Note: This page contains sample records for the topic quantum mechanical-molecular mechanical from Science.gov.
While these samples are representative of the content of Science.gov,
they are not comprehensive nor are they the most current set.
We encourage you to perform a real-time search of Science.gov
to obtain the most current and comprehensive results.
Last update: November 12, 2013.
1

Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation  

NASA Astrophysics Data System (ADS)

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.

Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter

2013-08-01

2

Combined quantum mechanical\\/molecular mechanics modeling for large organometallic and metallobiochemical systems  

Microsoft Academic Search

A method of combined quantum mechanics\\/molecular mechanics has been developed to model larger organometallic and metallobiochemical systems where neither quantum mechanics nor molecular mechanics, applied separately, can solve the problem. An electronically transparent interface, which allows charge transfers between the quantum and classical fragments, is devised and realized by employing a special iterative procedure of double (intrafragment and interfragment) self-consistent

Max Kangchien Leong

1997-01-01

3

Biological Applications of Hybrid Quantum Mechanics/Molecular Mechanics Calculation  

PubMed Central

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 tRNALeu, 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.

Kang, Jiyoung; Hagiwara, Yohsuke; Tateno, Masaru

2012-01-01

4

The role of magnesium in hydrolysis of triphosphates in water: Quantum mechanical\\/molecular mechanical modeling  

Microsoft Academic Search

The mechanism of hydrolysis of deprotonated methyl triphosphate (MTP) to methyl diphosphate (MDP) and inorganic phosphate\\u000a (Pi) in water clusters in the presence and absence of magnesium cations has been modeled. Modeling has been performed by the\\u000a effective fragment potential-based quantum mechanical\\/molecular mechanical method. The energies and energy derivatives in\\u000a the quantum subsystem including MTP, reacting water molecules, and Mg2+

A. V. Rogov; B. L. Grigorenko; A. V. Bochenkova; A. A. Granovskii; A. V. Nemukhin

2007-01-01

5

Combined quantum mechanical/molecular mechanics modeling for large organometallic and metallobiochemical systems  

NASA Astrophysics Data System (ADS)

A method of combined quantum mechanics/molecular mechanics has been developed to model larger organometallic and metallobiochemical systems where neither quantum mechanics nor molecular mechanics, applied separately, can solve the problem. An electronically transparent interface, which allows charge transfers between the quantum and classical fragments, is devised and realized by employing a special iterative procedure of double (intrafragment and interfragment) self-consistent calculations. The combined QM/MM scheme was successfully applied to model iron picket-fence porphyrin, vitamin B12, aquocobalamin, and vitamin B12 coenzyme molecules.

Leong, Max Kangchien

6

Converting fructose to 5-hydroxymethylfurfural: a quantum mechanics\\/molecular mechanics study of the mechanism and energetics  

Microsoft Academic Search

We studied the energetics of the closed-ring mechanism of the acid-catalysed dehydration of d-fructose to 5-hydroxymethylfurfural (HMF) by carrying out canonical ensemble free-energy calculations using bias-sampling, hybrid Quantum Mechanics\\/Molecular Mechanics Molecular Dynamics simulations with explicit water solvent at 363K. The quantum mechanical calculations are performed at the PM3 theory level. We find that the reaction proceeds via intramolecular proton and

Stavros Caratzoulas; Dionisios G. Vlachos

2011-01-01

7

Quantum mechanics and mixed quantum mechanics\\/molecular mechanics simulations of model nerve agents with acetylcholinesterase  

Microsoft Academic Search

.  ?The accurate modeling of biological processes presents major computational difficulties owing to the inherent complexity\\u000a of the macromolecular systems of interest. Simulations of biochemical reactivity tend to require highly computationally intensive\\u000a quantum mechanical methods, but localized chemical effects tend to depend significantly on properties of the extended biological\\u000a environment – a regime far more readily examined with lower-level classical empirical

M. M. Hurley; J. B. Wright; G. H. Lushington; W. E. White

2003-01-01

8

Catalytic mechanism of RNA backbone cleavage by ribonuclease H from quantum mechanics/molecular mechanics simulations.  

PubMed

We use quantum mechanics/molecular mechanics simulations to study the cleavage of the ribonucleic acid (RNA) backbone catalyzed by ribonuclease H. This protein is a prototypical member of a large family of enzymes that use two-metal catalysis to process nucleic acids. By combining Hamiltonian replica exchange with a finite-temperature string method, we calculate the free energy surface underlying the RNA-cleavage reaction and characterize its mechanism. We find that the reaction proceeds in two steps. In a first step, catalyzed primarily by magnesium ion A and its ligands, a water molecule attacks the scissile phosphate. Consistent with thiol-substitution experiments, a water proton is transferred to the downstream phosphate group. The transient phosphorane formed as a result of this nucleophilic attack decays by breaking the bond between the phosphate and the ribose oxygen. In the resulting intermediate, the dissociated but unprotonated leaving group forms an alkoxide coordinated to magnesium ion B. In a second step, the reaction is completed by protonation of the leaving group, with a neutral Asp132 as a likely proton donor. The overall reaction barrier of ?15 kcal mol(-1), encountered in the first step, together with the cost of protonating Asp132, is consistent with the slow measured rate of ?1-100/min. The two-step mechanism is also consistent with the bell-shaped pH dependence of the reaction rate. The nonmonotonic relative motion of the magnesium ions along the reaction pathway agrees with X-ray crystal structures. Proton-transfer reactions and changes in the metal ion coordination emerge as central factors in the RNA-cleavage reaction. PMID:21539371

Rosta, Edina; Nowotny, Marcin; Yang, Wei; Hummer, Gerhard

2011-05-24

9

Ultrafast Quantum Mechanics/Molecular Mechanics Monte Carlo simulations using generalized multipole polarizabilities  

NASA Astrophysics Data System (ADS)

A fast and accurate Quantum Mechanics/Molecular Mechanics method is described for thermodynamic simulation of solutes (or active sites in flexible molecules) in polar environments. The solute is described quantum mechanically and is held fixed during averaging over solvent configurations, which are described by Molecular Mechanics. Quantum calculations during simulation are replaced by the evaluation of the response of the solute to the long range electric field of the solvent, using precalculated generalized electric moments and polarizabilities. This results in huge decrease of computational time without affecting the accuracy of the QM/MM results. Implementation in a Monte Carlo program accelerated the simulations of guanine and the phenylalanine dipeptide in TIP3P water by over four orders of magnitude. Polarizability is essential for accuracy. Its inclusion decreases the average signed energy error and its standard deviation from 5.69 to 0.003 and 1.22 to 0.013 kcal/mol, respectively, for the dipeptide. Hyperpolarizability contributions are insignificant.

Janowski, Tomasz; Wolinski, Krzysztof; Pulay, Peter

2012-03-01

10

Inactivation mechanism of glycerol dehydration by diol dehydratase from combined quantum mechanical/molecular mechanical calculations.  

PubMed

Inactivation of diol dehydratase during the glycerol dehydration reaction is studied on the basis of quantum mechanical/molecular mechanical calculations. Glycerol is not a chiral compound but contains a prochiral carbon atom. Once it is bound to the active site, the enzyme adopts two binding conformations. One is predominantly responsible for the product-forming reaction (G(R) conformation), and the other primarily contributes to inactivation (G(S) conformation). Reactant radical is converted into a product and byproduct in the product-forming reaction and inactivation, respectively. The OH group migrates from C2 to C1 in the product-forming reaction, whereas the transfer of a hydrogen from the 3-OH group of glycerol to C1 takes place during the inactivation. The activation barrier of the hydrogen transfer does not depend on the substrate-binding conformation. On the other hand, the activation barrier of OH group migration is sensitive to conformation and is 4.5 kcal/mol lower in the G(R) conformation than in the G(S) conformation. In the OH group migration, Glu170 plays a critical role in stabilizing the reactant radical in the G(S) conformation. Moreover, the hydrogen bonding interaction between Ser301 and the 3-OH group of glycerol lowers the activation barrier in G(R)-TS2. As a result, the difference in energy between the hydrogen transfer and the OH group migration is reduced in the G(S) conformation, which shows that the inactivation is favored in the G(S) conformation. PMID:23098175

Doitomi, Kazuki; Kamachi, Takashi; Toraya, Tetsuo; Yoshizawa, Kazunari

2012-11-02

11

Quantum mechanical/molecular mechanical (QM/MM) docking: an evaluation for known test systems  

NASA Astrophysics Data System (ADS)

A combined quantum mechanical/molecular mechanical (QM/MM) docking approach for the investigation of protein-inhibitor complexes is presented. Starting points for QM/MM optimizations are generated with AutoDock. The subsequent semiempirical AM1 QM/MM optimization of the complex obtained by the docking procedure gives a more detailed description of the binding mode and the electronic properties of the ligand. As we use a flexible protein environment in the QM/MM optimizations, we are able to simulate limited structural changes of the enzyme upon binding a ligand, even within a simple geometry optimization. The method was validated using a set of structurally known protein-inhibitor complexes, whose crystallographic data were taken from the Protein Data Bank. In addition to protein structures taken directly from complexes with the inhibitors, structures of uncomplexed HIV-1-protease and thrombin were also used successfully for QM/MM docking experiments. By comparing the resulting structures with those obtained using protein structures from protein-inhibitor complexes, we find that the method is able to simulate the effect of the induced fit when a simple optimization is adequate to reproduce the protein movement. Describing the ligand quantum mechanically gives a detailed view of its electronic properties, for example its polarization within the active site of the enzyme. This study suggests strongly that a QM/MM molecular dynamics approach will be able to simulate the induced fit in general cases.

Beierlein, Frank; Lanig, Harald; Schürer, Gudrun; Horn, Anselm H. C.; Clark, Timothy

12

Quantum Mechanical/Molecular Mechanical Studies on Spectral Tuning Mechanisms of Visual Pigments and Other Photoactive Proteins†  

PubMed Central

The protein environments surrounding the retinal tune electronic absorption maximum from 350 to 630 nm. Hybrid quantum mechanical/molecular mechanical (QM/MM) methods can be used in calculating excitation energies of retinal in its native protein environments and in studying the molecular basis of spectral tuning. We hereby review recent QM/MM results on the phototransduction of bovine rhodopsin, bacteriorhodopsin, sensory rhodopsin II, nonretinal photoactive yellow protein and their mutants.

Altun, Ahmet; Yokoyama, Shozo; Morokuma, Keiji

2008-01-01

13

Parallel iterative reaction path optimization in ab initio quantum mechanical\\/molecular mechanical modeling of enzyme reactions  

Microsoft Academic Search

The determination of reaction paths for enzyme systems remains a great challenge for current computational methods. In this paper we present an efficient method for the determination of minimum energy reaction paths with the ab initio quantum mechanical\\/molecular mechanical approach. Our method is based on an adaptation of the path optimization procedure by Ayala and Schlegel for small molecules in

Haiyan Liu; Zhenyu Lu; G. Andrés Cisneros; Weitao Yang

2004-01-01

14

Coupling and uncoupling mechanisms in the methoxythreonine mutant of cytochrome P450cam: a quantum mechanical\\/molecular mechanical study  

Microsoft Academic Search

The Thr252 residue plays a vital role in the catalytic cycle of cytochrome P450cam during the formation of the active species\\u000a (Compound I) from its precursor (Compound 0). We investigate the effect of replacing Thr252 by methoxythreonine (MeO-Thr)\\u000a on this protonation reaction (coupling) and on the competing formation of the ferric resting state and H2O2 (uncoupling) by combined quantum mechanical\\/molecular

Muhannad Altarsha; Tobias Benighaus; Devesh Kumar; Walter Thiel

2010-01-01

15

Gauge-origin independent magnetizabilities from hybrid quantum mechanics\\/molecular mechanics models: Theory and applications to liquid water  

Microsoft Academic Search

The theory of a hybrid quantum mechanics\\/molecular mechanics (QM\\/MM) approach for gauge-origin independent calculations of the molecular magnetizability using Hartree–Fock or Density Functional Theory is presented. The method is applied to liquid water using configurations generated from classical Molecular Dynamics simulation to calculate the statistical averaged magnetizability. Based on a comparison with experimental data, treating only one water molecule quantum

Kestutis Aidas; Jacob Kongsted; Christian B. Nielsen; Kurt V. Mikkelsen; Ove Christiansen; Kenneth Ruud

2007-01-01

16

Quantum Mechanics/Molecular Mechanics Electrostatic Embedding with Continuous and Discrete Functions  

PubMed Central

A quantum mechanics/molecular mechanics (QM/MM) implementation that uses the Gaussian electrostatic model (GEM) as the MM force field is presented. GEM relies on the reproduction of electronic density by using auxiliary basis sets to calculate each component of the intermolecular interaction. This hybrid method has been used, along with a conventional QM/MM (point charges) method, to determine the polarization on the QM subsystem by the MM environment in QM/MM calculations on 10 individual H2O dimers and a Mg2+-H2O dimer. We observe that GEM gives the correct polarization response in cases when the MM fragment has a small charge, while the point charges produce significant over-polarization of the QM subsystem and in several cases present an opposite sign for the polarization contribution. In the case when a large charge is located in the MM subsystem, for example, the Mg2+ ion, the opposite is observed at small distances. However, this is overcome by the use of a damped Hermite charge, which provides the correct polarization response.

Cisneros, G. Andres; Piquemal, Jean-Philip; Darden, Thomas A.

2009-01-01

17

Ab Initio Quantum Chemical and Mixed Quantum Mechanics/molecular Mechanics (qm/mm) Methods for Studying Enzymatic Catalysis  

NASA Astrophysics Data System (ADS)

We describe large scale ab initio quantum chemical and mixed quantum mechanics/molecular mechanics (QM/MM) methods for studying enzymatic reactions. First, technical aspects of the methodology are reviewed, including the hybrid density functional theory (DFT) methods that are typically employed for the QM aspect of the calculations, and various approaches to defining the interface between the QM and MM regions in QM/MM approaches. The modeling of the enzymatic catalytic cycle for three examples—methane monooxygenase, cytochrome P450, and triose phosphate isomerase—are discussed in some depth, followed by a brief summary of other systems that have been investigated by ab initio methods over the past several years. Finally, a discussion of the qualitative and quantitative conclusions concerning enzymatic catalysis that are available from modern ab initio approaches is presented, followed by a conclusion briefly summarizing future prospects.

Friesner, Richard A.; Guallar, Victor

2005-05-01

18

Coupled quantum mechanical\\/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets  

Microsoft Academic Search

Coupled quantum mechanical\\/molecular mechanical (QM\\/MM) calculations were used to study the effects of large defects and cracks on the mechanical properties of carbon nanotubes and graphene sheets. The semi-empirical method PM3 was used to treat the QM subdomains and a Tersoff-Brenner potential was used for the molecular mechanics; some of the QM calculations were also done using density functional theory

Roopam Khare; Steven L. Mielke; Jeffrey T. Paci; Sulin Zhang; Roberto Ballarini; George C. Schatz; Ted Belytschko

2007-01-01

19

Hybrid schemes based on quantum mechanics/molecular mechanics simulations goals to success, problems, and perspectives.  

PubMed

The development of characterization techniques, advanced synthesis methods, as well as molecular modeling has transformed the study of systems in a well-established research field. The current research challenges in biocatalysis and biotransformation evolve around enzyme discovery, design, and optimization. How can we find or create enzymes that catalyze important synthetic reactions, even reactions that may not exist in nature? What is the source of enzyme catalytic power? To answer these and other related questions, the standard strategies have evolved from trial-and-error methodologies based on chemical knowledge, accumulated experience, and common sense into a clearly multidisciplinary science that allows one to reach the molecular design of tailor-made enzyme catalysts. This is even more so when one refers to enzyme catalysts, for which the detailed structure and composition are known and can be manipulated to introduce well-defined residues which can be implicated in the chemical rearrangements taking place in the active site. The methods and techniques of theoretical and computational chemistry are becoming more and more important in both understanding the fundamental biological roles of enzymes and facilitating their utilization in biotechnology. Improvement of the catalytic function of enzymes is important from scientific and industrial viewpoints, and to put this fact in the actual perspective as well as the potentialities, we recommend the very recent report of Sanderson [Sanderson, K. (2011). Chemistry: enzyme expertise. Nature 471, 397.]. Great fundamental advances have been made toward the ab initio design of enzyme catalysts based on molecular modeling. This has been based on the molecular mechanistic knowledge of the reactions to be catalyzed, together with the development of advanced synthesis and characterization techniques. The corresponding molecular mechanism can be studied by means of powerful quantum chemical calculations. The catalytic active site can be optimized to improve the transition state analogues (TSA) and to enhance the catalytic activity, even improve the active site to favor a desired direction of some promiscuous enzymes. In this chapter, we give a brief introduction, the state of the art, and future prospects and implications of enzyme design. Current computational tools to assist experimentalists for the design and engineering of proteins with desired catalytic properties are described. The interplay between enzyme design, molecular simulations, and experiments will be presented to emphasize the interdisciplinary nature of this research field. This text highlights the recent advances and examples selected from our laboratory are shown, of how the applications of these tools are a first attempt to de novo design of protein active sites. Identification of neutral/advantageous/deleterious mutation platforms can be exploited to penetrate some of Nature's closely guarded secrets of chemical reactivity. In this chapter, we give a brief introduction, the state of the art, and future prospects and implications of enzyme design. The first part describes briefly how the molecular modeling is carried out. Then, we discuss the requirements of hybrid quantum mechanical/molecular mechanics molecular dynamics (QM/MM MD) simulations, analyzing what are the basis of these theoretical methodologies, how we can use them with a view to its application in the study of enzyme catalysis, and what are the best methodologies for assessing its catalytic potential. In the second part, we focus on some selected examples, taking as a common guide the chorismate to prephenate rearrangement, studying the corresponding molecular mechanism in vacuo, in solution and in an enzyme environment. In addition, examples involving catalytic antibodies (CAs) and promiscuous enzymes will be presented. Finally, a special emphasis is made to provide some hints about the logical evolution that can be anticipated in this research field. Moreover, it helps in understanding the open directions in this area of knowledge and highligh

Ferrer, Silvia; Ruiz-Pernía, Javier; Martí, Sergio; Moliner, Vicent; Tuñón, Iñaki; Bertrán, Juan; Andrés, Juan

2011-01-01

20

Determinants of Reactivity and Selectivity in Soluble Epoxide Hydrolase from Quantum Mechanics/Molecular Mechanics Modeling  

PubMed Central

Soluble epoxide hydrolase (sEH) is an enzyme involved in drug metabolism that catalyzes the hydrolysis of epoxides to form their corresponding diols. sEH has a broad substrate range and shows high regio- and enantioselectivity for nucleophilic ring opening by Asp333. Epoxide hydrolases therefore have potential synthetic applications. We have used combined quantum mechanics/molecular mechanics (QM/MM) umbrella sampling molecular dynamics (MD) simulations (at the AM1/CHARMM22 level) and high-level ab initio (SCS-MP2) QM/MM calculations to analyze the reactions, and determinants of selectivity, for two substrates: trans-stilbene oxide (t-SO) and trans-diphenylpropene oxide (t-DPPO). The calculated free energy barriers from the QM/MM (AM1/CHARMM22) umbrella sampling MD simulations show a lower barrier for phenyl attack in t-DPPO, compared with that for benzylic attack, in agreement with experiment. Activation barriers in agreement with experimental rate constants are obtained only with the highest level of QM theory (SCS-MP2) used. Our results show that the selectivity of the ring-opening reaction is influenced by several factors, including proximity to the nucleophile, electronic stabilization of the transition state, and hydrogen bonding to two active site tyrosine residues. The protonation state of His523 during nucleophilic attack has also been investigated, and our results show that the protonated form is most consistent with experimental findings. The work presented here illustrates how determinants of selectivity can be identified from QM/MM simulations. These insights may also provide useful information for the design of novel catalysts for use in the synthesis of enantiopure compounds.

2012-01-01

21

Free Energies of Chemical Reactions in Solution and in Enzymes with Ab Initio Quantum Mechanics\\/Molecular Mechanics Methods  

Microsoft Academic Search

Combined quantum mechanics\\/molecular mechanics (QM\\/MM) methods provide an accurate and efficient energetic description of complex chemical and biological systems, leading to significant advances in the understanding of chemical reactions in solution and in enzymes. Here we review progress in QM\\/MM methodology and applications, focusing on ab initio QM-based approaches. Ab initio QM\\/MM methods capitalize on the accuracy and reliability of

Hao Hu; Weitao Yang

2008-01-01

22

Quantum Mechanical/Molecular Mechanical Simulation Study of the Mechanism of Hairpin Ribozyme Catalysis  

PubMed Central

The molecular mechanism of hairpin ribozyme catalysis is studied with molecular dynamics simulations using a combined quantum mechanical and molecular mechanical (QM/MM) potential with a recently developed semiempirical AM1/d-PhoT model for phosphoryl transfer reactions. Simulations are used to derive one- and two-dimensional potentials of mean force to examine specific reaction paths and assess the feasibility of proposed general acid and base mechanisms. Density-functional calculations of truncated active site models provide complementary insight to the simulation results. Key factors utilized by the hairpin ribozyme to enhance the rate of transphosphorylation are presented, and the roles of A38 and G8 as general acid and base catalysts are discussed. The computational results are consistent with available experimental data, provide support for a general acid/base mechanism played by functional groups on the nucleobases, and offer important insight into the ability of RNA to act as a catalyst without explicit participation by divalent metal ions.

Nam, Kwangho; Gao, Jiali; York, Darrin M.

2009-01-01

23

Investigations of enzyme-catalysed reactions with combined quantum mechanics/molecular mechanics (QM/MM) methods  

NASA Astrophysics Data System (ADS)

Combined quantum mechanics/molecular mechanics (QM/MM or QM-MM) methods are an excellent approach for modelling the mechanisms of enzyme-catalysed reactions. QM/MM methods allow detailed modelling of reactions in enzymes by coupling quantum chemical calculations on the active site with a simpler, empirical `molecular mechanics' treatment of the rest of the protein. Possible reaction mechanisms can be compared and catalytic interactions analysed. QM/MM calculations can now be carried out for enzyme-catalysed reactions with quantum chemical methods of potentially very high accuracy. More approximate QM methods can allow extensive molecular simulations (e.g. molecular dynamics or Monte Carlo simulations). In this review, QM/MM techniques are outlined and some recent applications to enzyme-catalysed reactions are discussed.

Ranaghan, Kara E.; Mulholland, Adrian J.

24

The importance of reactant positioning in enzyme catalysis: A hybrid quantum mechanics/molecular mechanics study of a haloalkane dehalogenase  

PubMed Central

Hybrid quantum mechanics/molecular mechanics calculations using Austin Model 1 system-specific parameters were performed to study the SN2 displacement reaction of chloride from 1,2-dichloroethane (DCE) by nucleophilic attack of the carboxylate of acetate in the gas phase and by Asp-124 in the active site of haloalkane dehalogenase from Xanthobacter autotrophicus GJ10. The activation barrier for nucleophilic attack of acetate on DCE depends greatly on the reactants having a geometry resembling that in the enzyme or an optimized gas-phase structure. It was found in the gas-phase calculations that the activation barrier is 9 kcal/mol lower when dihedral constraints are used to restrict the carboxylate nucleophile geometry to that in the enzyme relative to the geometries for the reactants without dihedral constraints. The calculated quantum mechanics/molecular mechanics activation barriers for the enzymatic reaction are 16.2 and 19.4 kcal/mol when the geometry of the reactants is in a near attack conformer from molecular dynamics and in a conformer similar to the crystal structure (DCE is gauche), respectively. This haloalkane dehalogenase lowers the activation barrier for dehalogenation of DCE by 2–4 kcal/mol relative to the single point energies of the enzyme's quantum mechanics atoms in the gas phase. SN2 displacements of this sort in water are infinitely slower than in the gas phase. The modest lowering of the activation barrier by the enzyme relative to the reaction in the gas phase is consistent with mutation experiments.

Lau, Edmond Y.; Kahn, Kalju; Bash, Paul A.; Bruice, Thomas C.

