Scattering Relativity in Quantum Mechanics
Richard Shurtleff
2015-07-06
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the particle field translated along one displacement, particle states are translated along a possibly different displacement. Arbitrary phase results. And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when field and states are translated. It is shown that a path of extreme phase obeys a semiclassical equation for force with derived terms that can describe electromagnetism and gravitation.
Quantum statistical mechanics, L-series, Anabelian Geometry
Marcolli, Matilde
Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Adem Lectures, Mexico City, January 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12 Mechanics, L-series and Anabelian Geometry, arXiv:1009.0736 Matilde Marcolli Quantum statistical mechanics
Koller, Andrew; Olshanii, Maxim [Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125 (United States)
2011-12-15
We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSYQM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via supersymmetric chains to a potential-free Hamiltonian, explaining their reflectionless nature. While the reflectionless property in question has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. Our results indicate that the multisoliton solutions of the sine-Gordon and nonlinear Schroedinger equations can be systematically generated via the supersymmetric chains connecting Akulin's Hamiltonians. Our findings also explain a well-known but little-understood effect in laser physics: when a two-level atom, initially in the ground state, is subjected to a laser pulse of the form V(t)=(n({h_bar}/2{pi})/{tau})/cosh(t/{tau}), with n being an integer and {tau} being the pulse duration, it remains in the ground state after the pulse has been applied, for any choice of the laser detuning.
A new introductory quantum mechanics curriculum
NASA Astrophysics Data System (ADS)
Kohnle, Antje; Bozhinova, Inna; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth
2014-01-01
The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum-mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of the interpretive aspects of quantum mechanics and quantum information theory. This paper gives an overview of the resources available from the IOP website. The core text includes around 80 articles which are co-authored by leading experts, arranged in themes, and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is included in the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways, from being supplemental to existing courses to forming a complete programme.
Macroscopic Quantum Mechanics in a Classical Spacetime
Huan Yang; Haixing Miao; Da-Shin Lee; Bassam Helou; Yanbei Chen
2013-04-23
We apply the many-particle Schr\\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schr\\"odinger-Newton equation for their centers of mass, which are degrees of freedom that can be monitored and manipulated at the quantum mechanical levels by state-of-the-art optoemchanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, we found that its quantum uncertainty evolves in a different frequency from its classical eigenfrequency --- with a difference that depends on the internal structure of the object, and can be observable using current technology. For several objects, the Schr\\"odinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet they do not allow quantum uncertainty to be transferred from one object to another through gravity.
Three-Hilbert-Space Formulation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Znojil, Miloslav
2009-01-01
In paper [Znojil M., Phys. Rev. D 78 (2008), 085003, 5 pages, arXiv:0809.2874] the two-Hilbert-space (2HS, a.k.a. cryptohermitian) formulation of Quantum Mechanics has been revisited. In the present continuation of this study (with the spaces in question denoted as H(auxiliary) and H(standard)) we spot a weak point of the 2HS formalism which lies in the double role played by H(auxiliary). As long as this confluence of roles may (and did!) lead to confusion in the literature, we propose an amended, three-Hilbert-space (3HS) reformulation of the same theory. As a byproduct of our analysis of the formalism we offer an amendment of the Dirac's bra-ket notation and we also show how its use clarifies the concept of covariance in time-dependent cases. Via an elementary example we finally explain why in certain quantum systems the generator H(gen) of the time-evolution of the wave functions may differ from their Hamiltonian H.
Quantum mechanics of time travel through post-selected teleportation
Maccone, Lorenzo
This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based ...
CPT and Quantum Mechanics Tests with Kaons
Jose Bernabeu; John Ellis; Nick E. Mavromatos; Dimitri V. Nanopoulos; Joannis Papavassiliou
2006-07-28
In this review we first discuss the theoretical motivations for possible CPT violation and deviations from ordinary quantum-mechanical behavior of field-theoretic systems in the context of an extended class of quantum-gravity models. Then we proceed to a description of precision tests of CPT symmetry using mainly neutral kaons. We emphasize the possibly unique role of neutral meson factories in providing specific tests of models where the quantum-mechanical CPT operator is not well-defined, leading to modifications of Einstein-Podolsky-Rosen particle correlators. Finally, we present tests of CPT, T, and CP using charged kaons, and in particular K_l4 decays, which are interesting due to the high statistics attainable in experiments.
A Euclidean formulation of relativistic quantum mechanics
Philip Kopp; Wayne Polyzou
2011-06-21
In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear operators on a Hilbert space, it has many of the advantages of quantum mechanics. One interesting feature of this approach is that matrix elements of operators in normalizable states on the physical Hilbert space can be calculated directly using the Euclidean Green functions without performing an analytic continuation. The formalism is summarized in this paper. We discuss the motivation, advantages and difficulties in using this formalism. We discuss how to compute bound states, scattering cross sections, and finite Poincare transformations without using analytic continuation. A toy model is used to demonstrate how matrix elements of exp(-beta H) in normalizable states can be used to construct-sharp momentum transition matrix elements.
CS 294-2 Local Hamiltonians + Quantum NP 11/11/04 Fall 2004 Lecture 16
Vazirani, Umesh
, the (unitary) evolution of the system will be given by the unitary operator U = eiHt = ei(H1+H2+...+Hn that the Hamiltonian H of an n-qubit systemis a 2n Ã? 2n Hermitian matrix and the evolution of the state of the system matrix. Suppose that each qubit in the n-qubit system evolves independently of the other qubits according
Stainless steel optimization from quantum mechanical calculations
Levente Vitos; Pavel A. Korzhavyi; Börje Johansson
2003-01-01
Alloy steel design has always faced a central problem: designing for a specific property very rarely produces a simultaneous significant improvement in other properties. For instance, it is difficult to design a material that combines high values of two of the most important mechanical characteristics of metals, hardness and ductility. Here we use the most recent quantum theories of random
Euclidean formulation of relativistic quantum mechanics
W. N. Polyzou; Philip Kopp
2009-08-10
We discuss preliminary work on a formulation of relativistic quantum mechanics that uses reflection-positive Euclidean Green functions or their generating functionals as phenomenological input. We discuss the construction of a Poincare invariant S-matrix from matrix element of exp(- \\beta H).
Quantum mechanics with applications to quarkonium
C. Quigg; Jonathan L. Rosner
1979-01-01
Some methods of nonrelativistic quantum mechanics which are particularly useful for studying the variation of bound-state parameters with constituent mass and excitation energy are reviewed. These techniques rely upon elementary scaling arguments and on the semiclassical (WKB) approximation. They are of general interest, but are applied here to the study of bound systems of a heavy quark and antiquark. Properties
Physical Interpretations of Nilpotent Quantum Mechanics
Peter Rowlands
2010-01-01
Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization,
WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN
Rosner, Jonathan L.
WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN PHYS 342 Final Project March 10, 2011 Contents of Postselection 4 4. Impossible Spin Measurements 5 5. Hardy's Paradox 5 6. Controversy over Weak Measurement 8 7 of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to be 100." [1] The topic
Dissipation in Quantum Mechanics. The Harmonic Oscillator
I. R. Senitzky
1960-01-01
The need for a quantum-mechanical formalism for systems with dissipation which is applicable to the radiation field of a cavity is discussed. Two methods that have been used in this connection are described. The first, which starts with the classical Newtonian equation of motion for a damped oscillator and applies the conventional formal quantization techniques, leads to an exact solution;
Quantum Mechanics Studies of Cellobiose Conformations
Technology Transfer Automated Retrieval System (TEKTRAN)
Three regions of the Phi,Psi space of cellobiose were analyzed with quantum mechanics. A central region, in which most crystal structures are found, was covered by a 9 x 9 grid of 20° increments of Phi and Psi. Besides these 81 constrained minimizations, we studied two central sub-regions and two re...
Is Quantum Mechanics needed to explain consciousness ?