2000-01-01

25

Quantum mechanics/molecular mechanics investigation of the mechanism of phosphate transfer in human uridine-cytidine kinase 2  

PubMed Central

The mechanisms of enzyme-catalyzed phosphate transfer and hydrolysis reactions are of great interest due to their importance and abundance in biochemistry. The reaction may proceed in a stepwise fashion, with either a pentavalent phosphorane or a metaphosphate anion intermediate, or by a concerted SN2 mechanism. Despite much theoretical work focused on a few key enzymes, a consensus for the mechanism has not been reached, and examples of all three possibilities have been demonstrated. We have investigated the mechanism of human uridine-cytidine kinase 2 (UCK2, EC 2.7.1.48), which catalyzes the transfer of a phosphate group from ATP to the ribose 5?-hydroxyl of cytidine and uridine. UCK2 is normally expressed in human placenta, but is overexpressed in certain cancer cells, where it is responsible for activating a class of antitumor prodrugs. The UCK2 mechanism was investigated by generating a 2D potential energy surface as a function of the P–O bonds forming and breaking, with energies calculated using a quantum mechanics/molecular mechanics potential (B3LYP/6–31G(d):AMBER). The mechanism of phosphate transfer is shown to be concerted, and is accompanied by concerted proton transfer from the 5?-hydroxyl to a conserved active site aspartic acid that serves as a catalytic base. The calculated barrier for this reaction is 15.1 kcal/mol, in relatively good agreement with the experimental barrier of 17.5 kcal/mol. The interactions of the enzyme active site with the reactant, transition state, and product are examined for their implications on the design of anticancer prodrugs or positron emission tomography (PET) reporter probes for this enzyme.

Smith, Adam J. T.; Li, Ying; Houk, K. N.

2011-01-01

26

Phosphorylation Reaction in cAPK Protein Kinase - Free Energy Quantum Mechanic/Molecular Mechanics Simulations.  

SciTech Connect

Protein kinases catalyze the transfer of the ?-phosphoryl group from ATP, a key regulatory process governing signalling pathways in eukaryotic cells. The structure of the active site in these enzymes is highly conserved implying common catalytic mechanism. In this work we investigate the reaction process in cAPK protein kinase (PKA) using a combined quantum mechanics and molecular mechanics approach. The novel computational features of our work include reaction pathway determination with nudged elastic band methodology and calculation of free energy profiles of the reaction process taking into account finite temperature fluctuations of the protein environment. We find that the transfer of the ?-phosphoryl group in the protein environment is an exothermic reaction with the reaction barrier of 15 kcal/mol.

Valiev, Marat; Yang, Jie; Adams, Joseph; Taylor, Susan S.; Weare, John H.

2007-11-29

27

Hybrid quantum mechanical/molecular mechanical investigation of the beta-1,4-galactosyltransferase-I mechanism.  

PubMed

The enzyme beta-1,4-galactosyltransferase-1 (beta4Gal-T1) catalyzes the transfer of a galactose residue from UDP-Gal to the C4-hydroxyl group of N-acetylglucosamine. The catalytic mechanism of beta4Gal-T1 was investigated using the hybrid quantum mechanical/molecular mechanical (QM/MM) method, with the QM portion containing 253 atoms treated with density functional theory (DFT) at the BP/DZP and BP/TZ2P levels. The remaining parts of the beta4Gal-T1 complex, 4527 atoms in all, were modeled using the AMBER molecular force field. A theoretical model of the Michaelis complex was built using the X-ray structure of beta4Gal-T1 in a complex with the donor or acceptor substrate, respectively. The hybrid QM(DFT)/MM calculations identified an S(N)2-type transition state for the nucleophilic attack of the O4(a) oxygen on the anomeric carbon C1 and the breaking of the C1-O1 glycosidic linkage. The activation barrier found for this process is 15 kcal/mol. In the transition state (TS) model, the sugar donor is partially cleaved from pyrophosphate, while nucleophilic oxygen O4(a) remains protonated with a low barrier hydrogen bond to the catalytic base D318. The structure of TS is characterized by the O4(a)-C1 and C1-O1 distances of 2.703 and 2.092 A, respectively. When the obtained reaction sequence was used, the nature of the captured intermediate resembling the transition state structure (PDB/2FYD) was elucidated. This modeling QM/MM study has provided detailed insight into the mechanism of the Gal transfer catalyzed by beta4Gal-T1 and has supplied further evidence for a concerted S(N)2-type displacement mechanism employed by inverting glycosyltransferases. PMID:19627105

Krupicka, Martin; Tvaroska, Igor

2009-08-13

28

Conical intersections in solution: Formulation, algorithm, and implementation with combined quantum mechanics/molecular mechanics method  

PubMed Central

The significance of conical intersections in photophysics, photochemistry, and photodissociation of polyatomic molecules in gas phase has been demonstrated by numerous experimental and theoretical studies. Optimization of conical intersections of small- and medium-size molecules in gas phase has currently become a routine optimization process, as it has been implemented in many electronic structure packages. However, optimization of conical intersections of small- and medium-size molecules in solution or macromolecules remains inefficient, even poorly defined, due to large number of degrees of freedom and costly evaluations of gradient difference and nonadiabatic coupling vectors. In this work, based on the sequential quantum mechanics and molecular mechanics (QM?MM) and QM?MM-minimum free energy path methods, we have designed two conical intersection optimization methods for small- and medium-size molecules in solution or macromolecules. The first one is sequential QM conical intersection optimization and MM minimization for potential energy surfaces; the second one is sequential QM conical intersection optimization and MM sampling for potential of mean force surfaces, i.e., free energy surfaces. In such methods, the region where electronic structures change remarkably is placed into the QM subsystem, while the rest of the system is placed into the MM subsystem; thus, dimensionalities of gradient difference and nonadiabatic coupling vectors are decreased due to the relatively small QM subsystem. Furthermore, in comparison with the concurrent optimization scheme, sequential QM conical intersection optimization and MM minimization or sampling reduce the number of evaluations of gradient difference and nonadiabatic coupling vectors because these vectors need to be calculated only when the QM subsystem moves, independent of the MM minimization or sampling. Taken together, costly evaluations of gradient difference and nonadiabatic coupling vectors in solution or macromolecules can be reduced significantly. Test optimizations of conical intersections of cyclopropanone and acetaldehyde in aqueous solution have been carried out successfully.

Cui, Ganglong; Yang, Weitao

2011-01-01

29

A polarizable force-field model for quantum-mechanical-molecular-mechanical Hamiltonian using expansion of point charges into orbitals  

NASA Astrophysics Data System (ADS)

We present an ab initio polarizable representation of classical molecular mechanics (MM) atoms by employing an angular momentum-based expansion scheme of the point charges into partial wave orbitals. The charge density represented by these orbitals can be fully polarized, and for hybrid quantum-mechanical-molecular-mechanical (QM/MM) calculations, mutual polarization within the QM/MM Hamiltonian can be obtained. We present the mathematical formulation and the analytical expressions for the energy and forces pertaining to the method. We further develop a variational scheme to appropriately determine the expansion coefficients and then validate the method by considering polarizations of ions by the QM system employing the hybrid GROMACS-CPMD QM/MM program. Finally, we present a simpler prescription for adding isotropic polarizability to MM atoms in a QM/MM simulation. Employing this simpler scheme, we present QM/MM energy minimization results for the classic case of a water dimer and a hydrogen sulfide dimer. Also, we present single-point QM/MM results with and without the polarization to study the change in the ionization potential of tetrahydrobiopterin (BH4) in water and the change in the interaction energy of solvated BH4 (described by MM) with the P450 heme described by QM. The model can be employed for the development of an extensive classical polarizable force-field.

Biswas, P. K.; Gogonea, Valentin

2008-10-01

30

A polarizable force-field model for quantum-mechanical-molecular-mechanical Hamiltonian using expansion of point charges into orbitals.  

PubMed

We present an ab initio polarizable representation of classical molecular mechanics (MM) atoms by employing an angular momentum-based expansion scheme of the point charges into partial wave orbitals. The charge density represented by these orbitals can be fully polarized, and for hybrid quantum-mechanical-molecular-mechanical (QM/MM) calculations, mutual polarization within the QM/MM Hamiltonian can be obtained. We present the mathematical formulation and the analytical expressions for the energy and forces pertaining to the method. We further develop a variational scheme to appropriately determine the expansion coefficients and then validate the method by considering polarizations of ions by the QM system employing the hybrid GROMACS-CPMD QM/MM program. Finally, we present a simpler prescription for adding isotropic polarizability to MM atoms in a QM/MM simulation. Employing this simpler scheme, we present QM/MM energy minimization results for the classic case of a water dimer and a hydrogen sulfide dimer. Also, we present single-point QM/MM results with and without the polarization to study the change in the ionization potential of tetrahydrobiopterin (BH(4)) in water and the change in the interaction energy of solvated BH(4) (described by MM) with the P(450) heme described by QM. The model can be employed for the development of an extensive classical polarizable force-field. PMID:19045177

Biswas, P K; Gogonea, Valentin

2008-10-21

31

Nuclear magnetic shielding constants of liquid water: Insights from hybrid quantum mechanics\\/molecular mechanics models  

Microsoft Academic Search

We present a gauge-origin independent method for the calculation of nuclear magnetic shielding tensors of molecules in a structured and polarizable environment. The method is based on a combination of density functional theory (DFT) or Hartree-Fock wave functions with molecular mechanics. The method is unique in the sense that it includes three important properties that need to be fulfilled in

Jacob Kongsted; Christian B. Nielsen; Kurt V. Mikkelsen; Ove Christiansen; Kenneth Ruud

2007-01-01

32

The Role of Magnesium for Geometry and Charge in GTP Hydrolysis, Revealed by Quantum Mechanics/Molecular Mechanics Simulations  

PubMed Central

The coordination of the magnesium ion in proteins by triphosphates plays an important role in catalytic hydrolysis of GTP or ATP, either in signal transduction or energy conversion. For example, in Ras the magnesium ion contributes to the catalysis of GTP hydrolysis. The cleavage of GTP to GDP and Pi in Ras switches off cellular signaling. We analyzed GTP hydrolysis in water, Ras, and Ras·Ras-GTPase-activating protein using quantum mechanics/molecular mechanics simulations. By comparison of the theoretical IR-difference spectra for magnesium ion coordinated triphosphate to experimental ones, the simulations are validated. We elucidated thereby how the magnesium ion contributes to catalysis. It provides a temporary storage for the electrons taken from the triphosphate and it returns them after bond cleavage and Pi release back to the diphosphate. Furthermore, the Ras·Mg2+ complex forces the triphosphate into a stretched conformation in which the ?- and ?-phosphates are coordinated in a bidentate manner. In this conformation, the triphosphate elongates the bond, which has to be cleaved during hydrolysis. Furthermore, the ?-phosphate adopts a more planar structure, driving the conformation of the molecule closer to the hydrolysis transition state. GTPase-activating protein enhances these changes in GTP conformation and charge distribution via the intruding arginine finger.

Rudack, Till; Xia, Fei; Schlitter, Jurgen; Kotting, Carsten; Gerwert, Klaus

2012-01-01

33

Calculating solution redox free energies with ab initio quantum mechanical/molecular mechanical minimum free energy path method  

PubMed Central

A quantum mechanical?molecular mechanical minimum free energy path (QM?MM-MFEP) method was developed to calculate the redox free energies of large systems in solution with greatly enhanced efficiency for conformation sampling. The QM?MM-MFEP method describes the thermodynamics of a system on the potential of mean force surface of the solute degrees of freedom. The molecular dynamics (MD) sampling is only carried out with the QM subsystem fixed. It thus avoids “on-the-fly” QM calculations and thus overcomes the high computational cost in the direct QM?MM MD sampling. In the applications to two metal complexes in aqueous solution, the new QM?MM-MFEP method yielded redox free energies in good agreement with those calculated from the direct QM?MM MD method. Two larger biologically important redox molecules, lumichrome and riboflavin, were further investigated to demonstrate the efficiency of the method. The enhanced efficiency and uncompromised accuracy are especially significant for biochemical systems. The QM?MM-MFEP method thus provides an efficient approach to free energy simulation of complex electron transfer reactions.

Zeng, Xiancheng; Hu, Hao; Hu, Xiangqian; Yang, Weitao

2009-01-01

34

Calculating solution redox free energies with ab initio quantum mechanical/molecular mechanical minimum free energy path method.  

PubMed

A quantum mechanical/molecular mechanical minimum free energy path (QM/MM-MFEP) method was developed to calculate the redox free energies of large systems in solution with greatly enhanced efficiency for conformation sampling. The QM/MM-MFEP method describes the thermodynamics of a system on the potential of mean force surface of the solute degrees of freedom. The molecular dynamics (MD) sampling is only carried out with the QM subsystem fixed. It thus avoids "on-the-fly" QM calculations and thus overcomes the high computational cost in the direct QM/MM MD sampling. In the applications to two metal complexes in aqueous solution, the new QM/MM-MFEP method yielded redox free energies in good agreement with those calculated from the direct QM/MM MD method. Two larger biologically important redox molecules, lumichrome and riboflavin, were further investigated to demonstrate the efficiency of the method. The enhanced efficiency and uncompromised accuracy are especially significant for biochemical systems. The QM/MM-MFEP method thus provides an efficient approach to free energy simulation of complex electron transfer reactions. PMID:19405565

Zeng, Xiancheng; Hu, Hao; Hu, Xiangqian; Yang, Weitao

2009-04-28

35

Calculating solution redox free energies with ab initio quantum mechanical/molecular mechanical minimum free energy path method  

SciTech Connect

A quantum mechanical/molecular mechanical minimum free energy path (QM/MM-MFEP) method was developed to calculate the redox free energies of large systems in solution with greatly enhanced efficiency for conformation sampling. The QM/MM-MFEP method describes the thermodynamics of a system on the potential of mean force surface of the solute degrees of freedom. The molecular dynamics (MD) sampling is only carried out with the QM subsystem fixed. It thus avoids 'on-the-fly' QM calculations and thus overcomes the high computational cost in the direct QM/MM MD sampling. In the applications to two metal complexes in aqueous solution, the new QM/MM-MFEP method yielded redox free energies in good agreement with those calculated from the direct QM/MM MD method. Two larger biologically important redox molecules, lumichrome and riboflavin, were further investigated to demonstrate the efficiency of the method. The enhanced efficiency and uncompromised accuracy are especially significant for biochemical systems. The QM/MM-MFEP method thus provides an efficient approach to free energy simulation of complex electron transfer reactions.

Zeng Xiancheng; Hu Hao; Hu Xiangqian; Yang Weitao [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States)

2009-04-28

36

Classical and quantum mechanical\\/molecular mechanical molecular dynamics simulations of alanine dipeptide in water: Comparisons with IR and vibrational circular dichroism spectra  

Microsoft Academic Search

We have implemented the combined quantum mechanical (QM)\\/molecular mechanical (MM) molecular dynamics (MD) simulations of alanine dipeptide in water along with the polarizable and nonpolarizable classical MD simulations with different models of water. For the QM\\/MM MD simulation, the alanine dipeptide is treated with the AM1 or PM3 approximations and the fluctuating solute dipole moment is calculated by the Mulliken

Kijeong Kwac; Kyung-Koo Lee; Jae Bum Han; Kwang-Im Oh; Minhaeng Cho

2008-01-01

37

Reaction path determination for quantum mechanical\\/molecular mechanical modeling of enzyme reactions by combining first order and second order ``chain-of-replicas'' methods  

Microsoft Academic Search

A two-step procedure for the determination of reaction paths in enzyme systems is presented. This procedure combines two chain-of-states methods: a quantum mechanical\\/molecular mechanical (QM\\/MM) implementation of the nudged elastic band (NEB) method and a second order parallel path optimizer method both recently developed in our laboratory. In the first step, a reaction path determination is performed with the NEB

G. Andrés Cisneros; Haiyan Liu; Zhenyu Lu; Weitao Yang

2005-01-01

38

Cooperative effects in the structuring of fluoride water clusters: Ab initio hybrid quantum mechanical\\/molecular mechanical model incorporating polarizable fluctuating charge solvent  

Microsoft Academic Search

A new hybrid quantum mechanical\\/molecular mechanical model of solvation is developed and used to describe the structure and dynamics of small fluoride\\/water clusters, using an ab initio wave function to model the ion and a fluctuating charge potential to model the waters. Appropriate parameters for the water-water and fluoride-water interactions are derived, with the fluoride anion being described by density

Richard A. Bryce; Mark A. Vincent; Nathaniel O. J. Malcolm; Ian H. Hillier; Neil A. Burton

1998-01-01

39

Cooperative effects in the structuring of fluoride water clusters: Ab initio hybrid quantum mechanical\\/molecular mechanical model incorporating polarizable fluctuating charge solvent  

Microsoft Academic Search

A new hybrid quantum mechanical\\/molecular mechanical model of solvation is developed and used to describe the structure and dynamics of small fluoride\\/water clusters, using an ab initio wave function to model the ion and a fluctuating charge potential to model the waters. Appropriate parameters for the water–water and fluoride–water interactions are derived, with the fluoride anion being described by density

Richard A. Bryce; Mark A. Vincent; Nathaniel O. J. Malcolm; Ian H. Hillier; Neil A. Burton

1998-01-01

40

Classical and quantum mechanical/molecular mechanical molecular dynamics simulations of alanine dipeptide in water: comparisons with IR and vibrational circular dichroism spectra.  

PubMed

We have implemented the combined quantum mechanical (QM)/molecular mechanical (MM) molecular dynamics (MD) simulations of alanine dipeptide in water along with the polarizable and nonpolarizable classical MD simulations with different models of water. For the QM/MM MD simulation, the alanine dipeptide is treated with the AM1 or PM3 approximations and the fluctuating solute dipole moment is calculated by the Mulliken population analysis. For the classical MD simulations, the solute is treated with the polarizable or nonpolarizable AMBER and polarizable CHARMM force fields and water is treated with the TIP3P, TIP4P, or TIP5P model. It is found that the relative populations of right-handed alpha-helix and extended beta and P(II) conformations in the simulation trajectory strongly depend on the simulation method. For the QM/MM MD simulations, the PM3/MM shows that the P(II) conformation is dominant, whereas the AM1/MM predicts that the dominant conformation is alpha(R). Polarizable CHARMM force field gives almost exclusively P(II) conformation and other force fields predict that both alpha-helical and extended (beta and P(II)) conformations are populated with varying extents. Solvation environment around the dipeptide is investigated by examining the radial distribution functions and numbers and lifetimes of hydrogen bonds. Comparing the simulated IR and vibrational circular dichroism spectra with experimental results, we concluded that the dipeptide adopts the P(II) conformation and PM3/MM, AMBER03 with TIP4P water, and AMBER polarizable force fields are acceptable for structure determination of the dipeptide considered in this paper. PMID:18345930

Kwac, Kijeong; Lee, Kyung-Koo; Han, Jae Bum; Oh, Kwang-Im; Cho, Minhaeng

2008-03-14

41

Catalytic Mechanism of Hyaluronate Lyase from Spectrococcus pneumonia: Quantum Mechanical/Molecular Mechanical and Density Functional Theory Studies.  

PubMed

Hyaluronate lyase from Spectrococcus pneumonia can degrade hyaluronic acid, which is one of the major components in the extracellular matrix. The major functions of hyaluronan are to regulate water balance and osmotic pressure and act as an ion-exchange resin. It has been suggested in our previous molecular dynamics simulation that the binding of the substrate molecule could lead to the ionization of Y408 and protonation of H399. Followed by our recent molecular dynamics simulation of the enzyme-substrate complex, a unified proton abstraction and donation mechanism for this enzyme can be established using a combined quantum mechanical and molecular mechanical approach and density functional theory method. Y408 is shown to serve as the general base in the proton abstraction, while general acid is the next proton donation step. Overall, this reaction can be classified into syn-elimination reaction mechanism. The neutralization effects of C5 carboxylate group by several polar residues such as N349 and H399 were also examined. Finally, in combination of our previous molecular dynamics simulations, a complete catalytic cycle for the degradation of hyaluronan tetrasaccharide catalyzed by the hyaluronate lyase from Spectrococcus pneumonia is proposed. PMID:23944739

Zheng, Min; Xu, Dingguo

2013-08-27

42

The generalized hybrid orbital method for combined quantum mechanical\\/molecular mechanical calculations: formulation and tests of the analytical derivatives  

Microsoft Academic Search

.  ?Hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials are becoming increasingly important for studying\\u000a condensed-phase systems but one of the outstanding problems in the field has been how to treat covalent bonds between atoms\\u000a of the QM and MM regions. Recently, we presented a generalized hybrid orbital (GHO) method that was designed to tackle this\\u000a problem for hybrid potentials

Patricia Amara; Martin J. Field; Cristobal Alhambra; Jiali Gao

2000-01-01

43

Comparison of linear-scaling semiempirical methods and combined quantum mechanical/molecular mechanical methods applied to enzyme reactions  

NASA Astrophysics Data System (ADS)

Two theoretical methodologies - a combined quantum mechanical and molecular mechanical (QM/MM) model and a linear-scaling semiempirical SCF method (MOZYME) - were used to calculate energy profiles for an enzyme reaction path, that for hydride-ion transfer between 8-methylpterin and nicotinamide adenine dinucleotide phosphate (NADPH) in dihydrofolate reductase (DHFR). Profiles from the QM/MM model, which divides the system into QM and MM regions, were compared with those from MOZYME, which treats the entire ligand-protein complex quantum mechanically. If the coordinates of the MM region vary little, it is possible to define a QM/MM model for the DHFR reaction that gives energetics close to those from MOZYME. However, the QM/MM and MOZYME energies diverge when the MM geometry changes, largely due to the MM electrostatic energy. `Switching off' polarisation of the QM region by the MM region produced larger changes especially in the transition-state region. The results suggest caution should be used when generating reaction paths for QM/MM methods.

Titmuss, Stephen J.; Cummins, Peter L.; Bliznyuk, Andrey A.; Rendell, Alistair P.; Gready, Jill E.

2000-03-01

44

Phosphorylation reaction in cAPK protein kinase-free energy quantum mechanical/molecular mechanics simulations.  

PubMed

We present results of a theoretical analysis of the phosphorylation reaction in cAMP-dependent protein kinase using a combined quantum mechanical and molecular mechanics (QM/MM) approach. Detailed analysis of the reaction pathway is provided using a novel QM/MM implementation of the nudged elastic band method, finite temperature fluctuations of the protein environment are taken into account using free energy calculations, and an analysis of hydrogen bond interactions is performed on the basis of calculated frequency shifts. The late transfer of the substrate proton to the conserved aspartate (D166), the activation free energy of 15 kcal/mol, and the slight exothermic (-3 kcal/mol) character of the reaction are all consistent with the experimental data. The near attack conformation of D166 in the reactant state is maintained by interactions with threonine-201, asparagine-177, and most notably by a conserved water molecule serving as a strong structural link between the primary metal ion and the D166. The secondary Mg ion acts as a Lewis acid, attacking the beta-gamma bridging oxygen of ATP. This interaction, along with a strong hydrogen bond between the D166 and the substrate, contributes to the stabilization of the transition state. Lys-168 maintains a hydrogen bond to a transferring phosphoryl group throughout a reaction process. This interaction increases in the product state and contributes to its stabilization. PMID:17983217

Valiev, Marat; Yang, Jie; Adams, Joseph A; Taylor, Susan S; Weare, John H

2007-11-06

45

Prediction of organic molecular crystal geometries from MP2-level fragment quantum mechanical/molecular mechanical calculations  

NASA Astrophysics Data System (ADS)

The fragment-based hybrid many-body interaction (HMBI) model provides a computationally affordable means of applying electronic structure wavefunction methods to molecular crystals. It combines a quantum mechanical treatment of individual molecules in the unit cell and their short-range pairwise interactions with a polarizable molecular mechanics force-field treatment of long-range and many-body interactions. Here, we report the implementation of analytic nuclear gradients for the periodic model to enable full relaxation of both the atomic positions and crystal lattice parameters. Using a set of five, chemically diverse molecular crystals, we compare the quality of the HMBI MP2/aug-cc-pVDZ-level structures with those obtained from dispersion-corrected periodic density functional theory, B3LYP-D*, and from the Amoeba polarizable force field. The MP2-level structures largely agree with the experimental lattice parameters to within 2%, and the root-mean-square deviations in the atomic coordinates are less than 0.2 A?. These MP2 structures are almost as good as those predicted from periodic B3LYP-D*/TZP and are significantly better than those obtained with B3LYP-D*/6-31G(d,p) or with the Amoeba force field.

Nanda, Kaushik D.; Beran, Gregory J. O.

2012-11-01

46

Catalytic mechanism of human DNA polymerase ? with Mg2+ and Mn2+ from ab initio quantum mechanical/molecular mechanical studies  

PubMed Central

DNA polymerases play a crucial role in the cell cycle due to their involvement in genome replication and repair. Understanding the reaction mechanism by which these polymerases carry out their function can provide insights into these processes. Recently, the crystal structures of human DNA polymerase ? (Pol?) have been reported both for pre- and post- catalytic complexes (García-Díaz et al., DNA Repair, 3, 1333, 2007). Here we employ the pre-catalytic complex as a starting structure for the determination of the catalytic mechanism of Pol? using ab initio quantum mechanical/molecular mechanical methods. The reaction path has been calculated using Mg2+ and Mn2+ as the catalytic metals. In both cases the reaction proceeds through a two step mechanism where the 3?-OH of the primer sugar ring is deprotonated by one of the conserved Asp residues (D490) in the active site before the incorporation of the nucleotide to the nascent DNA chain. A significant charge transfer is observed between both metals and some residues in the active site as the reaction proceeds. The optimized reactant and product structures agree with the reported crystal structures. In addition, the calculated reaction barriers for both metals are close to experimentally estimated barriers. Energy decomposition analysis to explain individual residue contributions suggests that several amino acids surrounding the active site are important for catalysis. Some of these residues, including R420, R488 and E529, have been implicated in catalysis by previous mutagenesis experiments on the homologous residues on Pol?. Furthermore, Pol? residues R420 and E529 found to be important from the energy decomposition analysis, are homologous to residues R183 and E295 in Pol?, both of which are linked to cancer. In addition, residues R386, E391, K422 and K472 appear to have an important role in catalysis and could be a potential target for mutagenesis experiments. There is partial conservation of these residues across the Pol X family of DNA polymerases.

Cisneros, G. Andres; Perera, Lalith; Garcia-Diaz, Miguel; Bebenek, Katarzyna; Kunkel, Thomas A.; Pedersen, Lee G.

2008-01-01

47

Quantum mechanical/molecular mechanical study of mechanisms of heme degradation by the enzyme heme oxygenase: the strategic function of the water cluster.  

PubMed

Heme degradation by heme oxygenase (HO) enzymes is important in maintaining iron homeostasis and prevention of oxidative stress, etc. In response to mechanistic uncertainties, we performed quantum mechanical/molecular mechanical investigations of the heme hydroxylation by HO, in the native route and with the oxygen surrogate donor H2O2. It is demonstrated that H2O2 cannot be deprotonated to yield Fe(III)OOH, and hence the surrogate reaction starts from the FeHOOH complex. The calculations show that, when starting from either Fe(III)OOH or Fe(III)HOOH, the fully concerted mechanism involving O-O bond breakage and O-C(meso) bond formation is highly disfavored. The low-energy mechanism involves a nonsynchronous, effectively concerted pathway, in which the active species undergoes first O-O bond homolysis followed by a barrier-free (small with Fe(III)HOOH) hydroxyl radical attack on the meso position of the porphyrin. During the reaction of Fe(III)HOOH, formation of the Por+*FeIV=O species, compound I, competes with heme hydroxylation, thereby reducing the efficiency of the surrogate route. All these conclusions are in accord with experimental findings (Chu, G. C.; Katakura, K.; Zhang, X.; Yoshida, T.; Ikeda-Saito, M. J. Biol. Chem. 1999, 274, 21319). The study highlights the role of the water cluster in the distal pocket in creating "function" for the enzyme; this cluster affects the O-O cleavage and the O-Cmeso formation, but more so it is responsible for the orientation of the hydroxyl radical and for the observed alpha-meso regioselectivity of hydroxylation (Ortiz de Montellano, P. R. Acc. Chem. Res. 1998, 31, 543). Differences/similarities with P450 and HRP are discussed. PMID:18201087

Chen, Hui; Moreau, Yohann; Derat, Etienne; Shaik, Sason

2008-01-18

48

Time-dependent density functional theory excited state nonadiabatic dynamics combined with quantum mechanical/molecular mechanical approach: Photodynamics of indole in water  

NASA Astrophysics Data System (ADS)

We present a combination of time-dependent density functional theory with the quantum mechanical/molecular mechanical approach which can be applied to study nonadiabatic dynamical processes in molecular systems interacting with the environment. Our method is illustrated on the example of ultrafast excited state dynamics of indole in water. We compare the mechanisms of nonradiative relaxation and the electronic state lifetimes for isolated indole, indole in a sphere of classical water, and indole + 3H2O embedded in a classical water sphere. In the case of isolated indole, the initial excitation to the S2 electronic state is followed by an ultrafast internal conversion to the S1 state with a time constant of 17 fs. The S1 state is long living (>30 ps) and deactivates to the ground state along the N-H stretching coordinate. This deactivation mechanism remains unchanged for indole in a classical water sphere. However, the lifetimes of the S2 and S1 electronic states are extended. The inclusion of three explicit water molecules opens a new relaxation channel which involves the electron transfer to the solvent, leading eventually to the formation of a solvated electron. The relaxation to the ground state takes place on a time scale of 60 fs and contributes to the lowering of the fluorescence quantum yield. Our simulations demonstrate the importance of including explicit water molecules in the theoretical treatment of solvated systems.

Wohlgemuth, Matthias; Bona?i?-Koutecký, Vlasta; Mitri?, Roland

2011-08-01

49

Antibiotic binding to monozinc CphA beta-lactamase from Aeromonas hydropila: quantum mechanical/molecular mechanical and density functional theory studies.  

PubMed

The active-site dynamics of apo CphA beta-lactamase from Aeromonas hydropila and its complex with a beta-lactam antibiotic molecule (biapenem) are simulated using a quantum mechanical/molecular mechanical (QM/MM) method and density functional theory (DFT). The quantum region in the QM/MM simulations, which includes the Zn(II) ion and its ligands, the antibiotic molecule, the catalytic water, and an active-site histidine residue, was treated using the self-consistent charge density functional tight binding (SCC-DFTB) model. Biapenem is docked at the active site unambiguously, based on a recent X-ray structure of an enzyme-intermediate complex. The substrate is found to form the fourth ligand of the zinc ion with its 3-carboxylate oxygen and to hydrogen bond with several active-site residues. The stability of the metal-ligand bonds and the hydrogen-bond network is confirmed by 500 ps molecular dynamics simulations of both the apo enzyme and the substrate-enzyme complex. The structure and dynamics of the substrate-enzyme complex provide valuable insights into the mode of catalysis in such enzymes that is central to the bacterial resistance to beta-lactam antibiotics. PMID:16220984

Xu, Dingguo; Zhou, Yanzi; Xie, Daiqian; Guo, Hua

2005-10-20

50

Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. Part I. Application of the Huzinaga equation.  

PubMed

Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods. PMID:23281055

Ferenczy, György G

2012-12-28

51

Amine oxidation mediated by lysine-specific demethylase 1: quantum mechanics/molecular mechanics insights into mechanism and role of lysine 661.  

PubMed

We report classical molecular dynamics (MD) simulations and combined quantum mechanics/molecular mechanics (QM/MM) calculations to elucidate the catalytic mechanism of the rate-determining amine oxidation step in the lysine-specific demethylase 1 (LSD1)-catalyzed demethylation of the histone tail lysine (H3K4), with flavin adenine dinucleotide (FAD) acting as cofactor. The oxidation of substrate lysine (sLys) involves the cleavage of an ?-CH bond accompanied by the transfer of a hydride ion equivalent to FAD, leading to an imine intermediate. This hydride transfer pathway is shown to be clearly favored for sLys oxidation over other proposed mechanisms, including the radical (or single-electron transfer) route as well as carbanion and polar-nucleophilic mechanisms. MD simulations on six NVT ensembles (covering different protonation states of sLys and K661 as well as the K661M mutant) identify two possible orientations of the reacting sLys and FAD subunits (called "downward" and "upward"). Calculations at the QM(B3LYP-D/6-31G*)/CHARMM22 level provide molecular-level insights into the mechanism, helping to understand how LSD1 achieves the activation of the rather inert methyl-CH bond in a metal-free environment. Factors such as proper alignment of sLys (downward orientation), transition-state stabilization (due to the protein environment and favorable orbital interactions), and product stabilization via adduct formation are found to be crucial for facilitating the oxidative ?-CH bond cleavage. The current study also sheds light on the role of important active-site residues (Y761, K661, and W695) and of the conserved water-bridge motif. The steric influence of Y761 helps to position the reaction partners properly, K661 is predicted to get deprotonated prior to substrate binding and to act as an active-site base that accepts a proton from sLys to enable the subsequent amine oxidation, and the water bridge that is stabilized by K661 and W695 mediates this proton transfer. PMID:23988016

Karasulu, Bora; Patil, Mahendra; Thiel, Walter

2013-08-29

52

A Molecular Dynamics (MD) and Quantum Mechanics/Molecular Mechanics (QM/MM) Study on Ornithine Cyclodeaminase (OCD): A Tale of Two Iminiums  

PubMed Central

Ornithine cyclodeaminase (OCD) is an NAD+-dependent deaminase that is found in bacterial species such as Pseudomonas putida. Importantly, it catalyzes the direct conversion of the amino acid L-ornithine to L-proline. Using molecular dynamics (MD) and a hybrid quantum mechanics/molecular mechanics (QM/MM) method in the ONIOM formalism, the catalytic mechanism of OCD has been examined. The rate limiting step is calculated to be the initial step in the overall mechanism: hydride transfer from the L-ornithine’s C?–H group to the NAD+ cofactor with concomitant formation of a C?=NH2 + Schiff base with a barrier of 90.6 kJ mol?1. Importantly, no water is observed within the active site during the MD simulations suitably positioned to hydrolyze the C?=NH2 + intermediate to form the corresponding carbonyl. Instead, the reaction proceeds via a non-hydrolytic mechanism involving direct nucleophilic attack of the ?-amine at the C?-position. This is then followed by cleavage and loss of the ?-NH2 group to give the ?1-pyrroline-2-carboxylate that is subsequently reduced to L-proline.

Ion, Bogdan F.; Bushnell, Eric A. C.; De Luna, Phil; Gauld, James W.

2012-01-01

53

Quantum Mechanics/Molecular Mechanics Studies on the Sulfoxidation of Dimethyl Sulfide by Compound I and Compound 0 of Cytochrome P450: Which Is the Better Oxidant?  

NASA Astrophysics Data System (ADS)

The cytochromes P450 are ubiquitous enzymes that are involved in key metabolizing processes in the body through the monoxygenation of substrates; however, their active oxidant is elusive. There have been reports that implicate that two oxidants, namely, the iron(IV)-oxo porphyrin cation radical (compound I) and the iron(III)-hydroperoxo complex (compound 0), both act as oxidants of sulfoxidation reactions, which contrasts theoretical studies on alkene epoxidation by compounds I and 0 that implicated compound 0 as a sluggish oxidant. To resolve this controversy and to establish the potency of compound I and compound 0 in sulfoxidation reactions, we have studied dimethyl sulfide sulfoxidation by both oxidants using the quantum mechanics/molecular mechanics (QM/MM) technique on cytochrome P450 enzymes and have set up a model of two P450 isozymes: P450cam and P450BM3. The calculations support earlier gas-phase density functional theory modeling and show that compound 0 is a sluggish oxidant that is unable to compete with compound I. Furthermore, compound I is shown to react with dimethyl sulfide via single-state reactivity on a dominant quartet spin state surface.

Porro, Cristina S.; Sutcliffe, Michael J.; de Visser, Sam P.

2009-06-01

54

Characterization of a Catalytic Ligand Bridging Metal Ions in Phosphodiesterases 4 and 5 by Molecular Dynamics Simulations and Hybrid Quantum Mechanical/Molecular Mechanical Calculations  

PubMed Central

Cyclic nucleotide phosphodiesterases (PDEs) constitute a large superfamily of enzymes regulating concentrations of intracellular second messengers cAMP and cGMP through PDE-catalyzed hydrolysis. Although three-dimensional x-ray crystal structures of PDE4 and PDE5 have been reported, it is uncertain whether a critical, second bridging ligand (BL2) in the active site is H2O or HO? because hydrogen atoms cannot be determined by x-ray diffraction. The identity of BL2 is theoretically determined by performing molecular dynamics simulations and hybrid quantum mechanical/molecular mechanical (QM/MM) calculations, for the first time, on the protein structures resolved by x-ray diffraction. The computational results confirm our previous suggestion, which was based on QM calculations on a simplified active site model, that BL2 in PDE4 should be HO?, rather than H2O, serving as the nucleophile to initialize the catalytic hydrolysis of cAMP. The molecular dynamics simulations and QM/MM calculations on PDE5 demonstrate for the first time that the BL2 in PDE5 should also be HO? rather than H2O as proposed in recently published reports on the x-ray crystal structures, which serves as the nucleophile to initialize the PDE5-catalyzed hydrolysis of cGMP. These fundamental structural insights provide a rational basis for future structure-based drug design targeting PDEs.

Xiong, Ying; Lu, Hai-Ting; Li, Yongjian; Yang, Guang-Fu; Zhan, Chang-Guo

2006-01-01

55

Quantum mechanics/molecular mechanics modeling of regioselectivity of drug metabolism in cytochrome P450 2C9.  

PubMed

Cytochrome P450 enzymes (P450s) are important in drug metabolism and have been linked to adverse drug reactions. P450s display broad substrate reactivity, and prediction of metabolites is complex. QM/MM studies of P450 reactivity have provided insight into important details of the reaction mechanisms and have the potential to make predictions of metabolite formation. Here we present a comprehensive study of the oxidation of three widely used pharmaceutical compounds (S-ibuprofen, diclofenac, and S-warfarin) by one of the major drug-metabolizing P450 isoforms, CYP2C9. The reaction barriers to substrate oxidation by the iron-oxo species (Compound I) have been calculated at the B3LYP-D/CHARMM27 level for different possible metabolism sites for each drug, on multiple pathways. In the cases of ibuprofen and warfarin, the process with the lowest activation energy is consistent with the experimentally preferred metabolite. For diclofenac, the pathway leading to the experimentally observed metabolite is not the one with the lowest activation energy. This apparent inconsistency with experiment might be explained by the two very different binding modes involved in oxidation at the two competing positions. The carboxylate of diclofenac interacts strongly with the CYP2C9 Arg108 side chain in the transition state for formation of the observed metabolite-but not in that for the competing pathway. We compare reaction barriers calculated both in the presence and in the absence of the protein and observe a marked improvement in selectivity prediction ability upon inclusion of the protein for all of the substrates studied. The barriers calculated with the protein are generally higher than those calculated in the gas phase. This suggests that active-site residues surrounding the substrate play an important role in controlling selectivity in CYP2C9. The results show that inclusion of sampling (particularly) and dispersion effects is important in making accurate predictions of drug metabolism selectivity of P450s using QM/MM methods. PMID:23641937

Lonsdale, Richard; Houghton, Kerensa T; ?urek, Jolanta; Bathelt, Christine M; Foloppe, Nicolas; de Groot, Marcel J; Harvey, Jeremy N; Mulholland, Adrian J

2013-05-16

56

Why does the G117H mutation considerably improve the activity of human butyrylcholinesterase against sarin? Insights from quantum mechanical/molecular mechanical free energy calculations.  

PubMed

Human butyrylcholinesterase (BChE) is recognized as the most promising bioscavenger for organophosphorus (OP) warfare nerve agents. The G117H mutant of human BChE has been identified as a potential catalytic bioscavenger with a remarkably improved activity against OP nerve agents such as sarin, but it still does not satisfy the clinical use. For further design of the higher-activity mutants against OP nerve agents, it is essential to understand how the G117H mutation improves the activity. The reaction mechanisms and the free energy profiles for spontaneous reactivation of wild-type BChE and its G117H mutant phosphorylated by sarin have been explored, in this study, by performing first-principles quantum mechanical/molecular mechanical free energy calculations, and the remarkable role of the G117H mutation on the activity has been elucidated. For both the wild-type and G117H mutant enzymes, H438 acts as a general base to initiate the spontaneous reactivation that consists of two reaction steps: the nucleophilic attack at the phosphorus by a water molecule and decomposition of the pentacoordinated phosphorus intermediate. The calculated overall free energy barriers, i.e., 30.2 and 23.9 kcal/mol for the wild type and G117H mutant, respectively, are in good agreement with available experimental kinetic data. On the basis of the calculated results, the mutated residue (H117 in the G117H mutant) cannot initiate the spontaneous reactivation as a general base. Instead, it skews the oxyanion hole and makes the phosphorus more open to the nucleophilic water molecule, resulting in a remarkable change in the rate-determining step and significantly improved catalytic activity of human BChE. PMID:23092211

Yao, Yuan; Liu, Junjun; Zhan, Chang-Guo

2012-10-23

57

Influence of the LOV domain on low-lying excited states of flavin: a combined quantum-mechanics/molecular-mechanics investigation.  

PubMed

The ground and low-lying excited states of flavin mononucleotide (FMN) in the light, oxygen, and voltage sensitive (LOV) domain of the blue-light photosensor YtvA of Bacillus subtilis were studied by means of combined quantum-mechanical/molecular-mechanical (QM/MM) methods. The FMN cofactor (without the side chain) was treated with density functional theory (DFT) for the geometry optimizations and a combination of DFT and multireference configuration interaction (MRCI) for the determination of the excitation energies, while the protein environment was represented by the CHARMM force field. In addition, several important amino acid side chains, including the reactive cysteine residue, were included in the QM region in order to probe their influence on the spectral properties of the cofactor in two protein conformations. Spin-orbit coupling was taken into account employing an efficient, nonempirical spin-orbit mean-field Hamiltonian. Our results reveal that the protein environment of YtvA-LOV induces spectral shifts for the (pi pi*) states that are similar to those in aqueous solution. In contrast, the blue shifts of the (n pi*) states are smaller in the protein environment, enabling a participation of these states in the decay processes of the optically bright S(1) state. Increased spin-orbit coupling between the initially populated S(1) state and the T(1) and T(2) states is found in YtvA-LOV as compared to free lumiflavine in water. The enhanced singlet-triplet coupling is brought about partially by configuration interaction with (n pi*) states at the slightly out-of-plane distorted minimum geometry. In addition, an external heavy-atom effect is observed when the sulfur atom of the nearby cysteine residue is included in the QM region, in line with experimental findings. PMID:19891470

Salzmann, Susanne; Silva-Junior, Mario R; Thiel, Walter; Marian, Christel M

2009-11-26

58

Mechanism of intramolecular C–H bond activation in [(LCu) 2(?-O) 2] 2+ (L=1,4,7-trialkyl-1,4,7-triazacyclononane): quantum mechanical\\/molecular mechanical modeling  

Microsoft Academic Search

N-dealkylation in [(LCu)2(?-O)2]2+ (L=1,4,7-tribenzyl-1,4,7-triazacyclononane) is predicted by quantum–mechanical\\/molecular–mechanical calculations using density functional theory to take place with the dioxocopper core in a bis(?-oxo) geometry via a mechanism involving internal hydrogen atom transfer of an equatorially located benzylic H to an oxo oxygen atom. This step is followed by a very-low barrier hydroxyl group rebound to generate an aminal that is

Christopher J. Cramer; Christopher R. Kinsinger; Youngshang Pak

2003-01-01

59

Fluorescence of tryptophan in designed hairpin and Trp-cage miniproteins: measurements of fluorescence yields and calculations by quantum mechanical molecular dynamics simulations.  

PubMed

The quantum yield of tryptophan (Trp) fluorescence was measured in 30 designed miniproteins (17 ?-hairpins and 13 Trp-cage peptides), each containing a single Trp residue. Measurements were made in D(2)O and H(2)O to distinguish between fluorescence quenching mechanisms involving electron and proton transfer in the hairpin peptides, and at two temperatures to check for effects of partial unfolding of the Trp-cage peptides. The extent of folding of all the peptides also was measured by NMR. The fluorescence yields ranged from 0.01 in some of the Trp-cage peptides to 0.27 in some hairpins. Fluorescence quenching was found to occur by electron transfer from the excited indole ring of the Trp to a backbone amide group or the protonated side chain of a nearby histidine, glutamate, aspartate, tyrosine, or cysteine residue. Ionized tyrosine side chains quenched strongly by resonance energy transfer or electron transfer to the excited indole ring. Hybrid classical/quantum mechanical molecular dynamics simulations were performed by a method that optimized induced electric dipoles separately for the ground and excited states in multiple ?-?* and charge-transfer (CT) excitations. Twenty 0.5 ns trajectories in the tryptophan's lowest excited singlet ?-?* state were run for each peptide, beginning by projections from trajectories in the ground state. Fluorescence quenching was correlated with the availability of a CT or exciton state that was strongly coupled to the ?-?* state and that matched or fell below the ?-?* state in energy. The fluorescence yields predicted by summing the calculated rates of charge and energy transfer are in good accord with the measured yields. PMID:23330783

McMillan, Andrew W; Kier, Brandon L; Shu, Irene; Byrne, Aimee; Andersen, Niels H; Parson, William W

2013-02-04

60

Solvent dielectric effect and side chain mutation on the structural stability of Burkholderia cepacia lipase active site: a quantum mechanical/molecular mechanics study.  

PubMed

Quantum mechanical and molecular dynamics methods were used to analyze the structure and stability of neutral and zwitterionic configurations of the extracted active site sequence from a Burkholderia cepacia lipase, histidyl-seryl-glutamin (His86-Ser87-Gln88) and its mutated form, histidyl-cysteyl-glutamin (His86-Cys87-Gln88) in vacuum and different solvents. The effects of solvent dielectric constant, explicit and implicit water molecules and side chain mutation on the structure and stability of this sequence in both neutral and zwitterionic forms are represented. The quantum mechanics computations represent that the relative stability of zwitterionic and neutral configurations depends on the solvent structure and its dielectric constant. Therefore, in vacuum and the considered non-polar solvents, the neutral form of the interested sequences is more stable than the zwitterionic form, while their zwitterionic form is more stable than the neutral form in the aqueous solution and the investigated polar solvents in most cases. However, on the potential energy surfaces calculated, there is a barrier to proton transfer from the positively charged ammonium group to the negatively charged carboxylat group or from the ammonium group to the adjacent carbonyl oxygen and or from side chain oxygen and sulfur to negatively charged carboxylat group. Molecular dynamics simulations (MD) were also performed by using periodic boundary conditions for the zwitterionic configuration of the hydrated molecules in a box of water molecules. The obtained results demonstrated that the presence of explicit water molecules provides the more compact structures of the studied molecules. These simulations also indicated that side chain mutation and replacement of sulfur with oxygen leads to reduction of molecular flexibility and packing. PMID:21710316

Tahan, A; Monajjemi, M

2011-06-28

61

A combined quantum mechanics/molecular mechanics study of the one- and two-photon absorption in the green fluorescent protein.  

PubMed

We present for the first time a QM/MM study of the one- and two-photon absorption spectra of the GFP chromophore embedded in the full protein environment described by an advanced quantum mechanically derived polarizable force field. The calculations are performed on a crystal structure of the green fluorescent protein (GFP) using the polarizable embedding density functional theory (PE-DFT) scheme. The importance of treating the protein environment explicitly with a polarizable force field and higher-order multipoles is demonstrated, as well as the importance of including water molecules close to the chromophore in the protein barrel. For the most advanced description we achieve good agreement with experimental findings, with a peak at 405 nm for the neutral and a peak at 475 nm for the anionic form of the GFP chromophore. The presence of a dark OPA state, as suggested by other studies to explain the discrepancies between OPA and TPA spectra, is not supported by our calculations. PMID:22407300

Steindal, Arnfinn Hykkerud; Olsen, Jógvan Magnus Haugaard; Ruud, Kenneth; Frediani, Luca; Kongsted, Jacob

2012-03-12

62

Simple and exact approach to the electronic polarization effect on the solvation free energy: Formulation for quantum-mechanical/ molecular-mechanical system and its applications to aqueous solutions  

NASA Astrophysics Data System (ADS)

We present a simple and exact numerical approach to compute the free energy contribution ?? in solvation due to the electron density polarization and fluctuation of a quantum-mechanical solute in the quantum-mechanical/molecular-mechanical (QM/MM) simulation combined with the theory of the energy representation (QM/MM-ER). Since the electron density fluctuation is responsible for the many-body QM-MM interactions, the standard version of the energy representation method cannot be applied directly. Instead of decomposing the QM-MM polarization energy into the pairwise additive and non-additive contributions, we take sum of the polarization energies in the QM-MM interaction and adopt it as a new energy coordinate for the method of energy representation. Then, it is demonstrated that the free energy ?? can be exactly formulated in terms of the energy distribution functions for the solution and reference systems with respect to this energy coordinate. The benchmark tests were performed to examine the numerical efficiency of the method with respect to the changes in the individual properties of the solvent and the solute. Explicitly, we computed the solvation free energy of a QM water molecule in ambient and supercritical water, and also the free-energy change associated with the isomerization reaction of glycine from neutral to zwitterionic structure in aqueous solution. In all the systems examined, it was demonstrated that the computed free energy ?? agrees with the experimental value, irrespective of the choice of the reference electron density of the QM solute. The present method was also applied to a prototype reaction of adenosine 5'-triphosphate hydrolysis where the effect of the electron density fluctuation is substantial due to the excess charge. It was demonstrated that the experimental free energy of the reaction has been accurately reproduced with the present approach.