Knud Thomsen
2007-11-13
In this short comment to a recent contribution by E. Manousakis [1] it is argued that the reported agreement between the measured time evolution of conscious states during binocular rivalry and predictions derived from quantum mechanical formalisms does not require any direct effect of QM. The recursive consumption analysis process in the Ouroboros Model can yield the same behavior.
Quantum Mechanical Effects in Gravitational Collapse
Eric Greenwood
2010-01-12
In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schr\\"odinger formalism. The Functional Schr\\"odinger formalism allows us to investigate the time-dependent evolutions of the quantum mechanical effects, which is beyond the scope of the usual methods used to investigate the quantum mechanical corrections of gravitational collapse. Utilizing the time-dependent nature of the Functional Schr\\"odinger formalism, we study the quantization of a spherically symmetric domain wall from the view point of an asymptotic and infalling observer, in the absence of radiation. To build a more realistic picture, we then study the time-dependent nature of the induced radiation during the collapse using a semi-classical approach. Using the domain wall and the induced radiation, we then study the time-dependent evolution of the entropy of the domain wall. Finally we make some remarks about the possible inclusion of backreaction into the system.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-01
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. PMID:26124252
Comparison of Classical and Quantum Mechanical Uncertainties.
ERIC Educational Resources Information Center
Peslak, John, Jr.
1979-01-01
Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)
Asymptotic freedom in the front-form Hamiltonian for quantum chromodynamics of gluons
Gomez-Rocha, Maria
2015-01-01
Asymptotic freedom of gluons in QCD is obtained in the leading terms of their renormalized Hamiltonian in the Fock space, instead of considering virtual Green's functions or scattering amplitudes. Namely, we calculate the three-gluon interaction term in the front-form Hamiltonian for effective gluons in the Minkowski space-time using the renormalization group procedure for effective particles (RGPEP), with a new generator. The resulting three-gluon vertex is a function of the scale parameter, $s$, that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant, $g_\\lambda$, depending on the associated momentum scale $\\lambda = 1/s$, is calculated in the series expansion in powers of $g_0 = g_{\\lambda_0}$ up to the terms of third order, assuming some small value for $g_0$ at some large $\\lambda_0$. The result exhibits the same finite sensitivity to small-$x$ regularization as the one obtained in an earlier RGPEP calculation, but the new calculation is simpler...
The Poincare-Birkhoff theorem in Quantum Mechanics
D. A. Wisniacki; M. Saraceno; F. J. Arranz; R. M. Benito; F. Borondo
2011-05-07
Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincar\\'e--Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta equal to the order of the classical resonance. Moreover, the associated classical phase space structures are mimicked in the quasiprobability density functions and their zeros.
Symmetry and environment effects on rectification mechanisms in quantum pumps
NASA Astrophysics Data System (ADS)
Arrachea, Liliana
2005-09-01
We consider a paradigmatic model of quantum pumps and discuss its rectification properties in the framework of a symmetry analysis proposed for ratchet systems. We discuss the role of the environment in breaking time-reversal symmetry and the possibility of a finite directed current in the Hamiltonian limit of annular systems.
Morozov, Alexandre V.
Comparison of Quantum Mechanics and Molecular Mechanics Dimerization Energy Landscapes for Pairs, quantum mechanical calculations on small molecule models, and molecular mechanics potential decomposition find reasonable qualitative agreement between molecular mechanics and quantum chemistry calculations
Consistent interpretations of quantum mechanics
Omnes, R. (Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris XI, Batiment 211, 91405 Orsay CEDEX (France))
1992-04-01
Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counterexamples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.
The Compton effect: Transition to quantum mechanics
NASA Astrophysics Data System (ADS)
Stuewer, R. H.
2000-11-01
The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite Robert A. Millikan's confirmation of Einstein's equation of the photoelectric effect in 1915. I then follow in some detail the experimental and theoretical research program that Arthur Holly Compton pursued between 1916 and 1922 at the University of Minnesota, the Westinghouse Lamp Company, the Cavendish Laboratory, and Washington University that culminated in his discovery of the Compton effect. Surprisingly, Compton was not influenced directly by Einstein's light-quantum hypothesis, in contrast to Peter Debye and H.A. Kramers, who discovered the quantum theory of scattering independently. I close by discussing the most significant response to that discovery, the Bohr-Kramers-Slater theory of 1924, its experimental refutation, and its influence on the emerging new quantum mechanics.
Time and the foundations of quantum mechanics
NASA Astrophysics Data System (ADS)
Pashby, Thomas
Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of `time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on re ection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.
BERNSTEIN PROCESSES, EUCLIDEAN QUANTUM MECHANICS AND INTEREST RATE MODELS
Lescot, Paul
works with J.-C. Zambrini, of the link between euclidean quantum mechanics, Bernstein processes = as a new parameter. In Zambrini's Euclidean Quantum Mechanics (see e.g. [1]), this equation splits into : 2
ABOUT A HUNDRED YEARS HAVE PASSED since quantum mechanics was first developed. Quantum
Bier, Martin
of Physical Law, noted: "I think I can safely say that nobody under- stands quantum mechanics."1 record in physics before he devoted himself at a later age Quantum Consciousness and Other Spooky MythsABOUT A HUNDRED YEARS HAVE PASSED since quantum mechanics was first developed. Quantum mechanics
Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics
Zambrini, Jean-Claude
Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics S. Albeverio, a new rigorous, but not probabilistic, Lagrangian version of nonrelativistic quantum mechanics is given in SchrÃ¶dinger's Euclidean quantum mechanics."1 There, a proba- bilistic i.e., "Euclidean" generalization
Modality, Potentiality and Contradiction in Quantum Mechanics
Christian de Ronde
2015-02-17
In [11], Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum mechanics (QM) attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause [1, 2, 3] have raised several arguments against this approach and claimed that, taking into account the square of opposition, quantum superpositions are better understood in terms of contrariety propositions rather than contradictory propositions. In [17] we defended the Paraconsistent Approach to Quantum Superpositions (PAQS) and provided arguments in favor of its development. In the present paper we attempt to analyze the meanings of modality, potentiality and contradiction in QM, and provide further arguments of why the PAQS is better suited, than the Contrariety Approach to Quantum Superpositions (CAQS) proposed by Arenhart and Krause, to face the interpretational questions that quantum technology is forcing us to consider.
A Signal Processing Model of Quantum Mechanics
Chris Thron; Johnny Watts
2012-05-08
This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing the amplitude and phase information of a modulated carrier wave. Particle transmission events are modeled as the outcome of a process of signal accumulation that occurs in an extra (non-spacetime) dimension. Besides giving a natural interpretation of the wavefunction and the Born rule, the model accommodates the collapse of the wave packet and other quantum paradoxes such as EPR and the Ahanorov-Bohm effect. The model also gives a new perspective on the 'relational' nature of quantum mechanics: that is, whether the wave function of a physical system is "real" or simply reflects the observer's partial knowledge of the system. We simulate the model for a 2-slit experiment, and indicate possible deviations of the model's predictions from conventional quantum mechanics. We also indicate how the theory may be extended to a field theory.
NASA Astrophysics Data System (ADS)
Marquette, Ian
2009-01-01
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integrals of motion. We construct the most general cubic algebra and we present specific realizations. We use them to calculate the energy spectrum. All classical and quantum superintegrable potentials separable in Cartesian coordinates with a third order integral are known. The general formalism is applied to quantum reducible and irreducible rational potentials separable in Cartesian coordinates in E2. We also discuss these potentials from the point of view of supersymmetric and PT-symmetric quantum mechanics.
Web-based Quantum Mechanics II Course
NSDL National Science Digital Library
Breinig, Marianne
This web site, authored by Marianne Breinig, is an entire web-based Quantum Mechanics II Course based at the University of Tennessee. It has instructional materials, in-class tutorials, simulations, links to other quantum resources, a discussion forum, homework assignments, and solutions. A schedule and syllabus are also included for easier implementation into a curriculum. Most of the tools on the website require a browser of Internet Explorer 4 or higher to function. This is a nice set of resources for students or instructors interested in physics.
Quantum mechanical coherence, resonance, and mind
Stapp, H.P.
1995-03-26
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Quantum Mechanical Scattering in Nanoscale Systems
NASA Astrophysics Data System (ADS)
Gianfrancesco, A. G.; Ilyashenko, A.; Boucher, C. R.; Ram-Mohan, L. R.
2012-02-01
We investigate quantum scattering using the finite element method. Unlike textbook treatments employing asymptotic boundary conditions (BCs), we use modified BCs, which permits computation close to the near-field region and reduces the Cauchy BCs to Dirichlet BCs, greatly simplifying the analysis. Scattering from any finite quantum mechanical potential can be modeled, including scattering in a finite waveguide geometry and in the open domain. Being numerical, our analysis goes beyond the Born Approximation, and the finite element approach allows us to transcend geometric constraints. Results of the formulation will be presented with several case studies, including spin dependent scattering, demonstrating the high accuracy and flexibility attained in this approach.
Quantum-mechanical phase locking in weak-link arrays
Widom, A. (Physics Department, Northeastern University, Boston, Massachusetts 02115 (United States)); Vittoria, C. (Department of Electrical Engineering, Northeastern University, Boston, Massachusetts 02115 (United States))
1991-12-01
Quantum-mechanical descriptions of arrays of Josephson weak links often invoke electric-field-energy storage in the weak-link capacitors. However, such quantum-electrodynamic mechanism is by no means a requirement for the notion of macroscopic quantum-mechanical wave functions for the array as a whole. These statements are illustrated for the phenomena of quantum-mechanical phase locking'' in one- and two-dimensional arrays in electromagnetic fields.
Deformation Quantization: From Quantum Mechanics to Quantum Field Theory
P. Tillman
2006-10-31
The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to quantum field theory. Also, we discuss some of the conceptual advantages of DQ and how DQ may be related to algebraic quantum field theory. Additionally, our previous results are summarized which includes the construction of the Fedosov star-product on dS/AdS. One of the goals of these results was to verify that DQ gave the same results as previous analyses of these spaces. Another was to verify that the formal series used in the conventional treatment converged by obtaining exact and nonperturbative results for these spaces.
Progress in Euclidean relativistic few-body quantum mechanics
Polyzou, Wayne
Progress in Euclidean relativistic few-body quantum mechanics Wayne Polyzou The University of Iowa Iowa City, IA 52242 October 9, 2012 Abstract We discuss recent progress in the Euclidean formulation of relativistic few-body quantum mechanics. 1 Introduction Euclidean relativistic quantum mechanics is a formalism
Harvard University Physics 143b: Quantum Mechanics II
Harvard University Physics 143b: Quantum Mechanics II Instructor : Subir Sachdev, Lyman 343@fas.harvard.edu This is the second half of an introductory course on quantum mechanics. The course will complete the text book: the photon 5. Relativistic quantum mechanics: the Dirac equation 6. Einstein-Podolsky-Rosen "paradox", Bell
Harvard University Physics 143b: Quantum Mechanics II
Harvard University Physics 143b: Quantum Mechanics II Instructor : Subir Sachdev, Lyman 343@physics.harvard.edu This is the second half of an introductory course on quantum mechanics. The course will complete the text book: the photon 5. Relativistic quantum mechanics: the Dirac equation 6. Scattering theory. 7. Einstein
Outline of Quantum Mechanics William G. Faris 1
Ueltschi, Daniel
Contents Outline of Quantum Mechanics William G. Faris 1 Inequalities for SchrÂ¨odinger Operators is the goal of the present lecture notes. They include an excellent introduction to quantum mechanics been de- veloped over the years for, and because of, quantum mechanics. These are the subject of two
The syllabus of the Course 624 Quantum Mechanics 2
The syllabus of the Course 624 Quantum Mechanics 2 Spring 2009. Instructor V.L. Pokrovsky. 1. Many-body quantum mechanics. Second quantization. Spin and statistics. Bose- Einstein condensation. 6's phase. Landau-Zener theory. Principal textbook: E. Merzbacher, Quantum Mechanics, 3-d edition, Wiley
Quantum statistical mechanics, L-series, Anabelian Geometry
Marcolli, Matilde
Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Colloquium, Harvard University, March 24, 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12 as partition functions of physical systems Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian
Quantum statistical mechanics, L-series, Anabelian Geometry
Marcolli, Matilde
Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Beijing, August 2013 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;joint work with Gunther Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;Number fields: finite
Predicting crystal structure by merging data mining with quantum mechanics
Ceder, Gerbrand
ARTICLES Predicting crystal structure by merging data mining with quantum mechanics CHRISTOPHER C@mit.edu Published online: 9 July 2006; doi:10.1038/nmat1691 Modern methods of quantum mechanics have proved with quantum mechanics if an algorithm to direct the search through the large space of possible structures
MSE 157: Quantum Mechanics of Nanoscale Materials Course Information
MSE 157: Quantum Mechanics of Nanoscale Materials Course Information Basic info Prof. Aaron there. Textbook The textbook for this course is Introduction to Quantum Mechanics by David Griffiths. We interest. Other recommended books for outside reading: Applied Quantum Mechanics by David Levi Applied
Quantum Mechanics as a Science -Religion Bridge By Stanley Klein
Klein, Stanley
Quantum Mechanics as a Science - Religion Bridge By Stanley Klein (May 1, 2002) Stanley Klein and for fitting contact lenses. Klein's interest in quantum mechanics and brain research has led him to explore of more than 20 years, DUALITY, summarizes his theme that the duality of quantum mechanics provides
The Objective Inde...niteness Interpretation of Quantum Mechanics
Wüthrich, Christian
The Objective Inde...niteness Interpretation of Quantum Mechanics David Ellerman University of California at Riverside Draft (not for quotation) May 28, 2013 Abstract Quantum mechanics (QM models indef- inite elements that become more de...nite as distinctions are made. If quantum mechanics
The Schrodinger Equation From a Quadratic Hamiltonian System
Wai Bong Yeung
1999-11-02
We regard the real and imaginary parts of the Schrodinger wave function as canonical conjugate variables.With this pair of conjugate variables and some other 2n pairs, we construct a quadratic Hamiltonian density. We then show that the Schrodinger Equation follows from the Hamilton's Equation of motion when the Planck frequency is much larger than the characteristic frequencies of the Hamiltonian system. The Hamiltonian and the normal mode solutions coincide, respectively, with the energy expectation value and the energy eigenstates of the corresponding quantum mechanical system.
Coulomb problem in non-commutative quantum mechanics
Galikova, Veronika; Presnajder, Peter [Faculty of Mathematics, Physics and Informatics, Comenius University of Bratislava, Mlynska dolina F2, Bratislava (Slovakia)] [Faculty of Mathematics, Physics and Informatics, Comenius University of Bratislava, Mlynska dolina F2, Bratislava (Slovakia)
2013-05-15
The aim of this paper is to find out how it would be possible for space non-commutativity (NC) to alter the quantum mechanics (QM) solution of the Coulomb problem. The NC parameter {lambda} is to be regarded as a measure of the non-commutativity - setting {lambda}= 0 which means a return to the standard quantum mechanics. As the very first step a rotationally invariant NC space R{sub {lambda}}{sup 3}, an analog of the Coulomb problem configuration space (R{sup 3} with the origin excluded) is introduced. R{sub {lambda}}{sup 3} is generated by NC coordinates realized as operators acting in an auxiliary (Fock) space F. The properly weighted Hilbert-Schmidt operators in F form H{sub {lambda}}, a NC analog of the Hilbert space of the wave functions. We will refer to them as 'wave functions' also in the NC case. The definition of a NC analog of the hamiltonian as a hermitian operator in H{sub {lambda}} is one of the key parts of this paper. The resulting problem is exactly solvable. The full solution is provided, including formulas for the bound states for E < 0 and low-energy scattering for E > 0 (both containing NC corrections analytic in {lambda}) and also formulas for high-energy scattering and unexpected bound states at ultra-high energy (both containing NC corrections singular in {lambda}). All the NC contributions to the known QM solutions either vanish or disappear in the limit {lambda}{yields} 0.