Takahashi, Hideaki; Omi, Atsushi; Morita, Akihiro; Matubayasi, Nobuyuki

2012-06-01

63

The nature of tryptophan radicals involved in the long-range electron transfer of lignin peroxidase and lignin peroxidase-like systems: Insights from quantum mechanical/molecular mechanics simulations.  

PubMed

A catalytically active tryptophan radical has been demonstrated to be involved in the long-range electron transfer to the heme cofactor of lignin peroxidase (LiP) from Phanerochaete chrysosporium although no direct detection by EPR spectroscopy of the tryptophan radical intermediate has been reported to date. An engineering-based approach has been used to manipulate the microenvironment of the redox-active tryptophan site in LiP and Coprinus cinereus Peroxidase (CiP), allowing the direct evidence of the tryptophan radical species. In light of the newly available EPR experimental data, we performed a quantum mechanical/molecular mechanics computational study to characterize the tryptophan radicals in the above protein matrices as well as in pristine LiP. The nature of the tryptophan radicals is discussed together with the analysis of their environment with the aim of understanding the different behavior of pristine LiP in comparison with that of LiP and CiP variants. PMID:22383280

Bernini, Caterina; Pogni, Rebecca; Basosi, Riccardo; Sinicropi, Adalgisa

2012-03-02

64

Solvatochromic shifts of polar and non-polar molecules in ambient and supercritical water: a sequential quantum mechanics/molecular mechanics study including solute-solvent electron exchange-correlation.  

PubMed

Polar and non-polar solutes (acetone and benzene) dissolved in ambient water and supercritical water are investigated theoretically using a sequential quantum mechanics (QM)/molecular mechanics (MM) method which combines classical molecular dynamics simulations and QM/MM calculations. From the detailed analysis of the dependence of the QM region size and point charge background region size as well as the different functionals, it is found that the inclusion of the solvent molecules within the first solvation shell into the QM region to account for the exchange-correlation between a solute and neighboring solvent molecules is important for the highly accurate spectral shift calculations, especially vital for the non-polar solutes whose interactions with the solvents are dominated by the quantum dispersions. At the same time, sufficiently large surrounding partial charge region (r(cutoff) ?15 A?) as well as the functional corrections to describe the long-range dispersion-corrections are also essential for the study of the electronic excited states in condensed phase. Our calculated solvatochromic shift values and their density dependencies at ambient and high temperature conditions are found to be in good agreements with experimental observations. This indicates that sound theoretical studies of solvatochromic shift can be achieved provided that a reasonable computational scheme with sufficiently large N(water) (QM) and r(cutoff) values is implemented. We also find both of aqueous acetone and aqueous benzene under high temperatures present three distinctive regions: low-density gas-like region, supercritical region, and high-density liquid-like region. The plateau behavior of solvatochromic shift in the supercritical region can be ascribed to the solvent clustering around the solute, which is a fundamental phenomenon of supercritical fluids (SCFs). The density dependence of our calculated coordination number of the first solvation shell nicely reproduces the trend of spectral shift and verifies the solvent clustering phenomenon of SCFs and its relationship with SCF's physicochemical properties. PMID:23231248

Ma, Haibo; Ma, Yingjin

2012-12-01

65

Solvatochromic shifts of polar and non-polar molecules in ambient and supercritical water: A sequential quantum mechanics/molecular mechanics study including solute-solvent electron exchange-correlation  

NASA Astrophysics Data System (ADS)

Polar and non-polar solutes (acetone and benzene) dissolved in ambient water and supercritical water are investigated theoretically using a sequential quantum mechanics (QM)/molecular mechanics (MM) method which combines classical molecular dynamics simulations and QM/MM calculations. From the detailed analysis of the dependence of the QM region size and point charge background region size as well as the different functionals, it is found that the inclusion of the solvent molecules within the first solvation shell into the QM region to account for the exchange-correlation between a solute and neighboring solvent molecules is important for the highly accurate spectral shift calculations, especially vital for the non-polar solutes whose interactions with the solvents are dominated by the quantum dispersions. At the same time, sufficiently large surrounding partial charge region (rcutoff >=15 A?) as well as the functional corrections to describe the long-range dispersion-corrections are also essential for the study of the electronic excited states in condensed phase. Our calculated solvatochromic shift values and their density dependencies at ambient and high temperature conditions are found to be in good agreements with experimental observations. This indicates that sound theoretical studies of solvatochromic shift can be achieved provided that a reasonable computational scheme with sufficiently large NwaterQM and rcutoff values is implemented. We also find both of aqueous acetone and aqueous benzene under high temperatures present three distinctive regions: low-density gas-like region, supercritical region, and high-density liquid-like region. The plateau behavior of solvatochromic shift in the supercritical region can be ascribed to the solvent clustering around the solute, which is a fundamental phenomenon of supercritical fluids (SCFs). The density dependence of our calculated coordination number of the first solvation shell nicely reproduces the trend of spectral shift and verifies the solvent clustering phenomenon of SCFs and its relationship with SCF's physicochemical properties.

Ma, Haibo; Ma, Yingjin

2012-12-01

66

Quantum Mechanics  

NSDL National Science Digital Library

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.

Michielsen, Kristel; De Raedt, Hans

2004-03-04

67

Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Quantum Mechanics aims to teach those parts of the subject which every physicist should know. The object is to display the inherent structure of quantum mechanics, concentrating on general principles and on methods of wide applicability without taking them to their full generality. This book will equip students to follow quantum-mechanical arguments in books and scientific papers, and to cope with simple cases. To bring the subject to life, the theory is applied to the all-important field of atomic physics. No prior knowledge of quantum mechanics is assumed. However, it would help most readers to have met some elementary wave mechanics before. Primarily written for students, it should also be of interest to experimental research workers who require a good grasp of quantum mechanics without the full formalism needed by the professional theorist. Quantum Mechanics features: A flow diagram allowing topics to be studied in different orders or omitted altogether. Optional "starred" and highlighted sections containing more advanced and specialized material for the more ambitious reader. Sets of problems at the end of each chapter to help student understanding. Hints and solutions to the problems are given at the end of the book.

Mandl, F.

1992-07-01

68

Hybrid Schemes Based on Quantum Mechanics\\/Molecular Mechanics Simulations  

Microsoft Academic Search

The development of characterization techniques, advanced synthesis methods, as well as molecular modeling has transformed the study of systems in a well-established research field. The current research challenges in biocatalysis and biotransformation evolve around enzyme discovery, design, and optimization. How can we find or create enzymes that catalyze important synthetic reactions, even reactions that may not exist in nature? What

Silvia Ferrer; Javier Ruiz-Pernía; Sergio Martí; Vicent Moliner; Iñaki Tuñón; Juan Bertrán; Juan Andrés

2011-01-01

69

Quantumness beyond quantum mechanics  

NASA Astrophysics Data System (ADS)

Bohmian mechanics allows us to understand quantum systems in the light of other quantum traits than the well-known ones (coherence, diffraction, interference, tunnelling, discreteness, entanglement, etc.). Here the discussion focusses precisely on two of these interesting aspects, which arise when quantum mechanics is thought within this theoretical framework: the non-crossing property, which allows for distinguishability without erasing interference patterns, and the possibility to define quantum probability tubes, along which the probability remains constant all the way. Furthermore, taking into account this hydrodynamic-like description as a link, it is also shown how this knowledge (concepts and ideas) can be straightforwardly transferred to other fields of physics (for example, the transmission of light along waveguides).

Sanz, Ángel S.

2012-05-01

70

quantum mechanics  

PubMed Central

-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.

Bender, Carl M; DeKieviet, Maarten; Klevansky, S. P.

2013-01-01

71

Quantum Deformations of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Based on a deformation of the quantum mechanical phase space we study q-deformations of quantum mechanics for qk=1 and 0quantum mechanics for qk=1 is given and the dynamics for the free Hamiltonian is studied. For 0quantum mechanics and the cases of the free Hamiltonian and the one with a x2-potential are solved in terms of basic hypergeometric functions.

Ubriaco, Marcelo R.

72

Quantum mechanical tunneling in methylamine dehydrogenase  

Microsoft Academic Search

We report a calculation for a trideuteration kinetic isotope effect (KIE) for the proton transfer step in the oxidation of methylamine by the quinoprotein methylamine dehydrogenase (MADH). The potential field includes 11025 atoms, and the dynamics are based on a quantum mechanical\\/molecular mechanical (QM\\/MM) direct dynamics simulation and canonical variational transition state theory with small-curvature multidimensional tunneling contributions. About 1%

Cristóbal Alhambra; Maria Luz Sánchez; José Corchado; Jiali Gao; Donald G. Truhlar

2001-01-01

73

Quantum cosmology and quantum mechanics.  

NASA Astrophysics Data System (ADS)

The interpretative framework of quantum mechanics loosely subsumed under the name "Copenhagen interpretation" contains two central assumptions which seem incompatible with a quantum cosmology built on a covariant quantum theory of spacetime. The first is a distinguished class of classical systems. The second is a distinguished time variable and its associated notion of causality. The first assumption is incompatible with the uniform application of quantum mechanics to the universe as a whole. The second is incompatible with the general covariance of gravitational theory. This paper explores the possibility that both of these distinguished features of our world arise, not as special features of the formalism of quantum mechanics, but rather as consequences of specific initial conditions for cosmology.

Hartle, J. B.

74

Quantum mechanics and symmetries  

Microsoft Academic Search

Symmetries have always played an important role in physics. With quantum mechanics, however, the interplay between physics and symmetries has reached a new dimension. The very structure of quantum mechanics invites the application of group theoretical methods to an extent that physicists would have been led to invent various concepts of group theory, such as Lie groups, by quantum mechanics

J. Wess

2000-01-01

75

Introduction to Quantum Mechanics  

Microsoft Academic Search

Discussed here is the mathematics of quantum mechanics at an introductory level. Hilbert spaces, the Bra-Ket notation, Fourier Transforms, the Schrodinger Wave Equation, and Quantum Computing are covered.

ROHIT TRIPATHI

1945-01-01

76

Introduction to Quantum Mechanics  

NSDL National Science Digital Library

This text is intended for junior/senior Quantum Mechanics courses. It covers the fundamentals of quantum theory in a concise manner, covering topics from the basic formalism through perturbation theory, the adiabatic approximation, and scattering.

Griffiths, David J.

2005-04-16

77

Ph 125 Quantum Mechanics  

NSDL National Science Digital Library

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.

Mabuchi, Hideo

2011-01-21

78

Ph 125 Quantum Mechanics  

NSDL National Science Digital Library

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.

Mabuchi, Hideo

2005-12-05

79

Quantum mechanics made transparent  

NASA Astrophysics Data System (ADS)

This article is a ``sampler,'' which shows how quantum mechanics may be presented to students in a way that makes apparent how natural quantum mechanics is as a description of the world. The mathematical machinery of Hilbert space, the idea of representing observables by operators, the Schrödinger equation, and the position-momentum uncertainty relation all follow from natural assumptions that students can readily accept. The basic ideas of quantum mechanics are developed from intuitive first principles to the point where one can connect with more traditional treatments of quantum mechanics.

Henry, Richard C.

1990-11-01

80

Quantum Mechanics Based Multiscale Modeling of Materials  

NASA Astrophysics Data System (ADS)

We present two quantum mechanics based multiscale approaches that can simulate extended defects in metals accurately and efficiently. The first approach (QCDFT) can treat multimillion atoms effectively via density functional theory (DFT). The method is an extension of the original quasicontinuum approach with DFT as its sole energetic formulation. The second method (QM/MM) has to do with quantum mechanics/molecular mechanics coupling based on the constrained density functional theory, which provides an exact framework for a self-consistent quantum mechanical embedding. Several important materials problems will be addressed using the multiscale modeling approaches, including hydrogen-assisted cracking in Al, magnetism-controlled dislocation properties in Fe and Si pipe diffusion along Al dislocation core.

Lu, Gang

2013-03-01

81

Quantum mechanics: Entanglement goes mechanical  

Microsoft Academic Search

A neat experiment shows that the mechanical vibration of two ion pairs separated by a few hundred micrometres is entangled - their motions are intrinsically and inseparably connected in a quantum way.

Rainer Blatt

2009-01-01

82

Advanced Visual Quantum Mechanics  

NSDL National Science Digital Library

This page provides links to a range of teaching materials for use in an upper-level undergraduate quantum mechanics course. These are developed from some of the concepts of the Visual Quantum Mechanics course for high school and introductory college classes. Materials inlcude tutorial activities in concepts of energy diagrams, probability, and wavefunctions, and some computer activities.

Axmann, Wally; Group, Kansas S.

2004-04-04

83

Quantum Mechanics Conceptual Survey  

NSDL National Science Digital Library

This web page is the home for the Quantum Mechanics Conceptual Survey (QMCS). The goal of this assessment is to provide an accurate measure of students' understanding of fundamental concepts in quantum mechanics. The QMCS is inspired by the many carefully researched and validated tests of conceptual understanding in physics. The authors developed the questions to be independent of notation unique to a specific course and avoiding jargon as much as possible. The questions in the QMCS are based on faculty interviews, textbooks and syllabi, existing assessments, research on student misconceptions in quantum mechanics, and student observations.

Mckagan, Sarah B.

2011-06-28

84

Is quantum mechanics exact?  

NASA Astrophysics Data System (ADS)

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.

Kapustin, Anton

2013-06-01

85

Visual Quantum Mechanics  

NSDL National Science Digital Library

Visual Quantum Mechanics provides illustrations of quantum mechanics using computer-generated animations. Visualizations provide learning experiences for beginners and offer new insights to the advanced student or researcher. This project includes the development of multimedia software for teaching and scientific software for the solution of the Shrodinger equation and the visualization of these solutions in two and three dimensions. The materials presented here are related to two texts by the author.

Thaller, Bernd

2004-07-10

86

Graduate quantum mechanics reform  

NASA Astrophysics Data System (ADS)

We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field of quantum mechanics over the last 50 years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We also find that students' ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. In contrast, we find that students' understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.

Carr, L. D.; McKagan, S. B.

2009-04-01

87

Supersymmetry in quantum mechanics  

SciTech Connect

An elementary introduction is given to the subject of supersymmetry in quantum mechanics which can be understood and appreciated by any one who has taken a first course in quantum mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics with n bound states, one can construct n new exactly solvable Hamiltonians having n - 1, n - 2,..., 0 bound states. The relationship between the eigenvalues, eigenfunctions and scattering matrix of the supersymmetric partner potentials is derived and a class of reflectionless potentials are explicitly constructed. We extend the operator method of solving the one-dimensional harmonic oscillator problem to a class of potentials called shape-invariant potentials. It is worth emphasizing that this class includes almost all the solvable problems that are found in the standard text books on quantum mechanics. Further, we show that given any potential with at least one bound state, one can very easily construct one continuous parameter family of potentials having same eigenvalues and s-matrix. The supersymmetry inspired WKB approximation (SWKB) is also discussed and it is shown that unlike the usual WKB, the lowest order SWKB approximation is exact for the shape-invariant potentials and further, this approximation is not only exact for large quantum numbers but by construction, it is also exact for the ground state. Finally, we also construct new exactly solvable periodic potentials by using the machinery of supersymmetric quantum mechanics.

Khare, Avinash [Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, Orissa (India)

2004-12-23

88

Physlets for Quantum Mechanics  

NSDL National Science Digital Library

This article presents the use of Physlet-based questions with proven pedagogical techniques to improve student conceptual understanding. Physlet problems are used in a Just-in-Time-Teaching approach. Most examples are from a senior level quantum mechanics class, although examples in introductory mechanics are also shown. Results of pre/post testing using the Quantum Mechanics Visualization Instrument (QMVI) show significant gain in understanding. Comparison is made with other QMVI results from undergraduate and graduate students. This article was cited as the best education article in the journal Computers in Science and Engineering for the American Institute of Physics' 75th anniversary. This citation is given below under Annotations.

Belloni, Mario; Christian, Wolfgang

2006-08-02

89

Visual Quantum Mechanics  

NSDL National Science Digital Library

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.

Group, Kansas S.; Zollman, Dean A.

2003-10-10

90

Decoherence in quantum mechanics  

SciTech Connect

Research Highlights: > We study decoherence in a simple quantum mechanical model using two approaches. > Following the conventional approach to decoherence we solve the master equation. > We also consider our novel correlator approach to decoherence. > The system's total entropy increase cannot reliably be calculated in the conventional approach. > This does follow correctly from our correlator approach. - Abstract: We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation. Secondly, we consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. We show that both methods can accurately predict decoherence time scales. However, the perturbative master equation generically suffers from instabilities which prevents us to reliably calculate the system's total entropy increase. We also discuss the relevance of the results in our quantum mechanical model for interacting field theories.

Koksma, Jurjen F., E-mail: J.F.Koksma@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Prokopec, Tomislav, E-mail: T.Prokopec@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Schmidt, Michael G., E-mail: M.G.Schmidt@thphys.uni-heidelberg.de [Institut fuer Theoretische Physik, Heidelberg University, Philosophenweg 16, D-69120 Heidelberg (Germany)

2011-06-15

91

Visual Quantum Mechanics  

NSDL National Science Digital Library

Visual Quantum Mechanics provides illustrations of quantum mechanics using computer-generated animations. Visualizations provide learning experiences for beginners and offer new insights to the advanced student or researcher. This project includes the development of multimedia software for teaching and scientific software for the solution of the Shrodinger equation and the visualization of these solutions in two and three dimensions. The materials presented here are related to two texts by the author. A German translation is also available. Quicktime is needed to view these movies.

Thaller, Bernd

2009-05-14

92

Noncommutative quantum mechanics  

NASA Astrophysics Data System (ADS)

A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter ?, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of ? the model can be solved by using perturbation theory.

Gamboa, J.; Loewe, M.; Rojas, J. C.

2001-09-01

93

Superposition and quantum mechanics  

SciTech Connect

This work is primarily concerned with finding those statements or observations from which quantum mechanics can reasonably be said to follow. Within the context of characterizing quantum mechanics as any probability field (with bounded probability density) whose associated stochastic velocity field is governed by a differential equation of first order in time, it is shown that the single statement required is the stipulation that the superposition principle is satisfied. This is demonstrated by showing that only the Schrodinger equation is an acceptable dynamic description for such probability fields if the superposition principle is to hold.

Cohn, J.

1986-08-01

94

Time Asymmetric Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width ? and exponentially decaying states of lifetime ?=h/? should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0?tquantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr

2011-09-01

95

Erratum to: “Quantum mechanical tunneling in methylamine dehydrogenase”  

Microsoft Academic Search

We report a calculation for a trideuteration kinetic isotope effect (KIE) for the proton transfer step in the oxidation of methylamine by the quinoprotein methylamine dehydrogenase (MADH). The potential field includes 11025 atoms, and the dynamics are based on a quantum mechanical\\/molecular mechanical (QM\\/MM) dynamics simulation and ensemble-averaged canonical variational transition state theory with small-curvature multidimensional tunneling contributions. About 1%

Cristóbal Alhambra; Maria Luz Sánchez; José C. Corchado; Jiali Gao; Donald G. Truhlar

2002-01-01

96

Alzheimer's Disease Promotion by Obesity: Induced Mechanisms--Molecular Links and Perspectives  

PubMed Central

The incidence of AD is increasing in parallel with the increase in life expectancy. At the same time the prevalence of metabolic syndrome and obesity is reaching epidemic proportions in western populations. Stress is one of the major inducers of visceral fat and obesity development, underlying accelerated aging processes. Adipose tissue is at present considered as an active endocrine organ, producing important mediators involved in metabolism regulation as well as in inflammatory mechanisms. Insulin and leptin resistance has been related to the dysregulation of energy balance and to the induction of a chronic inflammatory status which have been recognized as important cofactors in cognitive impairment and AD initiation and progression. The aim of this paper is to disclose the correlation between the onset and progression of AD and the stress-induced changes in lifestyle, leading to overnutrition and reduced physical activity, ending with metabolic syndrome and obesity. The involved molecular mechanisms will be briefly discussed, and advisable guide lines for the prevention of AD through lifestyle modifications will be proposed.

Businaro, Rita; Ippoliti, Flora; Ricci, Serafino; Canitano, Nicoletta; Fuso, Andrea

2012-01-01

97

Quantum Mechanics, Locality and Realism.  

National Technical Information Service (NTIS)

We show that the concept of locality is independent of the postulates of quantum mechanics. In particular, we show that under the assumption that nature is local, the quantum-mechanical predictions concerning experiments on correlated systems satisfy Bell...

J. W. de Roever M. Streng

1993-01-01

98

Introduction to Biological Quantum Mechanics.  

National Technical Information Service (NTIS)

There are observables and eigenstates in biology as well as in physical quantum mechanics. Furthermore, the basic principle of quantum mechanics that 'measurement of an observable of a physical system will find the system in an eigenstate of the observabl...

S. Goldman

1969-01-01

99

Holistic Aspects of Quantum Mechanics.  

National Technical Information Service (NTIS)

Aspects of quantum mechanics irreconcilable with classical physics are outlined. Quantum mechanics started with a negative statement about reality, namely: it is impossible to determine momentum and position of a particle simultaneously. Meanwhile it has ...

H. Pietschmann

1987-01-01

100

Development of a hybrid quantum mechanics-molecular mechanics model for predicting solvent effects  

Microsoft Academic Search

Solvent effects can significantly influence the structure, reactivity and spectroscopy of a molecule, and, therefore, proper modeling of these effects is crucial for predicting the behavior of molecules in solution. While this is not the first attempt to incorporate solvent effects into theoretical calculations, the new method presented here has fewer limitations on the types of systems to which it

Greg Martin Pearl

1998-01-01

101

Quantum Mechanics Survey (QMS)  

NSDL National Science Digital Library

This 31-question research-based multiple-choice test is designed to evaluate studentsâ conceptual understanding of quantum mechanics in junior-level courses. The survey is based on investigations of studentsâ difficulties in quantum mechanics and should be given in a 50-minute period. Statistical results have shown the survey to be reliable and valid. A summary of the construction and analysis of the survey is available in Surveying studentsâ understanding of quantum mechanics in one spatial dimension, Am. J. Phys. 80 (3), 252-259. This assessment is free for use by instructors in their classroom. However, as it takes years of development effort to create and validate reliable assessment instruments, the file is password-protected. Furthermore, the author requests that 1. students are not given copies following examination; and 2. none of the questions are incorporated into web-based question delivery systems without adequate security to prevent printing or unauthorized access by students. To obtain the password, please send a request with your name, email, institution, and a link to a page at your institution that confirms you are an instructor.

Singh, Chandralekha; Zhu, Guangtian

2012-04-29

102

Stretched DNA Investigated Using Molecular-Dynamics and Quantum-Mechanical Calculations  

Microsoft Academic Search

We combined atomistic molecular-dynamics simulations with quantum-mechanical calculations to investigate the sequence dependence of the stretching behavior of duplex DNA. Our combined quantum-mechanical\\/molecular-mechanical approach demonstrates that molecular-mechanical force fields are able to describe both the backbone and base-base interactions within the highly distorted nucleic acid structures produced by stretching the DNA from the 5? ends, which include conformations containing disassociated

Jan ?ezá?; Pavel Hobza; Sarah A. Harris

2010-01-01

103

Logical foundation of quantum mechanics  

Microsoft Academic Search

The subject of this article is the reconstruction of quantum mechanics on the basis of a formal language of quantum mechanical propositions. During recent years, research in the foundations of the language of science has given rise to adialogic semantics that is adequate in the case of a formal language for quantum physics. The system ofsequential logic which is comprised

E. W. Stachow; Theoretische Physik

1980-01-01

104

Reality Problem in Quantum Mechanics.  

National Technical Information Service (NTIS)

A series of 12 lectures on quantum mechanics and its interpretations: The more specific part begins with chapter 8: spin and polarization measurements; the Einstein-Podolski-Rosen paradox; interpretations of quantum theory; the role of the observer and th...

D. Flamm

1988-01-01

105

Algorithms Speedup From Quantum Mechanics.  

National Technical Information Service (NTIS)

This project was concerned primarily with one central theme which is the attempt to use quantum mechanics to design algorithms that perform better than conventional (non-quantum) algorithms for solving certain problems. We looked at a variety of approache...