Measurement and Fundamental Processes in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Jaeger, Gregg
2015-07-01
In the standard mathematical formulation of quantum mechanics, measurement is an additional, exceptional fundamental process rather than an often complex, but ordinary process which happens also to serve a particular epistemic function: during a measurement of one of its properties which is not already determined by a preceding measurement, a measured system, even if closed, is taken to change its state discontinuously rather than continuously as is usual. Many, including Bell, have been concerned about the fundamental role thus given to measurement in the foundation of the theory. Others, including the early Bohr and Schwinger, have suggested that quantum mechanics naturally incorporates the unavoidable uncontrollable disturbance of physical state that accompanies any local measurement without the need for an exceptional fundamental process or a special measurement theory. Disturbance is unanalyzable for Bohr, but for Schwinger it is due to physical interactions' being borne by fundamental particles having discrete properties and behavior which is beyond physical control. Here, Schwinger's approach is distinguished from more well known treatments of measurement, with the conclusion that, unlike most, it does not suffer under Bell's critique of quantum measurement. Finally, Schwinger's critique of measurement theory is explicated as a call for a deeper investigation of measurement processes that requires the use of a theory of quantum fields.
Does quantum mechanics require non-locality?
Ghenadie N. Mardari
2014-10-29
Non-commutative properties of single quanta must violate the limit of Bell's theorem, but not the boundary of Tsirelson's theorem. This is a consequence of three basic principles: superposition (every quantum is in many states at the same time), correspondence (only the net state of interference is real), and uncertainty (conjugate variables have inversely proportional spectra). The two conditions have only been verified with entangled pairs of quanta. It is not possible to perform incompatible measurements on the same entity. Hence, the principles of quantum mechanics cannot be verified directly. At least one of them could be wrong. Though, as shown by EPR, this can only be true if non-locality is at work. In light of the latest developments in quantum theory, even that assumption is insufficient. Non-local effects are either unable to cross Bell's limit, or forced to violate Tsirelson's bound. New layers of hidden variables are required to maintain belief in action-at-a-distance, but the three principles cannot be rejected in any case. Therefore, quantum mechanics is immune to this challenge. The hypothesis of non-locality is superfluous.
The preparation of states in quantum mechanics
Juerg Froehlich; Baptiste Schubnel
2014-09-28
The important problem of how to prepare a quantum mechanical system, $S$, in a specific initial state of interest - e.g., for the purposes of some experiment - is addressed. Three distinct methods of state preparation are described. One of these methods has the attractive feature that it enables one to prepare $S$ in a preassigned initial state with certainty; i.e., the probability of success in preparing $S$ in a given state is unity. This method relies on coupling $S$ to an open quantum-mechanical environment, $E$, in such a way that the dynamics of $S \\vee E$ pulls the state of $S$ towards an "attractor", which is the desired initial state of $S$. This method is analyzed in detail.
Quantum mechanics on phase space and teleportation
NASA Astrophysics Data System (ADS)
Messamah, Juba; Schroeck, Franklin E.; Hachemane, Mahmoud; Smida, Abdallah; Hamici, Amel H.
2015-03-01
The formalism of quantum mechanics on phase space is used to describe the standard protocol of quantum teleportation with continuous variables in order to partially investigate the interplay between this formalism and quantum information. Instead of the Wigner quasi-probability distributions used in the standard protocol, we use positive definite true probability densities which account for unsharp measurements through a proper wave function representing a non-ideal quantum measuring device. This is based on a result of Schroeck and may be taken on any relativistic or nonrelativistic phase space. The obtained formula is similar to a known formula in quantum optics, but contains the effect of the measuring device. It has been applied in three cases. In the first case, the two measuring devices, corresponding to the two entangled parts shared by Alice and Bob, are not entangled and described by two identical Gaussian wave functions with respect to the Heisenberg group. They lead to a probability density identical to the function which is analyzed and compared with the Wigner formalism. A new expression of the teleportation fidelity for a coherent state in terms of the quadrature variances is obtained. In the second case, these two measuring devices are entangled in a two-mode squeezed vacuum state. In the third case, two Gaussian states are combined in an entangled squeezed state. The overall observation is that the state of the measuring devices shared by Alice and Bob influences the fidelity of teleportation through their unsharpness and entanglement.
Applications of computational quantum mechanics
NASA Astrophysics Data System (ADS)
Temel, Burcin
This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts with novel properties. Doping a metal oxide may alter its intrinsic properties drastically. A catalytically non-active material can be activated by doping. In this study, we showed that pure zirconia (ZrO2) has almost no activity in methanol coupling reaction, whereas when it is doped with aluminum, the doped catalyst produces dimethyl ether (DME), which is valuable as an alternative future energy source.
Grounding quantum probability in psychological mechanism.
Love, Bradley C
2013-06-01
Pothos & Busemeyer (P&B) provide a compelling case that quantum probability (QP) theory is a better match to human judgment than is classical probability (CP) theory. However, any theory (QP, CP, or other) phrased solely at the computational level runs the risk of being underconstrained. One suggestion is to ground QP accounts in mechanism, to leverage a wide range of process-level data. PMID:23673043
Physical Interpretations of Nilpotent Quantum Mechanics
Rowlands, Peter
2010-01-01
Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization, and related issues.
Quantum Mechanics and Motion: A Modern Perspective
Gerald E. Marsh
2009-12-27
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum, yields a world-line. If a force acts on the particle, its probability distribution is accordingly modified. This must also be true for macroscopic objects, although now the description is far more complicated by the structure of matter and associated surface physics.
Chiral quantum mechanics (CQM) for antihydrogen systems
G. Van Hooydonk
2005-12-03
A first deception of QM on antiH already appears in one-center integrals for two-center systems (G. Van Hooydonk, physics/0511115). In reality, full QM is a theory for chiral systems but the QM establishment was wrong footed with a permutation of reference frames. With chiral quantum mechanics (CQM), the theoretical ban on natural antiH must be lifted as soon as possible.
Modern Quantum Mechanics Experiments for Undergraduates
NSDL National Science Digital Library
Beck, Mark
Authored by Mark Beck of Whitman College's Department of Physics, this site provides information about simplified quantum mechanics experiments such as the Grangier experiment and single photon interference. Included are a general description, an overview, course materials, experiments, external links and notes. Each experiment or lesson provides instructions and other need information such as images, charts or graphs. This series of resources could be used to enhance or create curricula in the field.
Collocation method for fractional quantum mechanics
Amore, Paolo; Hofmann, Christoph P.; Saenz, Ricardo A. [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diagonal 113 y 64 S/N, Sucursal 4, Casilla de correo 16, 1900 La Plata (Argentina)
2010-12-15
We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schroedinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed.
No Labeling Quantum Mechanics of Indiscernible Particles
NASA Astrophysics Data System (ADS)
Domenech, G.; Holik, F.; Kniznik, L.; Krause, D.
2010-12-01
Our aim in this paper is to show an example of the formalism we have developed to avoid the label-tensor-product-vector-space-formalism of quantum mechanics when dealing with indistinguishable quanta. States in this new vector space, that we call the Q-space, refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the unobservability of permutations, a goal of quasi-set theory.
Superconformal multi-black hole quantum mechanics
Jeremy Michelson; Andrew Strominger
1999-01-01
The quantum mechanics of N slowly-moving charged BPS black holes in five-dimensional Script N = 1 supergravity is considered. The moduli space metric of the N black holes is derived and shown to admit 4 supersymmetries. A near-horizon limit is found in which the dynamics of widely separated black holes decouples from that of strongly-interacting, near-coincident black holes. This decoupling
Physical Interpretations of Nilpotent Quantum Mechanics
Peter Rowlands
2010-04-09
Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization, and related issues.
Rezakhani, A. T.
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation ...
Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier
Chruscinski, Dariusz [Institute of Physics, Nicolaus Copernicus University, ul. Grudziadzka 5/7, 87-100 Torun (Poland)]. E-mail: darch@phys.uni.torun.pl
2006-04-15
We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.
Relativistic non-Hermitian quantum mechanics
NASA Astrophysics Data System (ADS)
Jones-Smith, Katherine; Mathur, Harsh
2014-06-01
We develop relativistic wave equations in the framework of the new non-Hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT-symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that, in particular, the mass matrix be Hermitian also allows for models that have no counterpart in conventional quantum mechanics. For example it is well known that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here, we show that the same quartet of Weyl spinors, when coupled by a non-Hermitian but PT-symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is nonzero. The PT-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a noninteracting theory it violates P and T individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions and are shown to maintain many of the canonical structures from Hermitian field theory, but with new and interesting possibilities permitted by the non-Hermiticity parameter m2.
Quantum mechanics and low energy nucleon dynamics
Renat Kh. Gainutdinov; Aigul A. Mutygullina
2004-08-25
We discuss the problem of consistency of quantum mechanics as applied to low energy nucleon dynamics with the symmetries of QCD. It is shown that the dynamics consistent with these symmetries is not governed by the Schrodinger equation. We present a new way to formulate the effective theory of nuclear forces as an inevitable consequence of the basic principles of quantum mechanics and the symmetries of strong interactions. We show that being formulated in this way the effective theory of nuclear forces can be put on the same firm theoretical grounds as the quantum mechanics of atomic phenomena. In this case the effective theory allows one to describe with a given accuracy not only two-nucleon scattering, but also the evolution of nucleon systems, and places the constraints on the off-shell behavior of the two-nucleon interaction. In this way we predict the off-shell behavior of the S wave two-nucleon T-matrix at very low energies when the pionless theory is applicable. Further extensions and applications of this approach are discussed.
The cosmic origin of quantum mechanics
Ding-Yu Chung
2001-02-18
In this paper, the base of quantum mechanics is the spontaneous tendency for a microscopic object to fractionalize instantly into quasistates and condense instantly quasistates. This quasistate is equivalent to the eigenfunction. An object with the fractionalization-condensation is equivalent to the unitary wavefunction. Nonlocal operation is explicitly required to maintain communication among all quasistates regardless of distance during the fractionalization process. Interference effect is explicitly required for the condensation of quasistates. The collapse of the fractionalization-condensation is explicitly required when the fractionalization-condensation is disrupted. The cosmic origin of quantum mechanics is derived from the cyclic fractionalization-condensation in the cyclic universe, consisting of the unobservable cosmic vacuum and the observable universe. The cyclic fractionalization-condensation allows quasistates to appear cyclically rather than simultaneously. The cosmic vacuum involves the gradual cyclic fractionalization-condensation between the high energy eleven dimensional and low energy four dimensional spacetime. The observable universe involves the drastic cyclic fractionalization-condensation consisting of the cosmic instant fractionalization (the big bang) into various dimensional particles and the expansion-contraction by mostly cosmic radiation and gravity. The cosmic instant fractionalization leads to the microscopic instant fractionalization-condensation (the standard quantum mechanics) that allows all quasistates from an object to appear simultaneously.
Transcritical bifurcations in nonintegrable Hamiltonian systems.
Brack, Matthias; Tanaka, Kaori
2008-04-01
We report on transcritical bifurcations of periodic orbits in nonintegrable two-dimensional Hamiltonian systems. We discuss their existence criteria and some of their properties using a recent mathematical description of transcritical bifurcations in families of symplectic maps. We then present numerical examples of transcritical bifurcations in a class of generalized Hénon-Heiles Hamiltonians and illustrate their stabilities and unfoldings under various perturbations of the Hamiltonians. We demonstrate that for Hamiltonians containing straight-line librating orbits, the transcritical bifurcation of these orbits is the typical case which occurs also in the absence of any discrete symmetries, while their isochronous pitchfork bifurcation is an exception. We determine the normal forms of both types of bifurcations and derive the uniform approximation required to include transcritically bifurcating orbits in the semiclassical trace formula for the density of states of the quantum Hamiltonian. We compute the coarse-grained density of states in a specific example both semiclassically and quantum mechanically and find excellent agreement of the results. PMID:18517708
NASA Astrophysics Data System (ADS)
Choi, Taeseung
2015-03-01
A relativistic spin operator is the difference between the total and the orbital angular momentum. As the unique position operator for a localized state, the remarkable Newton-Wigner position operator, which has all the desirable commutation relations of a position operator, can give a proper spin operator. Historically, the three important spin operators proposed by Bogolubov et al., Pryce, and Foldy-Woutheysen, respectively were investigated to manifest a spin operator corresponding to the Newton-Wigner position operator. We clarify a unique spin operator in relativistic quantum mechanics, which can be described by using the Dirac Hamiltonian.
Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force
M. A. Gonzalez Leon; J. Mateos Guilarte; M. de la Torre Mayado
2007-12-21
The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families of Razavy and Whittaker-Hill equations in the first approach. When the two centers have the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In the second approach, the spectral problems are much more difficult to solve but one can still find the zero-energy ground states.
Bhomian Mechanics vs. Standard Quantum Mechanics: a Difference in Experimental Predictions
Artur Szczepanski
2010-02-08
Standard Quantum Mechanics (QM) predicts an anti-intuitive fenomenon here referred to as "quantum autoscattering", which is excluded by Bhomian Mechanics. The scheme of a gedanken experiment testing the QM prediction is briefly discussed.
Unstable trajectories and the quantum mechanical uncertainty
Moser, Hans R. [Physics Institute, University of Zuerich, Winterthurerstrasse 190, CH-8057 Zuerich (Switzerland)], E-mail: moser@physik.uzh.ch
2008-08-15
There is still an ongoing discussion about various seemingly contradictory aspects of classical particle motion and its quantum mechanical counterpart. One of the best accepted viewpoints that intend to bridge the gap is the so-called Copenhagen Interpretation. A major issue there is to regard wave functions as probability amplitudes (usually for the position of a particle). However, the literature also reports on approaches that claim a trajectory for any quantum mechanical particle, Bohmian mechanics probably being the most prominent one among these ideas. We introduce a way to calculate trajectories as well, but our crucial ingredient is their well controlled local (thus also momentaneous) degree of instability. By construction, at every moment their unpredictability, i.e., their local separation rates of neighboring trajectories, is governed by the local value of the given modulus square of a wave function. We present extensive numerical simulations of the H and He atom, and for some velocity-related quantities, namely angular momentum and total energy, we inspect their agreement with the values appearing in wave mechanics. Further, we interpret the archetypal double slit interference experiment in the spirit of our findings. We also discuss many-particle problems far beyond He, which guides us to a variety of possible applications.
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Akhmedov, Evgeny Kh.; Kopp, Joachim; ,
2010-01-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Quantum mechanical virial theorem in systems with translational and rotational symmetry
Kuic, Domagoj
2009-01-01
Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G, H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J^{2}, J_{z} and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.
N=4, 3D supersymmetric quantum mechanics in a non-Abelian monopole background
Ivanov, Evgeny; Konyushikhin, Maxim [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation); SUBATECH, Universite de Nantes, 4 rue Alfred Kastler, BP 20722, Nantes 44307 (France) and Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, Moscow 117259 (Russian Federation)
2010-10-15
Using the harmonic superspace approach, we construct the 3D N=4 supersymmetric quantum mechanics of the supermultiplet (3,4,1) coupled to an external SU(2) gauge field. The off-shell N=4 supersymmetry requires the gauge field to be a static form of the 't Hooft ansatz for the 4D self-dual SU(2) gauge fields, that is a particular solution of Bogomolny equations for Bogomolny-Prasad-Sommerfeld monopoles. We present the explicit form of the corresponding superfield and component actions, as well as of the quantum Hamiltonian and N=4 supercharges. The latter can be used to describe a more general N=4 mechanics system, with an arbitrary Bogomolny-Prasad-Sommerfeld monopole background and on-shell N=4 supersymmetry. The essential feature of our construction is the use of semidynamical spin (4,4,0) multiplet with the Wess-Zumino type action.