E. Farhi J. Goldstone

2005-01-01

106

Stochastic mechanics and quantum theory  

Microsoft Academic Search

Stochastic mechanics may be regarded as both generalizing classical mechanics to processes with intrinsic randomness, as well as providing the sort of detailed description of microscopic events declared impossible under the traditional interpretation of quantum mechanics. It avoids the many conceptual difficulties which arise from the assumption that quantum mechanics, i.e., the wave function, provides a complete description of (microscopic)

Sheldon Goldstein

1987-01-01

107

Emergent mechanics, quantum and un-quantum  

NASA Astrophysics Data System (ADS)

There is great interest in quantum mechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantum mechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantum mechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications

Ralston, John P.

2013-10-01

108

Gravitomagnetism in quantum mechanics  

SciTech Connect

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.

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

109

Supersymmetric Quantum Mechanics  

SciTech Connect

Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulae concerning SUSY QM of first second order for one-dimensional arbitrary systems, we will illustrate the method through the trigonometric Poeschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.

David, J.; Fernandez, C. [Depto. de Fisica, Cinvestav, A.P. 14-740, 07000 Mexico D.F. (Mexico)

2010-10-11

110

Quantum Mechanics as Dualism  

NASA Astrophysics Data System (ADS)

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.

Jones, Robert

2011-03-01

111

Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime  

Microsoft Academic Search

These are the author's lectures at the 1992 Les Houches Summer School,\\u000a``Gravitation and Quantizations''. They develop a generalized\\u000asum-over-histories quantum mechanics for quantum cosmology that does not\\u000arequire either a preferred notion of time or a definition of measurement. The\\u000a``post-Everett'' quantum mechanics of closed systems is reviewed. Generalized\\u000aquantum theories are defined by three elements (1) the set

James B. Hartle

1993-01-01

112

Nonlocality, counterfactuals, and quantum mechanics  

NASA Astrophysics Data System (ADS)

Stapp [Am. J. Phys. 65, 300 (1997)] has recently argued from a version of the Hardy-type experiments that quantum mechanics must be nonlocal, independent of any additional assumptions such as realism or hidden variables. I argue either that his conclusions do not follow from his assumptions or that his assumptions are not true of quantum mechanics and can be interpreted as assigning an unwarranted level of reality to the value of certain quantum attributes.

Unruh, W.

1999-01-01

113

The emergence of quantum mechanics  

NASA Astrophysics Data System (ADS)

It is pointed out that a mathematical relation exists between cellular automata and quantum field theories. Although the proofs are far from perfect, they do suggest a new look at the origin of quantum mechanics: quantum mechanics may be nothing but a natural way to handle the statistical correlations of a cellular automaton. An essential role for the gravitational force in these considerations is suspected.

't Hooft, Gerard

2012-06-01

114

Probability Interpretation of Quantum Mechanics.  

ERIC Educational Resources Information Center

This paper draws attention to the frequency meaning of the probability concept and its implications for quantum mechanics. It emphasizes that the very meaning of probability implies the ensemble interpretation of both pure and mixed states. As a result some of the "paradoxical" aspects of quantum mechanics lose their counterintuitive character.…

Newton, Roger G.

1980-01-01

115

Quantum mechanics of cluster melting  

SciTech Connect

We present here prototype studies of the effects of quantum mechanics on the melting of clusters. Using equilibrium path integral methods, we examine the melting transition for small rare gas clusters. Argon and neon clusters are considered. We find the quantum-mechanical effects on the melting and coexistence properties of small neon clusters to be appreciable.

Beck, T.L.; Doll, J.D.; Freeman, D.L.

1989-05-15

116

Tensorial description of quantum mechanics  

NASA Astrophysics Data System (ADS)

Relevant algebraic structures for the description of quantum mechanics in the Heisenberg picture are replaced by tensor fields 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.

Clemente-Gallardo, J.; Marmo, G.

2013-03-01

117

Decoherence in Quantum Mechanics and Quantum Cosmology.  

National Technical Information Service (NTIS)

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 o...

J. B. Hartle

1992-01-01

118

Communication: Quantum mechanics without wavefunctions  

SciTech Connect

We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.

Schiff, Jeremy [Department of Mathematics, Bar-Ilan University, Ramat Gan 52900 (Israel); Poirier, Bill [Department of Chemistry and Biochemistry, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061 (United States) and Department of Physics, Texas Tech University, Box 41051, Lubbock, Texas 79409-1051 (United States)

2012-01-21

119

Quantum Mechanics from Classical Logic  

NASA Astrophysics Data System (ADS)

Although quantum mechanics is generally considered to be fundamentally incompatible with classical logic, it is argued here that the gap is not as great as it seems. Any classical, discrete, time reversible system can be naturally described using a quantum Hubert space, operators, and a Schrödinger equation. The quantum states generated this way resemble the ones in the real world so much that one wonders why this could not be used to interpret all of quantum mechanics this way. Indeed, such an interpretation leads to the most natural explanation as to why a wave function appears to "collapse" when a measurement is made, and why probabilities obey the Born rule. Because it is real quantum mechanics that we generate, Bell's inequalities should not be an obstacle.

't Hooft, Gerard

2012-05-01

120

Quantum mechanics from classical statistics  

SciTech Connect

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.

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

121

Interpolated mechanics-molecular mechanics study of internal rotation dynamics of the chromophore unit in blue fluorescent protein and its variants.  

PubMed

The excited state dynamics of the blue fluorescent protein (BFP) and its variants, azurite, EBFP1.2, and EBFP2.0, are studied using molecular dynamics (MD) simulations on potential energy surfaces (PESs) generated with the interpolated mechanics-molecular mechanics (IM/MM) scheme. This IM/MM strategy adopts the interpolated PES for an important area of the complex and the conventional force field for the remaining part. We focus on the internal rotation dynamics of the chromophore unit, which is directly related to its fluorescence property, and analyze the time evolutions of the nonrotated chromophore fractions based on trajectories over 10 ?s of aggregate simulation time. The characteristics obtained from the calculated time progresses of the nonrotated chromophore fractions in BFP and other variants agree well with experimentally observed properties. The results show that the MD simulation with an IM/MM potential is an attractive approach for studying excited state dynamics of fluorescent proteins in consideration of its efficiency and reliability. We also attempt to investigate the detailed roles that the mutated residues play in delaying the excited state chromophore twisting and thus improving the fluorescence property, and discuss the contributions by the Coulombic and the steric interactions between the chromophore and the mutated residues. PMID:22891786

Park, Jae Woo; Rhee, Young Min

2012-08-30

122

Permutation interpretation of quantum mechanics  

NASA Astrophysics Data System (ADS)

We analyse quantum concepts in a constructive finite background. Introduction of continuum or other actual infinities into physics leads to non-constructivity without any need for them in description of empirical observations. We argue that quantum behavior is a natural consequence of symmetries of dynamical systems. It is a result of fundamental impossibility to trace identity of indistinguishable objects in their evolution — only information about invariant combinations of such objects is available. General mathematical arguments imply that any quantum dynamics can be reduced to a sequence of permutations. Quantum phenomena, such as interferences, arise in invariant subspaces of permutation representations of the symmetry group of a system. Observable quantities can be expressed in terms of the permutation invariants. We demonstrate that for description of quantum phenomena there is no need to use such non-constructive number system as complex numbers. It is sufficient to employ the cyclotomic numbers — a minimal extension of the natural numbers which is suitable for quantum mechanics.

Kornyak, V. V.

2012-02-01

123

Realism, operationalism, and quantum mechanics  

Microsoft Academic Search

A comprehensive formal system is developed that amalgamates the operational and the realistic approaches to quantum mechanics. In this formalism, for example, a sharp distinction is made between events, operational propositions, and the properties of physical systems.

D. Foulis; C. Piron; C. Randall

1983-01-01

124

Singular potentials in quantum mechanics.  

National Technical Information Service (NTIS)

This paper is a review of some mathematical methods as recently developed and applied to deal with singular potentials in Quantum Mechanics. Regular and singular perturbative methods as well as variational treatments are considered. (author). 25 refs. (At...

V. C. Aguilera-Navarro E. Koo

1995-01-01

125

Computing With Quantum Mechanical Oscillators.  

National Technical Information Service (NTIS)

Despite the obvious practical considerations (e.g., stability, controllability), certain quantum mechanical systems seem to naturally lend themselves in a theoretical sense to the task of performing computations. The purpose of this report is to describe ...

A. D. Parks J. L. Solka

1991-01-01

126

Yang-Mills Quantum Mechanics.  

National Technical Information Service (NTIS)

Quantum mechanical properties of the Yang-Mills space homogeneous model are considered in the Schroedinger representation. By means of compact variables the dependence of the wave function on ''rotational'' degrees of freedom is separated and effective Ha...

G. K. Savvidy

1984-01-01

127

Measurement Theory in Quantum Mechanics.  

National Technical Information Service (NTIS)

It is assumed that consciousness, memory and liberty (within the limits of the quantum mechanics indeterminism) are fundamental properties of elementary particles. Then, using this assumption it is shown how measurements and observers may be introduced in...

G. Klein

1980-01-01

128

Quantum Mechanics in Insulators  

SciTech Connect

Atomic physics is undergoing a large revival because of the possibility of trapping and cooling ions and atoms both for individual quantum control as well as collective quantum states, such as Bose-Einstein condensates. The present lectures start from the 'atomic' physics of isolated atoms in semiconductors and insulators and proceed to coupling them together to yield magnets undergoing quantum phase transitions as well as displaying novel quantum states with no classical analogs. The lectures are based on: G.-Y. Xu et al., Science 317, 1049-1052 (2007); G. Aeppli, P. Warburton, C. Renner, BT Technology Journal, 24, 163-169 (2006); H. M. Ronnow et al., Science 308, 392-395 (2005) and N. Q. Vinh et al., PNAS 105, 10649-10653 (2008).

Aeppli, G. [London Centre for Nanotechnology, 17-19 Gordon Street, London (United Kingdom); Department of Physics and Astronomy, University College of London, London (United Kingdom)

2009-08-20

129

Introduction to Quantum Mechanics: Assessment  

NSDL National Science Digital Library

This resource provides an assessment for students who have just learned the basics of quantum mechanics. The accompanying interactive lesson which may be used before this assessment is given may be found here. This five question assessment covers the concept of probability, electrons and some other basic concepts related to quantum mechanics. The other educational modules in this series can be found here. Instructors and students are encouraged to sign up with the Electron Technologies site here before starting to use these materials.

2012-03-20

130

Generalized quantum mechanics  

Microsoft Academic Search

A convex scheme of quantum theory is outlined where the states are not necessarily the density matrices in a Hilbert space. The physical interpretation of the scheme is given in terms of generalized “impossibility principles”. The geometry of the convex set of all pure and mixed states (called a statistical figure) is conditioned by the dynamics of the system. This

Bogdan Mielnik

1974-01-01

131

Quantum Mechanics Resource Packet  

NSDL National Science Digital Library

This website contains a collection of computational resources for use in a quantum physics class. Maple files are provided to introduce students to scientific computation. This collection includes suggested problems for use with the CUPS software. Topics covered include energy levels and wave functions for various potential wells and a 1-D lattice.

Moloney, Mike; Mitra-Kirtley, Sudipa; Joenathan, Charles; Western, Arthur; Mcinerney, Michael

2005-07-25

132

Bohmian Mechanics and Quantum Information  

NASA Astrophysics Data System (ADS)

Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and the like in quantum theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the idea that information plays a special role in physics naturally emerges in a Bohmian universe.

Goldstein, Sheldon

2010-04-01

133

PT quantum mechanics - Recent results  

NASA Astrophysics Data System (ADS)

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 = p2+ix3 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 = p2+ix3 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 = p2-x4, 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?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.

Bender, Carl M.

2012-09-01

134

PT quantum mechanics - Recent results  

SciTech Connect

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.

Bender, Carl M. [Physics Department, Washington University, St. Louis, MO 63130 (United States)

2012-09-26

135

Physicalism Versus Quantum Mechanics  

Microsoft Academic Search

The widely held philosophical position called “physicalism” has been described and defended in a recent book by Jaegwon Kim.\\u000a The physicalist position claims that the world is basically purely physical. However, “physical” is interpreted in a way predicated,\\u000a in effect, upon certain properties of classical physics that are contradicted by the precepts of orthodox quantum physics.\\u000a Kim’s arguments reveal two

Henry P. Stapp

136

Quantum Mechanics Tutorials  

NSDL National Science Digital Library

This website contains a collection of materials for use in a small group tutorial setting. The materials are a part of a model applied quantum physics course at the University of Maryland which is directed toward science and engineering students. This web page contains links to research and resources, such as pretests, tutorials, homework, and handouts. (A password must be obtained for access to resources)

Redish, Edward F.; Steinberg, Richard N.; Wittmann, Michael C.

2005-08-07

137

Quantum Mechanical Earth: Where Orbitals Become Orbits  

ERIC Educational Resources Information Center

|Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…

Keeports, David

2012-01-01

138

Self-Referential Quantum Mechanics  

NASA Astrophysics Data System (ADS)

A nonlinear quantum mechanics based upon the nonlinear logarithmic Schrodinger equation, is developed which has the property of self-reference, that is, the nonlinear term is dependent upon the square of the wavefunction. The self-referential system is examined in terms of its mathematical properties, the definition of the wavefunction, and the nonlinear system in the feedback between equation and solution. Theta operators are introduced which make possible new operations in the quantum phase. Two interpretations are presented utilizing the nonlinear quantum system: the idealistic interpretation based upon consciousness focused upon the measurement problem, and the statistical interpretation focused upon stochastic quantum fluctuations. Experimental properties are examined, beginning with a proposed analog of the Bohm-Aharonov experiment. Interference due to difference in path length for a split electron beam is effected in a region of spacetime where electromagnetic field and the vector potential are enclosed within but screened to be zero at the paths. If the wavefunction's geometrical phase contribution along the paths is different, then there should be interference induced purely by the wave-function alone. A positive result would be due to a purely wavefunction dependent effect. The spin phase of the wavefunction is postulated to be the source of the zitterbewegung of the electron. Reduction of the wavefunction in measurement is examined for self -referential quantum systems arising from consciousness and then arising from a stochastic quantum spacetime model. These results are applied to the mind-brain as a quantum processor producing a behavioral double slit experiment (ideation experiments) and nonlocal transferred potentials in an EPR-style experiment. Looking at the universe as a whole as a quantum self-referential system, leads to a modified zitterbewegung Wheeler-DeWitt equation; and, the transition from quantum-to-classical on a cosmological scale for the measurement problem is accomplished for an expanding-only deSitter quantum spacetime.

Mitchell, Mark Kenneth

1993-01-01

139

The transitions among classical mechanics, quantum mechanics, and stochastic quantum mechanics  

NASA Astrophysics Data System (ADS)

Various formalisms for recasting quantum mechanics in the framework of classical mechanics on phase space are reviewed and compared. Recent results in stochastic quantum mechanics are shown to avoid the difficulties encountered by the earlier approach of Wigner, as well as to avoid the well-known incompatibilities of relativity and ordinary quantum theory. Specific mappings among the various formalisms are given.

Schroeck, Franklin E.

1982-09-01

140

Remarks on Osmosis, Quantum Mechanics, and Gravity  

NASA Astrophysics Data System (ADS)

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.

Carroll, Robert

2012-05-01

141

Kowalevski top in quantum mechanics  

NASA Astrophysics Data System (ADS)

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.

Matsuyama, A.

2013-09-01

142

Faster than Hermitian quantum mechanics.  

PubMed

Given an initial quantum state |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(F)>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi(I)> to |psi(F)> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing. PMID:17358747

Bender, Carl M; Brody, Dorje C; Jones, Hugh F; Meister, Bernhard K

2007-01-24

143

OSP: Quantum-mechanical Measurement  

NSDL National Science Digital Library

This set of quantum mechanics java applets, part of the Open Source Physics project, provides simulations that demonstrate the effect of measurement on the time-dependence of quantum states. Exercises are available that demonstrate the results of measurement of energy, position, and momentum on states in potential wells (square well, harmonic oscillator, asymmetric well, etc). Eigenstates, superpositions of eigenstates, and wave packets can all be studied. Tutorials are also available. The material stresses the measurement of a quantum-mechanical wave function. The simulations can be delivered either through the OSP Launcher interface or embedded in html pages. The source code is available, and users are invited to contribute to the collection's development by submitting improvements. The simulations are available through the "View attached documents" link below.

Belloni, Mario; Christian, Wolfgang

2006-06-27

144

Effective equations for the quantum pendulum from momentous quantum mechanics  

SciTech Connect

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.

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

145

Capacity and quantum mechanical tunneling  

Microsoft Academic Search

We connect the notion of capacity of sets in the theory of symmetric Markov process and Dirichlet forms with the notion of tunneling through the boundary of sets in quantum mechanics. In particular we show that for diffusion processes the notion appropriate to a boundary without tunneling is more refined than simply capacity zero. We also discuss several examples in

S. Albeverio; M. Fukushima; W. Karwowski; L. Streit

1981-01-01

146

Self-Referential Quantum Mechanics  

Microsoft Academic Search

A nonlinear quantum mechanics based upon the nonlinear logarithmic Schrodinger equation, is developed which has the property of self-reference, that is, the nonlinear term is dependent upon the square of the wavefunction. The self-referential system is examined in terms of its mathematical properties, the definition of the wavefunction, and the nonlinear system in the feedback between equation and solution. Theta

Mark Kenneth Mitchell

1993-01-01

147

Quantum Mechanics and Physical Reality  

Microsoft Academic Search

IN a recent article by A. Einstein, B. Podolsky and N. Rosen, which appeared in the Physical Review of May 15, and was reviewed in NATURE of June 22, the question of the completeness of quantum mechanical description has been discussed on the basis of a ``criterion of physical reality'', which the authors formulate as follows : ``If, without in

N. Bohr

1935-01-01

148

Negative Observations in Quantum Mechanics  

Microsoft Academic Search

In quantum mechanics, it is possible to make observations that affect\\u000aphysical entities without there being a physical interaction between the\\u000aobserver and the physical entity measured. Epstein (1945) and Renninger (1960)\\u000adiscussed this situation, and Renninger called this type of observation a\\u000a\\

Douglas M. Snyder

1999-01-01

149

Quantum mechanics, relativity and time  

Microsoft Academic Search

A discussion on quantum mechanics, general relativity and their relations is introduced. The assumption of the absolute validity of conservation laws and the extension to a 5D-space lead to reconsider several shortcomings and paradoxes of modern physics under a new light without the necessity to take into account symmetry breakings. In this picture, starting from first principles, and after a

Giuseppe Basini; Salvatore Capozziello

2005-01-01

150

Collective Motion in Quantum Mechanics  

Microsoft Academic Search

A general method of discussing quantum-mechanical problems involving collective motion is proposed, in which the emphasis is placed on consideration of sets of states rather than single states, and in which the additional collective co-ordinates are not redundant but used to describe the sets. The method is applied to a number of relatively simple examples: plasma oscillations of an electron

T. H. R. Skyrme

1957-01-01

151

Quantum Mechanical Methods for Enzyme Kinetics  

Microsoft Academic Search

This review discusses methods for the incorporation of quantum mechanical effects into enzyme kinetics simulations in which the enzyme is an explicit part of the model. We emphasize three aspects: (a) use of quantum mechanical electronic structure methods such as molecular orbital theory and density functional theory, usually in conjunction with molecular mechanics; (b) treating vibrational motions quantum mechanically, either

Jiali Gao; Donald G. Truhlar

2002-01-01

152

Probable Inference and Quantum Mechanics  

SciTech Connect

In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.

Grandy, W. T. Jr. [Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82070 (United States)

2009-12-08

153

Topics in quantum mechanics  

SciTech Connect

The present paper deals with three independent subjects. I. We show how for classical canonical transformation we can pass, with the help of Wigner distribution functions, from their representation U in the configurational Hilbert space to a kernel K in phase space. The latter is a much more transparent way of looking at representations of canonical transformations, as the classical limit is reached when ({Dirac_h}/2{pi}){yields}0 and successive quantum corrections are related with powers of ({Dirac_h}/2{pi}){sup 2n}, n=1,2,... . II. We discuss the coherent states solution for a charged particle in a constant magnetic field and show that it is the appropriate one for getting the classical limit of the problem, i.e., motion in a circle around any point in the plane perpendicular to the field and with the square of the radius proportional to the energy of the particle. III. We show that it is possible to have just one equation involving n{alpha}'s and {beta} matrices to get relativistic wave equations that can have spins with values up to n/2. We then decompose the {alpha}'s and {beta}'s into direct products of ordinary spin matrices and a new type of them that we call sign spin. The problem reduces then to that of the generators of a SU(4) group, entirely similar to the one in the spin-isospin theory of nuclear physics. For a free particle of arbitrary spin the symmetry group is actually the unitary symplectic subgroup of SU(4), i.e., Sp(4). As the latter is isomorphic to O(5), we can characterize our states by the canonical chain O(5) superset of O(4) superset of O(3) superset of O(2), and from it obtain the spin and mass content of our relativistic equation.

Moshinsky, Marcos [Instituto de Fisica-UNAM. Apartado Postal 20-364, 01000 Mexico, D.F. (Mexico)

1999-03-06

154

Student understanding of quantum mechanics  

NSDL National Science Digital Library

We investigate the difficulties of advanced undergraduate students toward the end of a full year upper-level quantum mechanics course with concepts related to quantum measurements and time development. Our analysis is based upon a test administered to 89 students from six universities and interviews with 9 students. Strikingly, most students shared the same difficulties despite variations in background, teaching styles, and textbooks. Concepts related to stationary states, eigenstates, and time dependence of expectation values were found to be particularly difficult. An analysis of written tests and interviews suggests that widespread misconceptions originate from an inability to discriminate between related concepts and a tendency to overgeneralize.

Singh, Chandralekha

2005-11-23

155

On Quantum Mechanics on Noncommutative Quantum Phase Space  

Microsoft Academic Search

In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM) is showed to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two noncommutativity parameters possesses a lower bound in direct relation with Heisenberg incertitude relations,

A. E. F. Djemai; H. Smail

2003-01-01

156

A quantum mechanical model of interference  

Microsoft Academic Search

In this paper an ideal quantum mechanical model of interference is constructed, in particular, the role of the quantum mechanical phase difference of two harmonic modes on the interference picture is investigated.

A. Shalom; J. Zak

1973-01-01

157

Mechanisms, molecular and sero-epidemiology of antimicrobial resistance in bacterial respiratory pathogens isolated from Japanese children  

Microsoft Academic Search

BACKGROUND: The clinical management of community-acquired respiratory tract infections (RTIs) is complicated by the increasing worldwide prevalence of antibacterial resistance, in particular, ?-lactam and macrolide resistance, among the most common causative bacterial pathogens. This study aimed to determine the mechanisms and molecular- and sero-epidemiology of antibacterial resistance among the key paediatric respiratory pathogens in Japan. METHODS: Isolates were collected at

Keisuke Sunakawa; David J Farrell

2007-01-01

158

Quantum mechanics of black holes.  

PubMed

The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely. PMID:22859480

Witten, Edward

2012-08-01

159

Three-space from quantum mechanics  

SciTech Connect

We formulate a discrete quantum-mechanical precursor to spacetime geometry. The objective is to provide the foundation for a quantum mechanics that is rooted exclusively in quantum-mechanical concepts, with all classical features, including the three-dimensional spatial continuum, emerging dynamically.

Chew, G.F.; Stapp, H.P.

1988-08-01

160

Quantum mechanics and the psyche  

NASA Astrophysics Data System (ADS)

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.

Galli Carminati, G.; Martin, F.

2008-07-01

161

What is an Essentially Quantum Mechanical Effect?  

Microsoft Academic Search

Abstract When asking whether consciousness is an “essentially quantum effect”, one must first lay down criteria for considering an effect ,quantum ,mechanical. After a brief survey ,of the ,interpretations of quantum theory, three such sufficient criteria are proposed and examined: wave-particle duality (or collapse), entanglement (“non-locality”), and quantum condensation (involving “identical” particles). A fourth criteria could involve the use of

Osvaldo Pessoa Jr

162

Superconformal black hole quantum mechanics  

Microsoft Academic Search

In recent work, the superconformal quantum mechanics describing D0 branes in the AdS2 × S2 × CY3 attractor geometry of a Calabi-Yau black hole with D4 brane charges pA has been constructed and found to contain a large degeneracy of chiral primary bound states. In this paper it is shown that the asymptotic growth of chiral primaries for N D0

Davide Gaiotto; Andrew Strominger; Xi Yin

2005-01-01

163

Teaching quantum mechanics on an introductory level  

NSDL National Science Digital Library

We present a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. In the context of virtual laboratories, the students discover from the very beginning how quantum phenomena deviate from our classical everyday experience. The results of the evaluation of the course show that most of the students acquired appropriate quantum mechanical conceptions, and that many of the common misconceptions encountered in traditional instruction have been avoided.