Quantum Mechanical Study on Tunnelling and Ballistic Transport of Nanometer Si MOSFETs
NASA Astrophysics Data System (ADS)
Deng, Hui-Xiong; Jiang, Xiang-Wei; Tang, Li-Ming
2010-05-01
Using self-consistent calculations of million-atom Schrödinger-Poisson equations, we investigate the I-V characteristics of tunnelling and ballistic transport of nanometer metal oxide semiconductor held effect transistors (MOSFET) based on a full 3-D quantum mechanical simulation under nonequilibtium condition. Atomistic empirical pseudopotentials are used to describe the device Hamiltonian and the underlying bulk band structure. We find that the ballistic transport dominates the I-V characteristics, whereas the effects of tunnelling cannot be neglected with the maximal value up to 0.8 mA/?m when the channel length of MOSFET scales down to 25 nm. The effects of tunnelling transport lower the threshold voltage Vt. The ballistic current based on fully 3-D quantum mechanical simulation is relatively large and has small on-off ratio compared with results derived from the calculation methods of Luo et al.
NASA Astrophysics Data System (ADS)
Sakimoto, Kazuhiro
2002-01-01
A rigorous full quantum-mechanical wave-packet calculation is carried out to study the protonium formation pbar+H-->pbarp+e. The present paper directly solves the time-dependent Schrödinger equation for the heavy particle Coulomb collision system. A discrete-variable-representation technique is used to evaluate the action of the Hamiltonian operator on the wave packet. The cross sections for the protonium formation are obtained at center-of-mass translational energies up to 10 eV. The present quantum-mechanical results are compared with those of previous studies based on classical trajectory Monte Carlo and semiclassical methods. Applicability of the adiabatic molecular picture to the protonium formation is also discussed.
Quantum mechanics with coordinate dependent noncommutativity
Kupriyanov, V. G. [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)] [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)
2013-11-15
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
Euclidean formulation of relativistic quantum mechanics W. N. Polyzou1
Polyzou, Wayne
Euclidean formulation of relativistic quantum mechanics W. N. Polyzou1 and Philip Kopp1 1 of relativistic quantum mechanics that uses reflection-positive Euclidean Green functions or generating functionals as phenomenological input. This work is motivated by the Euclidean axioms of quantum field theory
QUANTUM MECHANICS IN SNYDER SPACE Mark K. Transtrum
Hart, Gus
QUANTUM MECHANICS IN SNYDER SPACE by Mark K. Transtrum Submitted to Brigham Young University and two dimensions. I discuss the relation between Snyder space and noncommutative quantum mechanics Huele, Advisor Date Eric Hintz, Research Coordinator Date Scott Sommerfeldt, Chair #12;ABSTRACT QUANTUM
Quantum Mechanics Joachim Burgd orfer and Stefan Rotter
Rotter, Stefan
1 1 Quantum Mechanics Joachim BurgdË? orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution 29 1.8.3 Resonances 30 1.9 Semiclassical Mechanics 31 1.9.1 The WKB Approximation 31 1.9.2 The EBK
Burton, Geoffrey R.
Quantum Information Theory Quantum mechanics makes probabilistic predictions about experiments algebra and probability. Previous experience with quantum mechanics is helpful, but not required. Instead lead to the development of a theory of quantum information that generalises previous notions
Statistical Quantum Mechanics of Many Universes
Gamboa-Rios, J
2003-01-01
The quantum statistical mechanics of generally covariant systems --particles, strings and membranes-- on noncommutative field spaces is studied. We discuss how to introduce non-local communication among different systems via noncommutativity. This idea is applied to cosmology where we argue that due to the breaking of relativistic invariance one can consider a privileged reference system where many universes interact as a quantum gas in a reservoir. If roughly speaking, we approximate the universes as tensionless membranes, then, the interaction among universes provided by noncommutativity is harmonic. The oscillation frequency for each universe is proportional to $B/M$, where $B$ is the noncommutativity parameter --that we identify as the primordial magnetic field, {\\it i.e.} $\\sim 10^{-16} {GeV}^2$- and $M$ is the mass of the universe ($\\sim 10^{77} {GeV}$) and, therefore each universe have the pulsation frequency $\\omega \\sim 10^{-68} s^{-1}$.
Nielsen, Steven O.
FIG. 1: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. FIG. 2: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. 1 #12;FIG. 3: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect
Missing Link Between Probability Theory and Quantum Mechanics: the Riesz-Fejer Theorem
NASA Astrophysics Data System (ADS)
Fröhner, F. H.
1998-08-01
Quantum mechanics is spectacularly successful on the technical level but the meaning of its rules remains shrouded in mystery even more than seventy years after its inception. Quantum-mechanical probabilities are often considered as fundamentally different from classical probabilities, in disre-gard of the work of Cox (1946) -and of Schrödinger (1947) -on the foundations of probability theory. One central question concerns the superposition principle, i. e. the need to work with inter-fering wave functions, the absolute squares of which are probabilities. Other questions concern the relationship between spin and statistics or the collapse of the wave function when new data become available. These questions are reconsidered from the Bayesian point of view. The superposition principle is found to be a consequence of an apparently little-loiown mathematical theorem for non-negative Fourier polynomials published by Fejer in 1915 that implies wave-mechanical inter-ference already for classical probabilities. Combined with the classical Hamiltonian equations for free and accelerated motion, gauge invariance and particle indistinguishability, it yields all basic quantum features -wave-particle duality, operator calculus, uncertainty relations, Schrödinger equation, CPT invariance and even the spin-statistics relationship -which demystifies quantum mechanics to quite some extent.
Nonunique C operator in PT Quantum Mechanics
Carl M. Bender; S. P. Klevansky
2009-05-28
The three simultaneous algebraic equations, $C^2=1$, $[C,PT]=0$, $[C,H]=0$, which determine the $C$ operator for a non-Hermitian $PT$-symmetric Hamiltonian $H$, are shown to have a nonunique solution. Specifically, the $C$ operator for the Hamiltonian $H={1/2}p^2+{1/2}\\mu^2q^2+i\\epsilon q^3$ is determined perturbatively to first order in $\\epsilon$ and it is demonstrated that the $C$ operator contains an infinite number of arbitrary parameters. For each different $C$ operator, the corresponding equivalent isospectral Dirac-Hermitian Hamiltonian $h$ is calculated.
5.74 Introductory Quantum Mechanics II, Spring 2003
Tokmakoff, Andrei
Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...
5.74 Introductory Quantum Mechanics II, Spring 2007
Tokmakoff, Andrei
Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...
5.74 Introductory Quantum Mechanics II, Spring 2005
Tokmakoff, Andrei
Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...
Lecture Script: Introduction to Computational Quantum Mechanics
Roman Schmied
2015-06-05
This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013 and in the Spring semester of 2015. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding analytical as well as numerical solutions and their visualization. Most of these calculations are too complicated to be done by hand. Even relatively simple problems, such as two interacting particles in a one-dimensional trap, do not have analytic solutions and require the use of computers for their solution and visualization. More complex problems scale exponentially with the number of degrees of freedom, and make the use of large computer simulations unavoidable. The course is taught using the Mathematica programming language; however, the concepts presented are readily translated to any other programming language.
The Smith chart and quantum mechanics
Rosner, J.L. (Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637 (United States))
1993-04-01
The Schroedinger equation and the equation describing the behavior of voltage on a transmission line are both linear second-order equations, which may be solved by convenient matrix methods. By drawing analogies between these two problems, it is shown that a method used for antenna impedance matching based on the Smith chart corresponds in quantum mechanics to a simple conformal transformation of the logarithmic derivative of the wave function. One thereby can arrive at an elementary derivation of the Wentzel--Kramers--Brillouin quantization condition.
Position-dependent noncommutativity in quantum mechanics
M. Gomes; V. G. Kupriyanov
2009-06-15
The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinates [x^{i},x^{j}]=\\omega^{ij}(x), and construct the complete algebra of commutation relations, including the operators of momenta. The constructed algebra is a deformation of a standard Heisenberg algebra and obey the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativety.
Hidden geometric character of relativistic quantum mechanics
Almeida, Jose B. [Physics Department, Universidade do Minho, 4710-057 Braga (Portugal)
2007-01-15
Geometry can be an unsuspected source of equations with physical relevance, as everybody is aware since Einstein formulated the general theory of relativity. However, efforts to extend a similar type of reasoning to other areas of physics, namely, electrodynamics, quantum mechanics, and particle physics, usually had very limited success; particularly in quantum mechanics the standard formalism is such that any possible relation to geometry is impossible to detect; other authors have previously trod the geometric path to quantum mechanics, some of that work being referred to in the text. In this presentation we will follow an alternate route to show that quantum mechanics has indeed a strong geometric character. The paper makes use of geometric algebra, also known as Clifford algebra, in five-dimensional space-time. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from such choice and their consistency with experimental results. Given a metric space of any dimension, one can define monogenic functions, the natural extension of analytic functions to higher dimensions; such functions have null vector derivative and have previously been shown by other authors to play a decisive role in lower dimensional spaces. All monogenic functions have null Laplacian by consequence; in a hyperbolic space this fact leads inevitably to a wave equation with planelike solutions. This is also true for five-dimensional space-time and we will explore those solutions, establishing a parallel with the solutions of the free particle Dirac equation. For this purpose we will invoke the isomorphism between the complex algebra of 4x4 matrices, also known as Dirac's matrices. There is one problem with this isomorphism, because the solutions to Dirac's equation are usually known as spinors (column matrices) that do not belong to the 4x4 matrix algebra and as such are excluded from the isomorphism. We will show that a solution in terms of Dirac spinors is equivalent to a plane wave solution. Just as one finds in the standard formulation, monogenic functions can be naturally split into positive/negative energy together with left/right ones. This split is provided by geometric projectors and we will show that there is a second set of projectors providing an alternate fourfold split. The possible implications of this alternate split are not yet fully understood and are presently the subject of profound research.
Wigner Measures in Noncommutative Quantum Mechanics
C. Bastos; N. C. Dias; J. N. Prata
2009-07-25
We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner measure, for a Gaussian to be a noncommutative Wigner measure, and derive certain properties of the marginal distributions which are not shared by ordinary Wigner measures. Moreover, we derive the Robertson-Schr\\"odinger uncertainty principle. Finally, we show explicitly how the set of noncommutative Wigner measures relates to the sets of Liouville and (commutative) Wigner measures.
Euclidean Quantum Mechanics and Universal Nonlinear Filtering
Bhashyam Balaji
2008-09-25
An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr\\"odinger equation.
Improved lattice actions for supersymmetric quantum mechanics
Sebastian Schierenberg; Falk Bruckmann
2012-10-19
We analyze the Euclidean version of supersymmetric quantum mechanics on the lattice by means of a numerical path integral. We consider two different lattice derivatives and improve the actions containing them with respect to supersymmetry by systematically adding interaction terms with non-zero extent. To quantize this improvement, we measure boson and fermion masses and Ward identities for the naive as well as the improved models. The masses are degenerate in all models, but the magnitude of the Ward identities decreases significantly for both derivative operators using the improved actions. This is a clear sign that the breaking of supersymmetry due to lattice artifacts is reduced.
BiHermitian supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Zucchini, Roberto
2007-04-01
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kähler manifolds recently developed by Gualtieri in [33]. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li in [9].
The Ithaca Interpretation of Quantum Mechanics
Mermin, N David
1996-01-01
I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and I discuss two simple theorems. One, as far as I know, is new; the other was only noted a few years ago. Both have important implications for such a sensible interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)
The Ithaca Interpretation of Quantum Mechanics
N. David Mermin
1996-09-17
I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and I discuss two simple theorems. One, as far as I know, is new; the other was only noted a few years ago. Both have important implications for such a sensible interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)
Davidson potential and SUSYQM in the Bohr Hamiltonian
Georgoudis, P. E. [Institute of Nuclear and Particle Physics, National Center for Scientific Research Demokritos, GR-15310 Athens (Greece)
2013-06-10
The Bohr Hamiltonian is modified through the Shape Invariance principle of SUper-SYmmetric Quantum Mechanics for the Davidson potential. The modification is equivalent to a conformal transformation of Bohr's metric, generating a different {beta}-dependence of the moments of inertia.
A note on the Landauer principle in quantum statistical mechanics
Boyer, Edmond
A note on the Landauer principle in quantum statistical mechanics Vojkan Jaksi´c1 and Claude results concerning the derivation of the Landauer bound from the first principles of statistical mechanics and proof of the Landauer principle in the context of quantum statistical mechanics has led to a number
Quantum Mechanical Transport in Submicron Electronic Devices.
NASA Astrophysics Data System (ADS)
Bagwell, Philip Frederick
Electronic devices with characteristic dimensions of the order of 100 nm or less exhibit many novel quantum transport phenomena at low temperatures when the phase -breaking length becomes comparable to the device size. This thesis describes electron transport mechanisms and the resulting current-voltage relationships in quasi-one-dimensional wires, superlattices, and resonant tunneling devices. An intuitive 'convolution method' is developed to describe the energy averaging due to a finite bias voltage, finite temperature, disorder, and the influence of emitter dimensionality on these currents. We emphasize the dominant effect of evanescent or 'cutoff' electron waveguide modes in determining the shape of the electrical conductance versus Fermi energy in a confined geometry such as a quantum wire. Finally, we study experimentally the magnetoconductance of a novel Si 'grating gate' field effect transistor where the current path can be varied electrostatically in a single device from many narrow wires in parallel, to a modulated periodic potential, to a two-dimensional electron gas. Electron weak-localization, the classical Drude magnetoconductance, and the quantum Hall effect are modified by the periodic potential. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).
A quantum protective mechanism in photosynthesis
Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk
2015-01-01
Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life. PMID:25732807
A quantum protective mechanism in photosynthesis.
Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk
2015-01-01
Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life. PMID:25732807
Biological applications of hybrid quantum mechanics/molecular mechanics calculation.
Kang, Jiyoung; Hagiwara, Yohsuke; Tateno, Masaru
2012-01-01
Since in most cases biological macromolecular systems including solvent water molecules are remarkably large, the computational costs of performing ab initio calculations for the entire structures are prohibitive. Accordingly, QM calculations that are jointed with MM calculations are crucial to evaluate the long-range electrostatic interactions, which significantly affect the electronic structures of biological macromolecules. A UNIX-shell-based interface program connecting the quantum mechanics (QMs) and molecular mechanics (MMs) calculation engines, GAMESS and AMBER, was developed in our lab. The system was applied to a metalloenzyme, azurin, and PU.1-DNA complex; thereby, the significance of the environmental effects on the electronic structures of the site of interest was elucidated. Subsequently, hybrid QM/MM molecular dynamics (MD) simulation using the calculation system was employed for investigation of mechanisms of hydrolysis (editing reaction) in leucyl-tRNA synthetase complexed with the misaminoacylated tRNA(Leu), and a novel mechanism of the enzymatic reaction was revealed. Thus, our interface program can play a critical role as a powerful tool for state-of-the-art sophisticated hybrid ab initio QM/MM MD simulations of large systems, such as biological macromolecules. PMID:22536015
MacGregor, B.R.; McCoy, A.E.; Wickramasekara, S., E-mail: wickrama@grinnell.edu
2012-09-15
We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these representations determine the structure of quantum mechanics in non-inertial reference frames. Our representations of the Galilean line group contain the usual unitary projective representations of the Galilei group, but have a more intricate cocycle structure. The transformation formula for the Hamiltonian under the Galilean line group shows that in a non-inertial reference frame it acquires a fictitious potential energy term that is proportional to the inertial mass, suggesting the equivalence of inertial mass and gravitational mass in quantum mechanics. - Highlights: Black-Right-Pointing-Pointer A formulation of Galilean quantum mechanics in non-inertial reference frames is given. Black-Right-Pointing-Pointer The key concept is the Galilean line group, an infinite dimensional group. Black-Right-Pointing-Pointer Unitary, cocycle representations of the Galilean line group are constructed. Black-Right-Pointing-Pointer A non-central extension of the group underlies these representations. Black-Right-Pointing-Pointer Quantum equivalence principle and gravity emerge from these representations.