Mã¼ller, Rainer; Wiesner, Hartmut

2005-10-27

164

Facets of contextual realism in quantum mechanics  

SciTech Connect

In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.

Pan, Alok Kumar [LPTM (CNRS Unite 8089), Universite de Cergy-Pontoise, 95302 Cergy-Pontoise cedex (France); Home, Dipankar [CAPSS, Department of Physics, Bose Institute, Salt Lake, Calcutta 700091 (India)

2011-09-23

165

Trojan wavepackets in quantum mechanics equivalent to classical mechanics  

NASA Astrophysics Data System (ADS)

We formulate the theory of wavepackets moving on classical circular orbits in Hydrogen atom in rotating electromagnetic wave within the quantum mechanics equivalent to classical mechanics [1]. Unlike within the true quantum mechanics the wavepackets spreads during the time comparable with the time of full quantum revival within true quantum mechanics. Numerical solutions of the nonlinear Schrodingers equation are provided using non-linear split operator method for this equation. [1] D. Shay, Phys. Rev A, 13, 2261 (1976).

Kalinski, Matt

2005-05-01

166

Faster than Hermitian Quantum Mechanics  

SciTech Connect

Given an initial quantum state vertical bar {psi}{sub I}> and a final quantum state vertical bar {psi}{sub F}>, there exist Hamiltonians H under which vertical bar {psi}{sub I}> evolves into vertical bar {psi}{sub F}>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time {tau}? For Hermitian Hamiltonians {tau} has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, {tau} can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from vertical bar {psi}{sub I}> to vertical bar {psi}{sub F}> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.

Bender, Carl M. [Physics Department, Washington University, St. Louis, Missouri 63130 (United States); Department of Mathematics, Imperial College, London SW7 2BZ (United Kingdom); Brody, Dorje C. [Department of Mathematics, Imperial College, London SW7 2BZ (United Kingdom); Jones, Hugh F. [Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom); Meister, Bernhard K. [Department of Physics, Renmin University of China, Beijing 100872 (China)

2007-01-26

167

BOOK REVIEWS: Quantum Mechanics: Fundamentals  

NASA Astrophysics Data System (ADS)

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

Whitaker, A.

2004-02-01

168

SENSIBLE QUANTUM MECHANICS: ARE ONLY PERCEPTIONS  

Microsoft Academic Search

Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic, except, in a certain frequency sense, conscious perceptions. Sets of these perceptions can be deterministi- cally realized with measures given by expectation values of positive-operator- valued awareness operators in a quantum state of the universe which never jumps or collapses. Ratios of the measures

Don N. Page

169

Teaching Quantum Mechanics on an Introductory Level.  

ERIC Educational Resources Information Center

|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)|

Muller, Rainer; Wiesner, Hartmut

2002-01-01

170

Web-based Quantum Mechanics I Course  

NSDL National Science Digital Library

This web site is an entire web-based Quantum Mechanics I Course based at the University of Tennessee. It includes instructional materials, in-class tutorials, simulations, links to other quantum resources, homework assignments, and solutions.

Breinig, Marianne

2009-09-17

171

Simple Formulas for Improved Point-Charge Electrostatics in Classical Force Fields and Hybrid Quantum Mechanical/Molecular Mechanical Embedding  

PubMed Central

We present a simple damping scheme for point-charge electrostatics that could be used directly in classical force fields. The approach acts at the charge (or monopole) level only and allows the inclusion of short-range electrostatic penetration effects at a very low cost. Results are compared with density functional theory Coulomb intermolecular interaction energies and with several other methods such as distributed multipoles, damped distributed multipoles, and transferable Hermite-Gaussian densities. Realistic trends in the interactions are observed for atom-centered Mertz-Kollman corrected point-charge distributions. The approach allows increasing the selectivity of parameters in the case of metal complexes. In addition, two QM/MM calculations are presented where the damping function is employed to include the MM atoms located at the QM/MM boundary. The first calculation corresponds to the gas-phase proton transfer of aspartic acid through water and the second is the first step of the reaction catalyzed by the 4-oxalocrotonate tautomerase (4OT) enzyme. First, improved agreement is observed when using the damping approach compared with the conventional excluded charge method or when including all charges in the calculation. Second, in the case of 4OT, the damped charge approach is in agreement with previous calculations, whereas including all charges gives a significantly higher energy barrier. In both cases, no reparameterization of the van der Waals part of the force field was performed.

Cisneros, G. A.; Tholander, S. Na-Im; Parisel, O.; Darden, T. A.; Elking, D.; Perera, L.; Piquemal, J.-P.

2009-01-01

172

A quantum mechanical/molecular mechanical study of the aspartic protease plasmepsin IV complexed with allophenylnorstatine-based inhibitor  

NASA Astrophysics Data System (ADS)

Plasmepsin IV (PM IV) is a potential target for developing drugs against malaria. This Letter presents results of QM/MM dynamic simulations applied to the study of the protonation state of two aspartates (Asp34 and Asp214) catalytic residues of PM IV in complex with KNI-764 inhibitor. The potential of mean force profile was used to assign the protonation state of the two catalytic aspartates in PM IV-KNI-764 complex. The results indicate that protonation of the 214 residue is more favorable. In addition, energy terms decomposition was used to explore key interactions between the main residues and KNI-764 inhibitor.

Silva, Natália de Farias; Lameira, Jerônimo; Alves, Cláudio Nahum

2011-06-01

173

Communication: Constructing an implicit quantum mechanical/molecular mechanics solvent model by coarse-graining explicit solvent.  

PubMed

To avoid repeated, computationally expensive QM solute calculations while sampling MM solvent in QM/MM simulations, a new approach for constructing an implicit solvent model by coarse-graining the solvent properties over many explicit solvent configurations is proposed. The solvent is modeled using a polarizable force field that is parameterized in terms of distributed multipoles (electrostatics), polarizabilities (induction), and frequency-dependent polarizabilities (dispersion). The coarse-graining procedure exploits the ability to translate these properties to the center of each coarse-graining cell and average them over many solvent configurations before interacting them with the solute. A single coarse-grained QM/MM calculation of the interaction between a formamide solute and aqueous solvent reproduces the much more expensive average over many explicit QM/MM calculations with kJ/mol accuracy. PMID:24006967

Theel, Kelly L; Wen, Shuhao; Beran, Gregory J O

2013-08-28

174

Theoretical study of ion/macrocycle interactions using both hybrid quantum mechanical-molecular mechanical and ab initio methods  

SciTech Connect

Synthetic macrocycles have drawn much experimental and theoretical interest since Pederson first synthesized the crown-ether 18-crown-6 (18c6) in 1967. Crown-ethers show a remarkable range of specificity for a wide variety of cations that depends, in part, on the size of the ether, the type of donor atoms (e.g. oxygen, nitrogen, sulfur), and the polarity of the solvent. Crown-ethers and related macrocycles are of particular interest to research efforts in chemical separations applied to environmental remediation. For example, at the Hanford nuclear facility {sup 9O}Sr{sup 2+} and {sup 137}Cs{sup +} are two major generators of heat which complicate the disposal of nuclear waste. One example of the use of crown-ethers for radionuclide separation is the Strontium Extraction (SREX) process which uses di-t-butylcyclohexano-18-crown-6 for recovering {sup 9O}Sr{sup 2+} from acidic solution. A more thorough understanding of fundamental interactions of cation/crown-ether solution chemistry may provide the basis for rational design of new ligands useful in the separation of these and other radionuclides from radionuclide-containing waste streams at hazardous waste storage facilities. There is also a growing interest in the use of crown-ethers, cryptands, and other ligands for use in chemical sensors. Specifically, fluoroionophores, which consisting of a fluorophore (e.g. dye-molecule) linked to an ionophore (e.g. crown-ether), exhibit measurable changes in the photophysical properties of the fluorophore upon ion binding by the ionophore. Fluoroionophores would be useful for monitoring ground-water aquifers and industrial effluent streams for low-levels of hazardous radionuclides and other toxic metals.

Thompson, M.A.; Glendening, E.D.; Feller, D.; Kendall, R.

1995-08-01

175

Multiverse interpretation of quantum mechanics  

NASA Astrophysics Data System (ADS)

We argue that the many worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics. Decoherence—the modern version of wave-function collapse—is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the environment. In fact decoherence is absent in the complete description of any region larger than the future light cone of a measurement event. However, if one restricts to the causal diamond—the largest region that can be causally probed—then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many worlds (all possible decoherent causal diamond histories) in a single geometry. We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the Universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with a finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in hats (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.

Bousso, Raphael; Susskind, Leonard

2012-02-01

176

Fun with supersymmetric quantum mechanics  

SciTech Connect

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.

Freedman, B.; Cooper, F.

1984-04-01

177

Thermalization Processes in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

In quantum mechanics, the emergence of thermalization processes from unitary evolution has remained one of the greatest challenges. The two outstanding theories of this issue by Srednicki and Tasaki cannot address the concepts of temperature, heat, and work. Here, we present a theory using multiple quenches to examine the thermalization processes to advance thermodynamics concepts. To perform multiple quenches, one can vary one single control parameter (?) in a series of time evolutions, which create a set of density operators. The average of these density operators results into a diagonal operator with probability distribution function that can describe the emerging ensembles. Measuring probability distribution functions of key physical observables, temperature, equal to the derivative of energy with respect to entropy, can be easily measured. Therefore, simulations via multiple quenches can mimic dynamics in open quantum systems with much cheaper computational cost. They allow (1) tuning of temperature and entropy via ?, (2) measuring work distribution functions from distributions of a reaction coordinate, and (3) computing free-energy changes via Jarzynski's Equality. We hope that this approach can provide a new foundation and open up new directions for studying control of quantum systems.

Ngo, Van; Haas, Stephan

2013-03-01

178

Introduction to Quantum Mechanics Activity  

NSDL National Science Digital Library

This resource provides an introductory activity on "the basic quantum mechanics concepts about electrons that are essential to understanding modern and future technology- especially nanotechnology that will be vitally important to the industry." Core concepts include probability distribution, electron waves, diffraction, interference, tunneling, bound states and excited states. The interactive module allows students to test their knowledge as they learn. The material would be best for high school AP classes and college level students. The other educational modules in this series can be found here. Instructors and students are encouraged to sign up with the Electron Technologies site here before starting to use these materials.

2012-02-24

179

Quantum mechanical polar surface area.  

PubMed

A correlation has been established between the absorbed fraction of training-set molecules after oral administration in humans and the Quantum Mechanical Polar Surface Area (QMPSA). This correlation holds for the QMPSA calculated with structures where carboxyl groups are deprotonated. The correlation of the absorbed fraction and the QMPSA calculated on the neutral gas phase optimized structures is much less pronounced. This suggests that the absorption process is mainly determined by polar interactions of the drug molecules in water solution. Rules are given to derive the optimal polar/apolar ranges of the electrostatic potential. PMID:22391921

Schaftenaar, Gijs; de Vlieg, Jakob

2012-03-04

180

Tunneling in fractional quantum mechanics  

NASA Astrophysics Data System (ADS)

We study tunneling through delta and double delta potentials in fractional quantum mechanics. After solving the fractional Schrödinger equation for these potentials, we calculate the corresponding reflection and transmission coefficients. These coefficients have a very interesting behavior. In particular, we can have zero energy tunneling when the order of the Riesz fractional derivative is different from 2. For both potentials, the zero energy limit of the transmission coefficient is given by {T}_0 = \\cos ^2{(\\pi /\\alpha )}, where ? is the order of the derivative (1 < ? <= 2).

Capelas de Oliveira, E.; Vaz, Jayme, Jr.

2011-05-01

181

N=4 supersymmetric multidimensional quantum mechanics, partial SUSY breaking, and superconformal quantum mechanics  

Microsoft Academic Search

The multidimensional N=4 supersymmetric (SUSY) quantum mechanics (QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the SUSY QM considered, both classical and quantum N=4 algebras include central charges, and this opens various possibilities for partial supersymmetry breaking. It is shown that quantum-mechanical models with

E. E. Donets; A. Pashnev; J. Juan Rosales; M. M. Tsulaia

2000-01-01

182

Propagators in polymer quantum mechanics  

NASA Astrophysics Data System (ADS)

Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to represent some aspects of the loop quantization in a simpler context, and, on the other, it has been applied to each of the infinite mechanical modes of other systems. Indeed, this polymer approach was recently implemented for the free scalar field propagator. In this work we compute the polymer propagators of the free particle and a particle in a box; amusingly, just as in the non polymeric case, the one of the particle in a box may be computed also from that of the free particle using the method of images. We verify the propagators hereby obtained satisfy standard properties such as: consistency with initial conditions, composition and Green's function character. Furthermore they are also shown to reduce to the usual Schrödinger propagators in the limit of small parameter ?0, the length scale introduced in the polymer dynamics and which plays a role analog of that of Planck length in Quantum Gravity.

Flores-González, Ernesto; Morales-Técotl, Hugo A.; Reyes, Juan D.

2013-09-01

183

A Modern Approach to Quantum Mechanics  

NSDL National Science Digital Library

This textbook, unlike most others in the topic, introduces the basic quantum concepts using spin, rather than starting from wave mechanics. This grounding in quantum phenomena, rather than difficult mathematics, is then used to cover all the standard topics in quantum physics. Relationships to experimental results are stressed. An instructor's manual is available.

Townsend, John

2004-03-04

184

Interactive Learning Tutorials on Quantum Mechanics  

NSDL National Science Digital Library

We discuss the development and evaluation of quantum interactive learning tutorials (QuILTs), which are suitable for undergraduate courses in quantum mechanics. QuILTs are based on the investigation of student difficulties in learning quantum physics. They exploit computer-based visualization tools and help students build links between the formal and conceptual aspects of quantum physics without compromising the technical content. They can be used both as supplements to lectures or as self-study tools.

Singh, Chandralekha

2013-08-08

185

Bohmian mechanics and quantum field theory.  

PubMed

We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end. PMID:15447078

Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino

2004-08-23

186

Thermodynamic integration from classical to quantum mechanics  

SciTech Connect

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.

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

187

Relationship between quantum walks and relativistic quantum mechanics  

SciTech Connect

Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This article revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled forms of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schroedinger form. By showing the coin to be a means to make the walk reversible and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modeled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. The Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of the quantum walk, the maximum speed of walk propagation, and earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two-state system to which the study can be extended.

Chandrashekar, C. M. [Institute for Quantum Computing, University of Waterloo, Ontario N2L 3G1 (Canada); Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada); Banerjee, Subhashish [Chennai Mathematical Institute, Padur PO, Siruseri 603 103 (India); Srikanth, R. [Poornaprajna Institute of Scientific Research, Devanahalli, Bangalore 562 110 (India); Raman Research Institute, Sadashiva Nagar, Bangalore 560 080 (India)

2010-06-15

188

Weyl Geometries, Fisher Information and Quantum Entropy in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

It is known that quantum mechanics can be interpreted as a non-Euclidean deformation of the space-time geometries by means Weyl geometries. We propose here a dynamical explanation of such approach by deriving Bohm potential from minimum condition of Fisher information connected to the entropy of a quantum system.

Fiscaletti, Davide; Licata, Ignazio

2012-11-01

189

Alternative decohering histories in quantum mechanics.  

NASA Astrophysics Data System (ADS)

The authors continue their efforts to understand, within the framework of the quantum mechanics of the universe as a whole, the quasi-classical domain of familiar experience as a feature emergent from the Hamiltonian of the elementary particles and the initial condition of the universe. Quantum mechanics assigns probabilities to exhaustive sets of alternative decoherent histories of the universe.

Gell-Mann, M.; Hartle, J. B.

190

Variational methods in relativistic quantum mechanics  

Microsoft Academic Search

This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to the Laplacian appearing in the equations of nonrelativistic quantum mechanics, the Dirac operator has a negative continuous spectrum which is not bounded from below.

Maria J. Esteban; Mathieu Lewin; Eric séré

2007-01-01

191

Macroscopicity of Mechanical Quantum Superposition States  

NASA Astrophysics Data System (ADS)

We propose an experimentally accessible, objective measure for the macroscopicity of superposition states in mechanical quantum systems. Based on the observable consequences of a minimal, macrorealist extension of quantum mechanics, it allows one to quantify the degree of macroscopicity achieved in different experiments.

Nimmrichter, Stefan; Hornberger, Klaus

2013-04-01

192

On the quantum mechanics of supermembranes  

Microsoft Academic Search

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

Bernard de Wit; J. Hoppe; H. Nicolai

1988-01-01

193

Noncommutative Quantum Mechanics with Path Integral  

Microsoft Academic Search

We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment of the usual formalism. In particular, we found explicit connections between quadratic Hamiltonians and Lagrangians, in their commutative and noncommutative regimes. In the quantum case we give

Branko Dragovich; Zoran Rakic

2005-01-01

194

Path Integral Approach to Noncommutative Quantum Mechanics  

Microsoft Academic Search

We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the another one with usual commutative coordinates and momenta. We found connection between quadratic classical Hamiltonians, as well as Lagrangians, in their commutative and noncommutative

Branko Dragovich; Zoran Rakic

2004-01-01

195

Quantum Mechanics in Terms of Symmetric Measurements  

NASA Astrophysics Data System (ADS)

In the neo-Bayesian view of quantum mechanics that Appleby, Caves, Pitowsky, Schack, the author, and others are developing, quantum states are taken to be compendia of partial beliefs about potential measurement outcomes, rather than objective properties of quantum systems. Different observers may validly have different quantum states for a single system, and the ultimate origin of each individual state assignment is taken to be unanalyzable within physical theory---its origin, instead, comes from prior probability assignments at stages of physical investigation or laboratory practice previous to quantum theory. The objective content of quantum mechanics thus resides somewhere else than in the quantum state, and various ideas for where that ``somewhere else'' is are presently under debate. What is overwhelmingly agreed upon in this effort is only the opening statement. Still, quantum states are not Bayesian probability assignments themselves, and different representations of the theory (in terms of state vectors or Wigner functions or C*-algebras, etc.) can take one further from or closer to a Bayesian point of view. It is thus worthwhile thinking about which representation might be the most propitious for the point of view and might quell some of the remaining debate. In this talk, I will present several results regarding a representation of quantum mechanics in terms of symmetric bases of positive-semidefinite operators. I also argue why this is probably the most natural representation for a Bayesian-style quantum mechanics.

Fuchs, Christopher

2006-03-01

196

Distribution Functions in Classical and Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The correspondence between classical and quantum mechanics is an important subject for the better understandings of ``quantum chaos''. In particular, it is very important to investigate the correspondence between distribution functions in classical mechanics and in phase space representation of quantum mechanics. This is the review of our recent progresses in the study of distribution functions in classical and quantum mechanics, namely distribution functions in classical mechanics and in coarse-grained classical mechanics as well as the Wigner function and the Husimi function. Topics dealt with include formulations of the Wigner representation, the Husimi representation and coarse-grained classical mechanics, and their applications to the analyses of the eigenstates and time developments of the distribution functions.

Takahashi, K.

197

Realist model approach to quantum mechanics  

NASA Astrophysics Data System (ADS)

The paper proves that quantum mechanics is compatible with the constructive realism of modern philosophy of science. The proof is based on the observation that properties of quantum systems that are uniquely determined by their preparations can be assumed objective without the difficulties that are encountered by the same assumption about values of observables. The resulting realist interpretation of quantum mechanics is made rigorous by studying the space of quantum states—the convex set of state operators. Prepared states are classified according to their statistical structure into indecomposable and decomposable instead of pure and mixed. Simple objective properties are defined and showed to form a Boolean lattice.

Hájí?ek, P.

2013-06-01

198

Quantum Mechanical Models Of The Fermi Shuttle  

SciTech Connect

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.

Sternberg, James [University of Tennessee, Department of Physics and Astronomy, Knoxville TN 37996 (United States)

2011-06-01

199

Quantum Physics Online: Wave Mechanics  

NSDL National Science Digital Library

This is a set of interactive Java applets illustrating the wave nature of quantum physics. Animations are used to illustrate propagation of wave packets, and scattering from potentials. There is also a simple illustration of a scanning tunneling microscope. These applets are part of an extensive collection of animations and simulations illustrating a large range of quantum topics, and an ongoing effort for developing a fully interactive quantum-physics class. Both French and English versions are available.

Joffre, Manuel

2004-03-28

200

Use of Quantum Mechanical Models in Studies of Reaction Mechanisms,  

National Technical Information Service (NTIS)

The problems involved in determining the mechanisms of reactions by quantum mechanical calculations are discussed. Various precautions must be taken if the results of any calculation are to be chemically meaningful. Ab initio studies of reactions must als...

M. J. Dewar

1988-01-01

201

Strange Bedfellows: Quantum Mechanics and Data Mining  

SciTech Connect

Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.

Weinstein, Marvin; /SLAC

2009-12-16

202

Quantum continuum mechanics made simple  

NASA Astrophysics Data System (ADS)

In this paper we further explore and develop the quantum continuum mechanics (QCM) of Tao et al. [Phys. Rev. Lett. 103, 086401 (2009)] with the aim of making it simpler to use in practice. Our simplifications relate to the non-interacting part of the QCM equations, and primarily refer to practical implementations in which the groundstate stress tensor is approximated by its Kohn-Sham (KS) version. We use the simplified approach to directly prove the exactness of QCM for one-electron systems via an orthonormal formulation. This proof sheds light on certain physical considerations contained in the QCM theory and their implication on QCM-based approximations. The one-electron proof then motivates an approximation to the QCM (exact under certain conditions) expanded on the wavefunctions of the KS equations. Particular attention is paid to the relationships between transitions from occupied to unoccupied KS orbitals and their approximations under the QCM. We also demonstrate the simplified QCM semianalytically on an example system.

Gould, Tim; Jansen, Georg; Tokatly, I. V.; Dobson, John F.

2012-05-01

203

A Real Ensemble Interpretation of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics. These laws are highly non-local and involve a new kind of interaction between the members of an ensemble that define a quantum state. These include a stochastic process by which individual systems copy the beables of other systems in the ensembles of which they are a member. The probabilities for these copy processes do not depend on where the systems are in space, but do depend on the distribution of beables in the ensemble. Macroscopic systems then are distinguished by being large and complex enough that they have no copies in the universe. They then cannot evolve by the copy law, and hence do not evolve stochastically according to quantum dynamics. This implies novel departures from quantum mechanics for systems in quantum states that can be expected to have few copies in the universe. At the same time, we are able to argue that the center of masses of large macroscopic systems do satisfy Newton's laws.

Smolin, Lee

2012-10-01

204

Quantum-Mechanical Dualities on the Torus  

NASA Astrophysics Data System (ADS)

On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal, i.e. independent of the observer on classical phase space. Such is the case in all standard applications of quantum mechanics. However, recent developments suggest that the notion of a quantum may not be universal. Transformations between observers that do not agree on the notion of an elementary quantum are called dualities. Classical phase spaces admitting more than one complex-differentiable structure thus provide a natural framework to study dualities in quantum mechanics. As an example we quantise a classical mechanics whose phase space is a torus and prove explicitly that it exhibits dualities.

Isidro, José M.

205

Active Quantum Mechanics: Tutorials and Writing Assignments  

NSDL National Science Digital Library

This web site contains active-learning tutorials and writing assignments for upper-level undergraduate quantum mechanics. The tutorials focus on the mathematical formalism of quantum mechanics. The writing assignments focus on the interpretation of quantum mechanics, and particularly the role of experiments. The topics cover range from introduction to the Schrodinger equation through perturbation theory. In the course using these materials, students work in small groups to complete worksheet-based tutorials during class time, and do fairly typical homework problems and writing assignments, on their own.

Timberlake, Todd

2011-08-01

206

Approach to Measurement to Quantum Mechanics.  

National Technical Information Service (NTIS)

An unconventional approach to the measurement problem in quantum mechanics is considered, the apparatus is treated as a classical system, belonging to the macro-world. In order to have a measurement the apparatus must interact with the quantum system. As ...

E. C. G. Sudarshan T. N. Sherry S. R. Gautam

1977-01-01

207

Web-based Quantum Mechanics II Course  

NSDL National Science Digital Library

This web site is an entire web-based Quantum Mechanics II Course based at the University of Tennessee; it has all instructional materials, in-class tutorials, simulations, links to other quantum resources, a discussion forum, homework assignments, and solutions.

Breinig, Marianne

2005-04-16

208

Quantum-Mechanical Model of Spacetime  

Microsoft Academic Search

We consider a possibility to construct a quantum-mechanical model of spacetime, where Planck size quantum black holes act as the fundamental constituents of space and time. Spacetime is assumed to be a graph, where black holes lie on the vertices. Our model implies that area has a discrete spectrum with equal spacing. At macroscopic length scales our model reproduces Einstein's

Jarmo Makela

2007-01-01

209

Stretched DNA investigated using molecular-dynamics and quantum-mechanical calculations.  

PubMed

We combined atomistic molecular-dynamics simulations with quantum-mechanical calculations to investigate the sequence dependence of the stretching behavior of duplex DNA. Our combined quantum-mechanical/molecular-mechanical approach demonstrates that molecular-mechanical force fields are able to describe both the backbone and base-base interactions within the highly distorted nucleic acid structures produced by stretching the DNA from the 5' ends, which include conformations containing disassociated basepairs, just as well as these force fields describe relaxed DNA conformations. The molecular-dynamics simulations indicate that the force-induced melting pathway is sequence-dependent and is influenced by the availability of noncanonical hydrogen-bond interactions that can assist the disassociation of the DNA basepairs. The biological implications of these results are discussed. PMID:20074515

Rezác, Jan; Hobza, Pavel; Harris, Sarah A

2010-01-01

210

Molecular and quantum mechanical studies on the monomer recognition of a highly-regular ?-helical antifreeze protein  

Microsoft Academic Search

The possible interaction models for an antifreeze protein from Tenebrio molitar (TmAFP) have been systematically studied using the methods of molecular mechanics, molecular dynamics and quantum chemistry.\\u000a It is hoped that these approaches would provide insights into the nature of interaction between protein monomers through sampling\\u000a a number of interaction possibilities and evaluating their interaction energies between two monomers in

Zuoyin Yang; Zongchao Jia; Ruozhuang Liu; Guangju Chen

2004-01-01

211

Test of quantum mechanics by neutron interferometry  

NASA Astrophysics Data System (ADS)

Interferometry with massive elementary particles combines particle and wave features in a direct way. In this respect, neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment, and they are subject to all basic interactions, and they are sensitive to topological effects, as well. They play a pionieering role in the development of interferometry with even heavier objects, like atoms, molecules and clusters. Deterministic and stochastic partial absorption experiments can be described by Bell-type inequalities. Recent neutron interferometry experiments based on postselection methods renewed the discussion about quantum nonlocality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates persisting coupling in phase space even in cases of spatially separated Schrödinger cat-like situations. These states are extremely fragile and sensitive to any kind of fluctuations or other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction region becomes impossible in principle. The transition from a quantum world to a classical one is still an open question and will be tackled by means of dedicated decoherence experiments. Recent measurements deal with quantum contextuality and quantum state reconstruction. The observed results agree with quantum mechanical laws and may stimulate further discussions about their interpretations.

Rauch, H.

2008-06-01

212

Symplectic Topology and Geometric Quantum Mechanics  

NASA Astrophysics Data System (ADS)

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.

Sanborn, Barbara

213

Relative-State Formulation of Quantum Mechanics  

NSDL National Science Digital Library

This entry in the Stanford Encyclopedia of Philosophy contains a comprehensive introduction of Everett's relative-state formulation of quantum mechanics. It explores the many attempts to reconstruct and interpret this no-collapse theory.

Barrett, Jeffrey A.

2010-04-12

214

Many-Worlds Interpretation of Quantum Mechanics  

NSDL National Science Digital Library

This entry in the Stanford Encyclopedia of Philosophy contains a comprehensive introduction to the many-worlds interpretation of quantum mechanics. It includes discussions of the probability, tests, and objections to this interpretation.

Vaidman, Lev

2010-04-09

215

Student Difficulties with Energy in Quantum Mechanics  

NSDL National Science Digital Library

This website contains the results of a study on student difficulties in understanding energy in quantum mechanics. The most common misconceptions are listed. This content was presented to the 1997 meeting of the AAPT.

Redish, Edward F.; Bao, Lei; Jolly, Pratibha

2005-07-26

216

Quantum mechanical effects on the shock Hugoniot.  

National Technical Information Service (NTIS)

Calculations of the locus of shock Hugoniot states of aluminum, using two equations of state that either omit or include a quantum mechanical treatment for the material's electronic excitations, will be presented. The difference between the loci will be a...

B. I. Bennett D. A. Liberman

1991-01-01

217

Symmetry and symmetry breaking in quantum mechanics.  

National Technical Information Service (NTIS)

In the world of infinitely small, the world of atoms, nuclei and particles, the quantum mechanics enforces its laws. The discovery of Quanta, this unbelievable castration of the Possible in grains of matter and radiation, in discrete energy levels compels...

P. Chomaz

1998-01-01

218

Quantum mechanical stabilization of Minkowski signature wormholes  

SciTech Connect

When one attempts to construct classical wormholes in Minkowski signature Lorentzian spacetimes violations of both the weak energy hypothesis and averaged weak energy hypothesis are encountered. Since the weak energy hypothesis is experimentally known to be violated quantum mechanically, this suggests that a quantum mechanical analysis of Minkowski signature wormholes is in order. In this note I perform a minisuperspace analysis of a simple class of Minkowski signature wormholes. By solving the Wheeler-de Witt equation for pure Einstein gravity on this minisuperspace the quantum mechanical wave function of the wormhole is obtained in closed form. The wormhole is shown to be quantum mechanically stabilized with an average radius of order the Planck length. 8 refs.

Visser, M.

1989-05-19

219

Supersymmetric q-deformed quantum mechanics  

SciTech Connect

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.

Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)

2012-06-27

220

Advantages of quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

Quantum mechanics formulated in terms of (wave) functions over phase space is shown to have numerous advantages over the standard approach. These advantages arise in the contexts of discussion of the theoretical framework and of descriptions of laboratory experiments.

Schroeck, F. E.

1994-01-01

221

Quantum Mechanics: Rigid Rotator Applet  

NSDL National Science Digital Library

This simulation shows time-dependent quantum state wavefunctions for the rigid rotator, the spherical harmonic states projected on a sphere. Position, angular momentum, and energy of the states can all be viewed, with phase shown with color. Energy-eigenstate wavefunctions, and combinations of states, can be created through changes in the amplitude and phase of the basis states using spinors, or through the creation of Gaussian wavefunctions with the mouse. The quantum numbers of the states are shown.

Falstad, Paul

2004-05-17

222

Macroscopic quantum mechanics in a classical spacetime.  

PubMed

We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a 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 Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different 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 Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another. PMID:23679686

Yang, Huan; Miao, Haixing; Lee, Da-Shin; Helou, Bassam; Chen, Yanbei

2013-04-22

223

SEI: Quantum Mechanics I Course Materials  

NSDL National Science Digital Library

This web site provides research-based materials for junior-level quantum mechanics I courses on quantum mechanics. Topics covered include the Schroedinger equation, bound state problems, Hilbert space and operators, the hydrogen atom, and spin. The course archives include documented student difficulties, learning goals, ConcepTests (clicker questions), class activities, homework, tutorials, and a conceptual assessment tool. All may be downloaded, although the assessment tools require permission from the authors for access.

Goldhaber, Steve; Pollock, Steven J.

2010-01-29

224

Entangled state representations in noncommutative quantum mechanics  

Microsoft Academic Search

We introduce new representations to formulate quantum mechanics on\\u000anoncommutative coordinate space, which explicitly display entanglement\\u000aproperties between degrees of freedom of different coordinate components and\\u000ahence could be called entangled state representations. Furthermore, we derive\\u000aunitary transformations between the new representations and the ordinary one\\u000aused in noncommutative quantum mechanics (NCQM) and obtain eigenfunctions of\\u000asome basic operators in

Sicong Jing; Qiu-Yu Liu; Hongyi Fan

2005-01-01

225

The Strange World of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction; 2. Classical magnetic needles; 3. The Stern-Gerlach experiment; 4. The conundrum of projections; repeated measurements; 5. Probability; 6. The Einstein-Podolsky-Rosen paradox; 7. Variations on a theme by Einstein; 8. Optical interference; 9. Quantal interference; 10. Amplitudes; 11. Working with amplitudes; 12. Two slit inventions; 13. Quantum cryptography; 14. Quantum mechanics of a bouncing ball; 15. The wavefunction; Appendix A: a brief history of quantum mechanics; Appendix B: putting weirdness to work; Appendix C: sources; Appendix D: general questions; Appendix E: bibliography; Appendix F: skeleton answers for selected problems; Index.

Styer, Daniel F.

2000-02-01

226

On reconciling quantum mechanics and local realism  

NASA Astrophysics Data System (ADS)

Accepting nonlocal quantum correlations requires us to reject special relativity and/or probability theory. We can retain both by revising our interpretation of quantum mechanics regarding the handling of separated systems, as quantum mechanics conflicts with local realism only in its treatment of separated systems. We cannot use the joint probability formula for cases of separated measurements. We use the marginals (partial traces) together with whatever priors we have from an understanding of the system. This program can reconcile quantum mechanics with local realism. An apparent obstacle to this program is the experimental evidence, but we argue that the experiments have been misinterpreted, and that when correctly interpreted they confirm local realism. We describe a local realistic account of one important Einstein-Poldosky-Rosen-Bohm (EPRB) experiment (Weihs et al6) that claims to demonstrate nonlocal entanglement. We present a local realistic system (experiment) that can be calibrated into both quantum and classical correlation domains via adjustment of parameters (`hidden variables') of the apparatus. Weihs incorrectly dismisses these parameters as uncritical. Nonlocal entanglement is seen to be an error. The rest of quantum mechanics remains intact, and remains highly valued as a powerful probability calculus for observables. Freed from the incoherent idea of nonlocal entanglement, we can leverage powerful classical ideas, such as semiclassical radiation theory, stochastic dynamics, classical noncommutativity/contextuality, measurement effects on state, etc., to augment or complement quantum mechanics. When properly interpreted and applied, quantum mechanics lives in peaceful harmony with the local realist conception, and both perspectives offer useful paradigms for describing systems.

Graft, Donald A.

2013-10-01

227

On the Classical Limit of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results of the standard approach, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper, we shall formulate the classical limit as a scaling limit in terms of an adimensional parameter ?. We shall take the first steps toward a comprehensive understanding of the classical limit, analyzing special cases of classical behavior in the framework of a precise formulation of quantum mechanics called Bohmian mechanics which contains in its own structure the possibility of describing real objects in an observer-independent way.

Allori, Valia; Zanghì, Nino

2009-01-01

228

Fourier transform identities in quantum mechanics and the quantum line  

NASA Astrophysics Data System (ADS)

We give a quantum-mechanical interpretation of some modular identities (LF)3=?L2 arising in conformal field theory and the theory of quantum groups in relation to the mapping class group of a torus. The interpretation follows by evaluating the identity in the case of a non-standard group of the real line. The operation L takes the form of the Fourier transform of wave functions in L2(R) with length scale ???/m. We find that this can be factorised as ?L=exp(-i?p2/2m?) exp(-ix2/2??) P exp(-i?p2/2m?), where x, p mare the usual quantum mechanical position and momentum operators, P is the parity and ?=(1-i)/?2 is a normalization constant determined by verifying the identity on wavepackets. We understand this further in terms of the observation that the Fourier transformation is realized on the wavefunctions in quantum mechanics as the evolution by a quantum harmonic oscillator of period 2?? for 1/4 of a cycle. SERC Advanced Fellow and Drapers Fellow of Pembroke College, Cambridge.

Lyubashenko, V. V.; Majid, S.

1992-06-01

229

Mind, matter, and quantum mechanics  

SciTech Connect

A theory of psychophysical phenomena is proposed. It resolves simultaneously four basic problems of science, namely the problems of the connections between: (1) mind and matter, (2), quantum theory and reality, (3) relativity theory and ''becoming,'' and (4) relativity theory and Bell's theorem.

Stapp, H.P.

1982-04-01

230

Fuzzy quantum logic II. The logics of unsharp quantum mechanics  

NASA Astrophysics Data System (ADS)

A survey of the main results of the Italian group about the logics of unsharp quantum mechanics is presented. In particular partial ordered structures playing with respect to effect operators (linear bounded operators F on a Hilbert space ? such that ????, 0?????2) the role played by orthomodular posets with respect to orthogonal projections (corresponding to “sharp” effects) are analyzed. These structures are generally characterized by the splitting of standard orthocomplementation on projectors into two nonusual orthocomplementations (a fuzzy-like and an intuitionistic-like) giving rise to different kinds of Brouwer-Zadeh (BZ) posets: de Morgan BZ posets, BZ* posets, and BZ3 posets. Physically relevant generalizations of ortho-pair semantics (paraconsistent, regular paraconsistent, and minimal quantum logics) are introduced and their relevance with respect to the logic of unsharp quantum mechanics are discussed.

Cattaneo, Gianpiero

1993-10-01

231

Quantum Mechanics, Spacetime Locality, and Gravity  

NASA Astrophysics Data System (ADS)

Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only one of the many, bringing an apparent arbitrariness in defining probabilities, called the measure problem. In this paper, we discuss how these two problems are related with each other, developing a picture for quantum measurement and cosmological histories in the quantum mechanical universe. In order to describe the cosmological dynamics correctly within the full quantum mechanical context, we need to identify the structure of the Hilbert space for a system with gravity. We argue that in order to keep spacetime locality, the Hilbert space for dynamical spacetime must be defined only in restricted spacetime regions: in and on the (stretched) apparent horizon as viewed from a fixed reference frame. This requirement arises from eliminating all the redundancies and overcountings in a general relativistic, global spacetime description of nature. It is responsible for horizon complementarity as well as the "observer dependence" of horizons/spacetime—these phenomena arise to represent changes of the reference frame in the relevant Hilbert space. This can be viewed as an extension of the Poincaré transformation in the quantum gravitational context. Given an initial condition, the evolution of the multiverse state obeys the laws of quantum mechanics—it evolves deterministically and unitarily. The beginning of the multiverse, however, is still an open issue.

Nomura, Yasunori

2013-08-01

232

Photon Quantum Mechanics in the Undergraduate Curriculum  

NASA Astrophysics Data System (ADS)

Although it has been discussed for centuries, the true nature of light is still being debated. In fact, the quantum mechanical aspects of light have only been observed within the past 30 years. Recent advances in technology have decreased the complexity of such tests, and the Department of Physics and Astronomy at Dickinson College has worked to infuse various quantum optics experiments throughout our curriculum. We describe a set of experiments that includes the existence of photons, single-photon interference, the quantum eraser, and tests of Bell's theorem. A primary motivation is bringing undergraduate students face to face with some of the fascinating and subtle aspects of quantum mechanics in a hands-on setting.

Pearson, Brett; Carson, Zack; Jackson, David

2011-06-01

233

Levitated Quantum Nano-Magneto-Mechanical Systems  

NASA Astrophysics Data System (ADS)

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 ?˜10-100MHz. As the supercurrents experience little damping this system will possess unprecendented motional quality factors, with Qmotion˜10^9-10^13, 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.

Cirio, Mauro; Twamley, Jason; Brennen, Gavin K.; Milburn, Gerard J.

2011-03-01

234

Quantum opto-mechanics: Quantum optical control of massive mechanical resonators  

Microsoft Academic Search

The toolbox of quantum optics allows to achieve coherent quantum control over massive mechanical resonators by using radiation pressure of light inside optical cavities. Only recently, cavity-assisted ground state cooling of mechanical motion has been achieved both in the micro- and in the nanomechanical domain [1, 2]. Together with the strong coupling regime [3], this opens up a new parameter

Markus Aspelmeyer

2011-01-01

235

Graph reconstruction and quantum statistical mechanics  

NASA Astrophysics Data System (ADS)

We study how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator algebras reconstruct only topological information, but the statistical mechanical point of view allows for complete reconstruction of multigraphs with minimal degree three.

Cornelissen, Gunther; Marcolli, Matilde

2013-10-01

236

Variational methods in relativistic quantum mechanics  

Microsoft Academic Search

This review is devoted to the study of stationary solutions of linear and\\u000anonlinear equations from relativistic quantum mechanics, involving the Dirac\\u000aoperator. The solutions are found as critical points of an energy functional.\\u000aContrary to the Laplacian appearing in the equations of nonrelativistic quantum\\u000amechanics, the Dirac operator has a negative continuous spectrum which is not\\u000abounded from below.

Maria J. Esteban; Mathieu Lewin; ERIC SERE

2008-01-01

237

Quantum Mechanical Methods for Biomolecular Simulations  

Microsoft Academic Search

We discuss quantum mechanical methods for the description of the potential energy surface and for the treatment of nuclear\\u000a quantum effects in chemical and biological applications. Two novel electronic structure methods are described, including an\\u000a electronic structure-based explicit polarization (X-Pol) force field and an effective Hamiltonian molecular orbital and valence\\u000a bond (EH-MOVB) theory. In addition, we present two path integral

Kin-Yiu Wong; Lingchun Song; Wangshen Xie; Dan T. Major; Yen-Lin Lin; Alessandro Cembran; Jiali Gao

2009-01-01

238

Statistical mechanics of disordered quantum optimization  

NASA Astrophysics Data System (ADS)

The classical statistical mechanical approach to complexity theory proceeds from the study of ensembles of computationally intractable optimization problems as a species of unusual disordered magnetic systems. Over the last thirty years, researchers have used this approach to supplement worst-case hardness results encoded by complexity theory with detailed information about thermodynamic and dynamic phase transitions in the structure of typical cases. This exchange of ideas between classical statistical mechanics and computer science enabled the development of important heuristic algorithms such as simulated annealing and survey propagation and further refined our understanding of glassiness and critical slowing in physical disordered systems. In this thesis, we map out an analogous program in the quantum context. The question is simple: what can quantum statistical mechanics reveal about the difficulty of solving hard quantum optimization problems? Or more directly, what makes those problems hard even for quantum computers? In this pursuit, we introduce the study of ensembles of optimization problems whose complexity status is intrinsically quantum mechanical (Part I) and develop techniques to study quantum spin glasses and the transverse field adiabatic algorithm applied to classically hard random optimization problems (Part II). In particular, we introduce the study of random quantum satisfiability (QSAT) and identify the coarse aspects of its phase diagram, including a new form of entanglement transition. We generalize the cavity method to the study of quantum models and use it to study the transverse field Ising glass and frustrated AKLT models on the Bethe lattice. We further apply the cavity method to extract Griffiths-McCoy singularities in a diluted (classical) ferromagnet and finally observe that there are no Goldstone bosons on the Bethe lattice.

Laumann, Christopher Richard

239

Quantum-Opto-Mechanics: Towards quantum optical control of micromechanical resonators  

NASA Astrophysics Data System (ADS)

Current experiments aim to achieve coherent quantum control over massive mechanical resonators. Quantum optics provides a rich toolbox to prepare and detect mechanical quantum states, in particular by combining nano- and micromechanical resonators with high-finesse cavities. To realize the full potential of mechanical systems for quantum experiments eventually requires the conjunction of strongly coupled mechanical resonators with the preparation of quantum ground states. I will report our latest progress in Vienna towards these goals. I will also discuss the prospect of generating optomechanical quantum entanglement, which is at the heart of Schrödinger's cat paradox, and the possibility of mechanical quantum transducers as a new technology for quantum information processing.

Cole, Garrett

2009-05-01

240

Nonstandard extension of quantum logic and Dirac's bra-ket formalism of quantum mechanics  

Microsoft Academic Search

An extension of the quantum logical approach to the axiomatization of quantum mechanics usingnonstandard analysis methods is proposed. The physical meaning of a quantum logic as a lattice of propositions is conserved by its nonstandard extension. But not only the usual Hubert space formalism of quantum mechanics can be derived from the nonstandard extended quantum logic. Also the Dirac bra-ket

Arye Friedman

1994-01-01

241

Space and time from quantum mechanics  

SciTech Connect

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.

Chew, G.F.

1992-09-16

242

Space and time from quantum mechanics  

NASA Astrophysics Data System (ADS)

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.

Chew, G. F.

1992-09-01

243

Remarks on Dersarkissian's cosmic quantum mechanics  

NASA Astrophysics Data System (ADS)

Dersarkissian (1984) has proposed a cosmic quantum mechanics (CQM) characterized by the constant hg approximately equal to 10 to the 75th ergs approximately equal to 10 to the 102nd h, where h is Planck's constant of ordinary quantum mechanics; galaxies are the elementary particles of CQM. Uncertainty arguments in CQM give a number of constraints on the masses of galaxies and thus a concrete way to test CQM. A condition that has to be satisfied for a massive body to be subject to CQM is proposed.

Massa, C.

1985-12-01

244

Atomic physics tests of nonlinear quantum mechanics  

NASA Astrophysics Data System (ADS)

Atomic physics experiments which test a nonlinear generalization of quantum mechanics recently formulated by Weinberg are described. The experiments search for a dependence of hyperfine transition frequencies or nuclear spin precession frequencies on the relative populations of the hyperfine or nuclear spin states. The experiments set limits less than 10 ?Hz on the size of the possible nonlinear contributions to these frequencies. In some cases this can be interpreted as a limit of less than ~10-26 on the fraction of binding energy per nucleon that could be due to a nonlinear correction to a nuclear Hamiltonian. The possibility that a nonlinear addition to quantum mechanics violates causality is discussed.

Bollinger, J. J.; Heinzen, D. J.; Itano, Wayne M.; Gilbert, S. L.; Wineland, D. J.

1991-08-01

245

Two basic Uncertainty Relations in Quantum Mechanics  

SciTech Connect

In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schroedinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.

Angelow, Andrey [Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, 1784 Sofia (Bulgaria)

2011-04-07

246

Macroscopic Quantum Mechanics in a Classical Spacetime  

NASA Astrophysics Data System (ADS)

We apply the many-particle Schr"odinger-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 find 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 it is not allowed that quantum uncertainty to be transferred from one object to another through semiclassical gravity.

Yang, Huan

2013-04-01

247

Quantum mechanics is compatible with realism  

SciTech Connect

A new paradox of quantum mechanics has recently been proposed by an author claiming that any attempt to inject realism in physical theory is bound to lead to inconsistencies. In this paper the author shows that the mentioned paradox is not such a one and that at present there are no reasons to reject realism.

Burgos, M.E.

1987-08-01

248

Quantum mechanics and elements of reality  

Microsoft Academic Search

It is widely accepted that a Born probability of 1 is sufficient for the existence of a corresponding element of reality. Recently Vaidman has extended this idea to the ABL probabilities of the time-symmetrized version of quantum mechanics originated by Aharonov, Bergmann, and Lebowitz. Several authors have objected to Vaidman's time-symmetrized elements of reality without casting doubt on the widely

Ulrich Mohrhoff; Sri Aurobindo Ashram

1999-01-01

249

Student Difficulties with Quantum Mechanics Formalism  

NSDL National Science Digital Library

We discuss student difficulties in distinguishing between the physical space and Hilbert space and difficulties related to the Time-independent Schroedinger equation and measurements in quantum mechanics. These difficulties were identified by administering written surveys and by conducting individual interviews with students.

Singh, Chandralekha

2007-06-26

250

Mona Lisa - ineffable smile of quantum mechanics  

Microsoft Academic Search

The portrait of Mona Lisa is scrutinized with reference to quantum mechanics. The elements of different expressions are firstly recognized on her face. The contradictory details are then classified in two pictures that, undoubtedly representing distinct moods, confirm dichotomous character of the original. Consecutive discussion has lead to conclusion that the mysterious state Mona Lisa is in actually is coherent

Slobodan Prvanovic

2003-01-01

251

No time asymmetry from quantum mechanics  

NASA Astrophysics Data System (ADS)

With CPT-invariant initial conditions that commute with CPT-invariant final conditions, the respective probabilities (when defined) of a set of histories and its CPT reverse are equal, giving a CPT-symmetric universe. This leads me to question whether the asymmetry of the Gell-Mann-Hartle decoherence functional for ordinary quantum mechanics should be interpreted as an asymmetry of time.

Page, Don N.

1993-06-01

252

Quantum Mechanical Effects in Gravitational Collapse  

NASA Astrophysics Data System (ADS)

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 Schrödinger formalism. The Functional Schrödinger 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 Schrödinger 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.

Greenwood, Eric

2010-01-01

253

Vlasov hydrodynamics of a quantum mechanical model  

Microsoft Academic Search

We derive the Vlasov hydrodynamics from the microscopic equations of a quantum mechanical model, which simulates that of an assembly of gravitating particles. In addition we show that the local microscopic dynamics of the model corresponds, on a suitable time-scale, to that of an ideal Fermi gas.

Heide Narnhofer; Geoffrey L. Sewell

1981-01-01

254

Quantum mechanical model for Maya Blue  

Microsoft Academic Search

This work is about Maya Blue (MB), a pigment developed by Mesoamerican civilizations between the 5th and 16th centuries from an aluminosilicate mineral (palygorskite) and an organic dye (indigo). Two different supramolecular quantum-mechanical models afford explanations for the unusual stability of MB based on the oxidation of the indigo molecule during the heating process and its interaction with palygorskite. A

María E. Fuentes; Brisa Peña; César Contreras; Ana L. Montero; Russell Chianelli; Manuel Alvarado; Ramón Olivas; Luz M. Rodríguez; Héctor Camacho; Luis A. Montero-Cabrera

2008-01-01

255

A Quantum Mechanical Model of Spherical Supermembranes  

Microsoft Academic Search

We present a quantum mechanical model of spherical supermembranes. Using superfields to represent the Cartesian coordinates of the membrane, we are able to exactly determine its supersymmetric vacua. We find there are two classical vacua, one corresponding to an extended membrane and one corresponding to a point-like membrane. Instanton effects then lift these vacua to massive states. Similarities to spherical

John Conley; Ben Geller; Mark G. Jackson; Laura Pomerance; Sharad Shrivastava

2003-01-01

256

Quantum mechanical Liouville model with attractive potential.  

National Technical Information Service (NTIS)

We study the quantum mechanical Liouville model with attractive potential which is obtained by Hamiltonian symmetry reduction from the system of a free particle on SL(2,R). The classical reduced system consists of a pair of Liouville subsystems which are ...

H. Kobayashi I. Tsutsui

1995-01-01

257

The Importance of Causality in Quantum Mechanics  

Microsoft Academic Search

Christian theology preferentially favors some philosophical interpretations of quantum mechanics. By using a case study of stationary states of atoms this paper examines the various interpretations. The preferred interpretation is that all localized events in space- time are part of chains of contiguous events traversing space-time at a rate limited by the speed of light. This is the process of

William R. Wharton

258

The Quantum Mechanical Basis of Conceptual Chemistry  

Microsoft Academic Search

Summary.  An experimentalist approaching theory for an understanding of conceptual chemistry that can be related to measurable properties, focuses on the electron density distribution. One finds in the topology of the electron density the definition of an atom, of the bonding between atoms, and of the boundary condition for the extension of quantum mechanics to an open system – to an

Richard F. W. Bader

2005-01-01

259

Subjective and objective probabilities in quantum mechanics  

SciTech Connect

We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, and Schack, but our approach and emphasis are different. We also discuss the problem of choosing a noninformative prior for a density matrix.

Srednicki, Mark [Department of Physics, University of California, Santa Barbara, California 93106 (United States)

2005-05-15

260

Dissipation in Quantum Mechanics. The Harmonic Oscillator  

Microsoft Academic Search

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;

I. R. Senitzky

1960-01-01

261

Can quantum mechanics fool the cosmic censor?  

SciTech Connect

We revisit the mechanism for violating the weak cosmic-censorship conjecture (WCCC) by overspinning a nearly-extreme charged black hole. The mechanism consists of an incoming massless neutral scalar particle, with low energy and large angular momentum, tunneling into the hole. We investigate the effect of the large angular momentum of the incoming particle on the background geometry and address recent claims that such a backreaction would invalidate the mechanism. We show that the large angular momentum of the incident particle does not constitute an obvious impediment to the success of the overspinning quantum mechanism, although the induced backreaction turns out to be essential to restoring the validity of the WCCC in the classical regime. These results seem to endorse the view that the 'cosmic censor' may be oblivious to processes involving quantum effects.

Matsas, G. E. A.; Silva, A. R. R. da [Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, Sao Paulo, SP (Brazil); Richartz, M. [Instituto de Fisica Gleb Wataghin, UNICAMP, C. P. 6165, 13083-970, Campinas, SP (Brazil); Saa, A. [Departamento de Matematica Aplicada, UNICAMP, C. P. 6065, 13083-859, Campinas, SP (Brazil); Vanzella, D. A. T. [Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Avenida Trabalhador Sao-carlense, 400, C. P. 369, 13560-970, Sao Carlos, SP (Brazil)

2009-05-15

262

The Compton effect: Transition to quantum mechanics  

NASA Astrophysics Data System (ADS)

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.

Stuewer, R. H.

2000-11-01

263

A quantum mechanics lab on a chip.  

PubMed

Chip technology has evolved from the desire to further shrink the size of semiconductor devices. The high sensitivity of the electronic properties of nanostructured semiconductors can be used to detect humidity, temperature, magnetic fields and other fundamental quantities. This in turn can be used to use electronic devices for fluidic or biophysical measurements and drastically reduce the volume of such measurements. Small semiconductor devices on the other hand, if measured at low enough temperatures and other appropriate boundary conditions, clearly display quantum effects. The quantum mechanical properties of such small charged islands, also called artificial atoms, can be measured by transport experiments and an energy spectrum similar to the one of real atoms can be detected. A variety of other quantum systems, such as tunnel barriers or phase-coherent rings can also be realized with such techniques. By coupling different quantum circuits on a chip the charge flow can be monitored in a time-resolved fashion on the level of individual electrons. The perfection of such systems has advanced to a degree where basic quantum mechanical properties can be probed on a semiconductor chip. PMID:20664881

Ensslin, Klaus; Gustavsson, Simon; Gasser, Urszula; Küng, Bruno; Ihn, Thomas

2010-07-28

264

Simplified quantum mechanics of light detection for quantum cryptography  

NASA Astrophysics Data System (ADS)

Strong light signals are detected reliably on a time scale of a nanosecond; however, known detectors of weak light signals used in quantum key distribution (QKD) are much slower; they involve pulse-shaping arbiters based on flip-flops that take many nanoseconds to produce a stable output. Based on a recently shown logical independence of quantum particles from the devices that they are employed to explain, we make use of quantum mechanics fine-tuned so that particles serve not as rigid foundations but as improvised hypotheses useful in models that describe the recorded behavior of devices. On the experimental side, we augment the arbitrating flip-flop of a detector so that it fans out to a matched pair of auxiliary flip-flops, and show how this imparts to a detector a "self-awareness" of its own teetering, as announced by disagreements between the auxiliary flip-flops. We introduce a quantum model of this arrangement, invoking a pair of probe particles, and show this model corresponds well to an experiment. The matched pair of auxiliary flip-flops not only confirms the model of hesitation in a detector, but serves as an instrument, both conceptual and practical, that gives an added dimension to the characterization of signal sources.

Myers, John M.; Madjid, F. Hadi

2004-08-01

265

The Quantum Mechanics of the Universe  

NASA Astrophysics Data System (ADS)

Classical general relativity predicts that the universe had a singular origin. The author shows that the singularity can be removed by quantum mechanics, just as in the case of the classical model of the atom. It is proposed that the quantum state of the universe is defined by a path integral over compact positive definite metrics. In a simple model this boundary condition leads to a wave function which can be regarded as a superposition of wave functions peaked around classical oscillating solutions with a long inflationary period.

Hawking, S. W.

266

The quantum mechanics of the universe  

NASA Astrophysics Data System (ADS)

Classical general relativity predicts that the universe had a singular origin. The author shows that the singularity can be removed by quantum mechanics, just as in the case of the classical model of the atom. He proposes that the quantum state of the universe is defined by a path integral over compact positive definite metrics. It is shown that in a simple model this boundary condition leads to a wave function which can be regarded as a superposition of wave functions peaked around classical oscillating solutions with a long inflationary period.

Hawking, S. W.

267

Nano, Quantum, and Statistical Mechanics and Thermodynamics: Educational Sites  

NSDL National Science Digital Library

This collection of links provides access to web sites associated with nano, quantum, and statistical mechanics and thermodynamics. The links are arranged by type: basic principles (including classical thermodynamics), nano, quantum, and statistical mechanics, mathematical techniques, applications, and references.

268

Noncommutative Chern-Simons quantum mechanics  

SciTech Connect

Chern-Simons quantum mechanics is generalized to the noncommutative plane in this paper. Compared with the commutative counterpart, we find that in addition to the mass of the charged particle, there is a dimensionless parameter which behaves interestingly when it takes zero value. We study this model from both classical and quantum aspects. We show that the classical theory has continuous limits when both the parameters tend to zero while the quantum aspect (energy spectra) does not have. We must regularize the spectra of the full theory properly when these parameters tend to zero in order to get the finite results. We resort to the Dirac theory and the Faddeev-Jackiw reduction, respectively, to show that the regularization we made is proper.

Jing Jian [Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029 (China); Department of Physics and Electronic, School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Liu Fenghua [Department of Physics and Electronic, School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Chen Jianfeng [Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029 (China)

2008-12-15

269

Neutrino oscillations: Quantum mechanics vs. quantum field theory  

SciTech Connect

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.

Akhmedov, Evgeny Kh.; Kopp, Joachim

2010-01-01

270

The Double Rotation as Invariant of Motion in Quantum Mechanics  

Microsoft Academic Search

Quantum mechanics may loose its weirdness if systematically geometric algebra methods would be used more. Crucial aspect is to find laws of quantum mechanics be present in macroworld in form of description of motions rather than objects. To help to reach this goal we suggest to use double rotation as one of base invariants in quantum mechanics. We suggest to

Dainis Zeps

2009-01-01

271

Attaching Theories of Consciousness to Bohmian Quantum Mechanics  

Microsoft Academic Search

The de Broglie-Bohm theory of quantum mechanics (here simply called Bohmian Mechanics or BM) [1-10] is an augmentation of ``bare'' quantum mechanics (the bare theory being given by an algebra of operators and a quantum state that sets the expectation values of these operators) that includes a definite history or Bohmian trajectory. This definite trajectory gives BM a somewhat more

Don N. Page

1995-01-01

272

Information geometry, dynamics and discrete quantum mechanics  

NASA Astrophysics Data System (ADS)

We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the picture. We do this in three steps. Our starting point is information geometry, the natural geometry of the space of probability distributions. Dynamics requires additional structure. To evolve the Pk, we introduce coordinates Sk canonically conjugate to the Pk and a symplectic structure. We then seek to extend the metric structure of information geometry, to define a geometry over the full space of the Pk and Sk. Consistency between the metric tensor and the symplectic form forces us to introduce a Kähler geometry. The construction has notable features. A complex structure is obtained in a natural way. The canonical coordinates of the ?k = PkeiSk Kähler space are precisely the wave functions of quantum mechanics. The full group of unitary transformations is obtained. Finally, one may associate a Hilbert space with the Kähler space, which leads to the standard version of quantum theory. We also show that the metric that we derive here using purely geometrical arguments is precisely the one that leads to Wootters' expression for the statistical distance for quantum systems.

Reginatto, Marcel; Hall, Michael J. W.

2013-08-01

273

Quantum KAM technique and Yang{endash}Mills quantum mechanics  

SciTech Connect

We study a quantum analogue of the iterative perturbation theory by Kolmogorov used in the proof of the Kolmogorov{endash}Arnold{endash}Moser (KAM) theorem. The method is based on sequent canonical transformations with a {open_quote}{open_quote}running{close_quote}{close_quote} coupling constant {lambda}, {lambda}{sup 2}, {lambda}{sup 4}, etc. The proposed scheme, as its classical predecessor, is {open_quote}{open_quote}superconvergent{close_quote}{close_quote} in the sense that after the {ital n}th step, a theory is solved to the accuracy of order {lambda}{sup 2{ital n}{minus}1}. It is shown that the Kolmogorov technique corresponds to an infinite resummation of the usual perturbative series. The corresponding expansion is convergent for the quantum anharmonic oscillator due to the fact that it turns out to be identical to the Pade series. The method is easily generalizable to many-dimensional cases. The Kolmogorov technique is further applied to a non-perturbative treatment of Yang{endash}Mills quantum mechanics. A controllable expansion for the wave function near the origin is constructed. For large fields, we build an asymptotic adiabatic expansion in inverse powers of the field. This asymptotic solution contains arbitrary constants which are not fixed by the boundary conditions at infinity. To find them, we approximately match the two expansions in an intermediate region. We also discuss some analogies between this problem and the method of QCD sum rules. Copyright {copyright} 1995 Academic Press, Inc.

Halperin, I. [Department of Physics, Technion-Israel Institute of Technology, Haifa 32000 (Israel)

1995-12-01

274

Quantum Mechanics, Gravity, and the Multiverse  

NASA Astrophysics Data System (ADS)

The discovery of accelerating expansion of the universe has led us to take the dramatic view that our universe may be one of the many universes in which low energy physical laws take different forms: the multiverse. I explain why/how this view is supported both observationally and theoretically, especially by string theory and eternal inflation. I then describe how quantum mechanics plays a crucial role in understanding the multiverse, even at the largest distance scales. The resulting picture leads to a revolutionary change of our view of spacetime and gravity, and completely unifies the paradigm of the eternally inflating multiverse with the many worlds interpretation of quantum mechanics. The picture also provides a solution to a long-standing problem in eternal inflation, called the measure problem, which I briefly describe.

Nomura, Yasunori

2012-04-01

275

Supersymmetry in problems of quantum mechanics  

SciTech Connect

A connection is discussed between the group SU(2) and supersymmetry for a series of quantum mechanical problems. It is pointed out that the impossibility of factorizing Hamiltonians obtained based on representations of the group SU(2) indicates that the sypersymmetry of the system is broken. The authors consider a solution of the anharmonic oscillator problem, and they study properties of solutions for a series of problems for which supersymmetry is possible. They further construct a supersymmetric matrix Hamiltonian and determine supercharges.

Bagrov, V.G.; Vshivtsev, A.S.

1989-01-01

276

Singular potentials in nonrelativistic quantum mechanics  

Microsoft Academic Search

Summary  The mathematical aspects of singular potentials in nonrelativistic quantum mechanics are studied in terms of the self-adjoint\\u000a transformations related to singular differential operators in the space L2(0, ?). The physical content is expressed by the spectral decompositions and for attractive potentials found to be determined\\u000a only up to a parameter denning a particular extension. In general it is not possible

K. Meetz

1964-01-01

277

Auxiliary nRules of Quantum Mechanics  

Microsoft Academic Search

Standard quantum mechanics makes use of four auxiliary rules that allow the\\u000aSchrodinger solutions to be related to laboratory experience, such as the Born\\u000arule that connects square modulus to probability. These rules (here called the\\u000asRules) lead to some unacceptable results. They do not allow the primary\\u000aobserver to be part of the system. They do not allow individual

Richard A Mould

2005-01-01

278

Grounding quantum probability in psychological mechanism.  

PubMed

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

Love, Bradley C

2013-06-01

279

Nonlinear Lattice Within Supersymmetric Quantum Mechanics Formalism  

NASA Astrophysics Data System (ADS)

In the last decades, the study of nonlinear one dimensional lattices has attracted much attention of the scientific community. One of these lattices is related to a simplified model for the DNA molecule, allowing to recover experimental results, such as the denaturation of DNA double helix. Inspired by this model we construct a Hamiltonian for a reflectionless potential through the Supersymmetric Quantum Mechanics formalism, SQM. Thermodynamical properties of such one dimensional lattice are evaluated aming possible biological applications.

Drigo Filho, E.; Ricotta, R. M.

2012-02-01

280

Quantum-mechanical noise in an interferometer  

Microsoft Academic Search

The interferometers now being developed to detect gravitational waves work by measuring the relative positions of widely separated masses. Two fundamental sources of quantum-mechanical noise determine the sensitivity of such an interferometer: (i) fluctuations in number of output photons (photon-counting error) and (ii) fluctuations in radiation pressure on the masses (radiation-pressure error). Because of the low power of available continuous-wave

Carlton Caves

1981-01-01

281

Collocation method for fractional quantum mechanics  

SciTech Connect

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.

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

282

Nine Formulations of Quantum Mechanics: Lecture  

NSDL National Science Digital Library

In this lecture, Dr. Daniel Styer, a physics professor at Oberlin College, guides the listener through nine formulations of quantum mechanics. Styer discusses each formulation's unique abilities and challenges, then offers his perspective on the application to undergraduate education. This lecture was delivered at the Kavli Institute for Physics, as a part of the Theorists at Undergraduate Institutions mini-program. Audio, video and slides are included.

Styer, Dan

2005-08-07

283

Commutator Anomaly in Noncommutative Quantum Mechanics  

NASA Astrophysics Data System (ADS)

In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.

Dulat, Sayipjamal; Li, Kang

284

Deformation quantization of noncommutative quantum mechanics  

Microsoft Academic Search

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantization. In this paper, we investigate the basic aspects of deformation quantization for noncommutative quantum mechanics (NCQM). We first prove some general relations of the Weyl correspondence in non-commuting phase-space. Then we derive explicit form of the Wigner

Sicong Jing; Fen Zuo; Taihua Heng

2004-01-01

285

Landau problem in noncommutative quantum mechanics  

Microsoft Academic Search

The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schrödinger equations on noncommutative (NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity. Then we discuss the noncommutative phase space case, namely, space-space and momentum-momentum non-commutative case, and we get the explicit expression of the Hamiltonian as

Dulat Sayipjamal; Kang Li

2008-01-01

286

Commutator Anomaly in Noncommutative Quantum Mechanics  

Microsoft Academic Search

In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical

Sayipjamal Dulat; Kang Li

2006-01-01

287

1/N expansion in noncommutative quantum mechanics  

SciTech Connect

We study the 1/N expansion in noncommutative quantum mechanics for the anharmonic and Coulombian potentials. The expansion for the anharmonic oscillator presented good convergence properties, but for the Coulombian potential, we found a divergent large N expansion when using the usual noncommutative generalization of the potential. We proposed a modified version of the noncommutative Coulombian potential which provides a well-behaved 1/N expansion.

Ferrari, A. F. [Universidade Federal do ABC, Centro de Ciencias Naturais e Humanas, Rua Santa Adelia, 166, 09210-170, Santo Andre, SP (Brazil); Gomes, M.; Stechhahn, C. A. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo - SP (Brazil)

2010-08-15

288

The 1925 Born and Jordan paper ``On quantum mechanics''  

NASA Astrophysics Data System (ADS)

The 1925 paper ``On quantum mechanics'' by M. Born and P. Jordan, and the sequel ``On quantum mechanics II'' by M. Born, W. Heisenberg, and P. Jordan, developed Heisenberg's pioneering theory into the first complete formulation of quantum mechanics. The Born and Jordan paper is the subject of the present article. This paper introduced matrices to physicists. We discuss the original postulates of quantum mechanics, present the two-part discovery of the law of commutation, and clarify the origin of Heisenberg's equation. We show how the 1925 proof of energy conservation and Bohr's frequency condition served as the gold standard with which to measure the validity of the new quantum mechanics.

Fedak, William A.; Prentis, Jeffrey J.

2009-02-01

289

Quantum mechanics-based properties for 3D-QSAR.  

PubMed

We have used a set of four local properties based on semiempirical molecular orbital calculations (electron density (?), hydrogen bond donor field (HDF), hydrogen bond acceptor field (HAF), and molecular lipophilicity potential (MLP)) for 3D-QSAR studies to overcome the limitations of the current force field-based molecular interaction fields (MIFs). These properties can be calculated rapidly and are thus amenable to high-throughput industrial applications. Their statistical performance was compared with that of conventional 3D-QSAR approaches using nine data sets (angiotensin converting enzyme inhibitors (ACE), acetylcholinesterase inhibitors (AchE), benzodiazepine receptor ligands (BZR), cyclooxygenase-2 inhibitors (COX2), dihydrofolate reductase inhibitors (DHFR), glycogen phosphorylase b inhibitors (GPB), thermolysin inhibitors (THER), thrombin inhibitors (THR), and serine protease factor Xa inhibitors (fXa)). The 3D-QSAR models generated were tested thoroughly for robustness and predictive ability. The average performance of the quantum mechanical molecular interaction field (QM-MIF) models for the nine data sets is better than that of the conventional force field-based MIFs. In the individual data sets, the QM-MIF models always perform better than, or as well as, the conventional approaches. It is particularly encouraging that the relative performance of the QM-MIF models improves in the external validation. In addition, the models generated showed statistical stability with respect to model building procedure variations such as grid spacing size and grid orientation. QM-MIF contour maps reproduce the features important for ligand binding for the example data set (factor Xa inhibitors), demonstrating the intuitive chemical interpretability of QM-MIFs. PMID:23692495

El Kerdawy, Ahmed; Güssregen, Stefan; Matter, Hans; Hennemann, Matthias; Clark, Timothy

2013-06-05

290

Connecting Spin and Statistics in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (-1)2 s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required.

Jabs, Arthur

2010-07-01

291

Adaptive Perturbation Theory I: Quantum Mechanics  

SciTech Connect

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.

Weinstein, Marvin; /SLAC

2005-10-19

292

Bohmian Mechanics In A Macroscopic Quantum System  

NASA Astrophysics Data System (ADS)

In the so called `causal' interpretation of quantum mechanics, an electron is considered as a particle and such particle is influenced not only by a classical but also by a so called quantum potential. This idea was developed by Professor Bohm in an important paper. In this paper we use some of the basics of this interpretation in a financial option pricing environment. The causal interpretation allows for trajectories. Path breaking work by Professors Bohm and Hiley and Khrennikov and Choustova have made that the causal interpretation is a step closer to potential applications in social science. In this paper we consider the wave function as a wave of information. We consider the gradient of the phase of this wave function and show how the option price could be influenced by this gradient.

Haven, Emmanuel

2006-01-01

293

From quantum mechanics to universal structures of conceptualization and feedback on quantum mechanics  

SciTech Connect

In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (states of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a general syntax of relativized conceptualization where any description is explicity and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualiztion. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides towards the answers. Globally the results obtained provide a basis for the future attempts at a general mathematical representation of the processes of conceptualization.

Mugur-Schaechter, M. (Univ. of Reims (France))

1993-01-01

294

Unstable trajectories and the quantum mechanical uncertainty  

SciTech Connect

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.

Moser, Hans R. [Physics Institute, University of Zuerich, Winterthurerstrasse 190, CH-8057 Zuerich (Switzerland)], E-mail: moser@physik.uzh.ch

2008-08-15

295

Unstable trajectories and the quantum mechanical uncertainty  

NASA Astrophysics Data System (ADS)

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.

Moser, Hans R.

2008-08-01

296

Reciprocal relativity of noninertial frames: quantum mechanics  

NASA Astrophysics Data System (ADS)

Noninertial transformations on time-position-momentum-energy space {t, q, p, e} with invariant Born-Green metric ds^{2}=-d t^{2}+\\frac{1}{c^{2}}\\,d q^{2}+\\frac{1}{b^{2}} \\big(d p^{2}-\\frac{1}{c^{2}}\\,d e^{2}\\big) and the symplectic metric -de ? dt + dp ? dq are studied. This {\\cal U}1,3) group of transformations contains the Lorentz group as the inertial special case and, in the limit of small forces and velocities, reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds2 = -dt2. The {\\cal U}( 1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. In the limit of b ? ?, spacetime is invariant. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary representations of its central extension. The same method of projective representations for the inhomogeneous {\\cal U}( 1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous {\\cal U}( 1,3) group is the cover of the quaplectic group {\\cal Q}( 1,3) ={\\cal U}( 1,3) \\otimes _{s}{\\cal H}(4) . {\\cal H}( 4) is the Weyl-Heisenberg group. The {\\cal H}( 4) group, and the associated Heisenberg commutation relations central to quantum mechanics, results directly from requiring projective representations. A set of second-order wave equations result from the representations of the Casimir operators.

Low, Stephen G.

2007-04-01

297

Direct Quantum Mechanical Simulations of Shocked Energetic Materials.  

National Technical Information Service (NTIS)

Quantum mechanical calculations based on density functional theory (DFT) are used to study dynamic behavior of shocked energetic materials (EM). In this work, we present results of quantum molecular dynamics (QMD) simulations of shocked pentaerythritol te...

B. M. Rice R. Balu W. D. Mattson

2008-01-01

298

QUANTUM MECHANICS: Enhanced: Schrodinger's Cat Is Out of the Hat.  

PubMed

In 1935, Erwin Schrödinger suggested his famous gedanken experiment of the cat that is simultaneously "dead" and "alive" inside its box until the box is opened. But as Tesche explains in her Perspective, such a macroscopic manifestation of quantum mechanics has remained elusive until recently. The experiments by van der Wal et al. are an important step toward demonstrating that quantum mechanics can describe macroscopic phenomena. The approach may be exploited in quantum computing