Angraini, Lily Maysari [STKIP Hamzanwadi Selong East Lombok, NTB, PostGraduate student at Physics Department UNS, Jl. Ir. Sutami 36 A, Surakarta (Indonesia); Suparmi,; Variani, Viska Inda [Physics Department UNS, Jl. Ir. Sutami 36 A, Surakarta (Indonesia)
2010-12-23
SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.
A fully 3D atomistic quantum mechanical study on random dopant induced effects in 25nm MOSFETs
Wang, Lin-Wang; Jiang, Xiang-Wei; Deng, Hui-Xiong; Luo, Jun-Wei; Li, Shu-Shen; Wang, Lin-Wang; Xia, Jian-Bai
2008-07-11
We present a fully 3D atomistic quantum mechanical simulation for nanometered MOSFET using a coupled Schroedinger equation and Poisson equation approach. Empirical pseudopotential is used to represent the single particle Hamiltonian and linear combination of bulk band (LCBB) method is used to solve the million atom Schroedinger's equation. We studied gate threshold fluctuations and threshold lowering due to the discrete dopant configurations. We compared our results with semiclassical simulation results. We found quantum mechanical effects increase the threshold fluctuation while decreases the threshold lowering. The increase of threshold fluctuation is in agreement with previous study based on approximated density gradient approach to represent the quantum mechanical effect. However, the decrease in threshold lowering is in contrast with the previous density gradient calculations.
Noncommutative quantum mechanics as a gauge theory
Bemfica, F. S.; Girotti, H. O. [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 - Porto Alegre, RS (Brazil)
2009-06-15
The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second-class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system into an Abelian gauge theory exhibiting only first class constraints. The appropriateness of the BFT embedding, as implemented in this work, is verified by showing that there exists a one to one mapping linking the second-class model with the gauge invariant sector of the gauge theory. As is known, the functional quantization of a gauge theory calls for the elimination of its gauge freedom. Then, we have at our disposal an infinite set of alternative descriptions for noncommutative quantum mechanics, one for each gauge. We study the relevant features of this infinite set of correspondences. The functional quantization of the gauge theory is explicitly performed for two gauges and the results compared with that corresponding to the second-class system. Within the operator framework the gauge theory is quantized by using Dirac's method.
Quantum Mechanical Study of Nanoscale MOSFET
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan
2001-01-01
The steady state characteristics of MOSFETS that are of practical Interest are the drive current, off-current, dope of drain current versus drain voltage, and threshold voltage. In this section, we show that quantum mechanical simulations yield significantly different results from drift-diffusion based methods. These differences arise because of the following quantum mechanical features: (I) polysilicon gate depletion in a manner opposite to the classical case (II) dependence of the resonant levels in the channel on the gate voltage, (III) tunneling of charge across the gate oxide and from source to drain, (IV) quasi-ballistic flow of electrons. Conclusions dI/dV versus V does not increase in a manner commensurate with the increase in number of subbands. - The increase in dI/dV with bias is much smaller then the increase in the number of subbands - a consequence of bragg reflection. Our calculations show an increase in transmission with length of contact, as seen in experiments. It is desirable for molecular electronics applications to have a small contact area, yet large coupling. In this case, the circumferential dependence of the nanotube wave function dictates: - Transmission in armchair tubes saturates around unity - Transmission in zigzag tubes saturates at two.
A Foundation Theory of Quantum Mechanics
Richard A Mould
2006-07-10
The nRules are empirical regularities that were discovered in macroscopic situations where the outcome is known. When they are projected theoretically into the microscopic domain they predict a novel ontology including the frequent collapse of an atomic wave function, thereby defining an nRule based foundation theory. Future experiments can potentially discriminate between this and other foundation theories of (non-relativistic) quantum mechanics. Important features of the nRules are: (1) they introduce probability through probability current rather than the Born rule, (2) they are valid independent of size (micro or macroscopic), (3) they apply to individual trials, not just to ensembles of trials. (4) they allow all observers to be continuously included in the system without ambiguity, (5) they account for the collapse of the wave function without introducing new or using old physical constants, and (6) in dense environments they provide a high frequency of stochastic localizations of quantum mechanical objects. Key words: measurement, stochastic choice, state reduction.
The formal path integral and quantum mechanics
Johnson-Freyd, Theo [Department of Mathematics, University of California - Berkeley, 970 Evans Hall, Berkeley, California 94720 (United States)
2010-11-15
Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.
Gorbatenko, M. V.; Neznamov, V. P. [Russian Federal Nuclear Center - All-Russian Research Institute of Experimental Physics, Sarov, Mira 37, Nizhni Novgorod region, 607188 (Russian Federation)
2010-11-15
The authors prove that the dynamics of spin 1/2 particles in stationary gravitational fields can be described using an approach, which builds upon the formalism of pseudo-Hermitian Hamiltonians. The proof consists in the analysis of three expressions for Hamiltonians, which are derived from the Dirac equation and describe the dynamics of spin 1/2 particles in the gravitational field of the Kerr solution. The Hamiltonians correspond to different choices of tetrad vectors and differ from each other. The differences between the Hamiltonians confirm the conclusion known from many studies that the Hamiltonians derived from the Dirac equation are nonunique. Application of standard pseudo-Hermitian quantum mechanics rules to each of these Hamiltonians produces the same Hermitian Hamiltonian. The eigenvalue spectrum of the resulting Hamiltonian is the same as that of the Hamiltonians derived from the Dirac equation with any chosen system of tetrad vectors. For description of the dynamics of spin 1/2 particles in stationary gravitational fields can be used not only the formalism of pseudo-Hermitian Hamiltonians but also an alternative approach, which employs the Parker scalar product. The authors show that the alternative approach is equivalent to the formalism of pseudo-Hermitian Hamiltonians.
Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory.
Schmidt, Steffen; Klevansky, S P
2013-04-28
This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H=p(2)+x(2)(ix)(?), H=p(2)+(x(2))(?) and H=p(2)-(x(2))(?). In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display PT symmetry. To do so, simple arguments that use the Wentzel-Kramers-Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and PT-symmetric quantum theory. PMID:23509377
Hamiltonian description of the ideal fluid
Morrison, P.J.
1994-01-01
Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems.
Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian.
Brennen, Gavin K; Miyake, Akimasa
2008-07-01
We propose a scheme for a ground-code measurement-based quantum computer, which enjoys two major advantages. First, every logical qubit is encoded in the gapped degenerate ground subspace of a spin-1 chain with nearest-neighbor two-body interactions, so that it equips built-in robustness against noise. Second, computation is processed by single-spin measurements along multiple chains dynamically coupled on demand, so as to keep teleporting only logical information into a gap-protected ground state of the residual chains after the interactions with spins to be measured are turned off. We describe implementations using trapped atoms or polar molecules in an optical lattice, where the gap is expected to be as large as 0.2 or 4.8 kHz, respectively. PMID:18764096
Quantum Transport in Crystals: Effective Mass Theorem and K·P Hamiltonians
NASA Astrophysics Data System (ADS)
Barletti, Luigi; Ben Abdallah, Naoufel
2011-11-01
In this paper the effective mass approximation and the k·p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period {?} of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k·p and effective mass models, well known in solid-state physics, are proved to be close (in the strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.
A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation
Lomonaco, S J
2000-01-01
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief ...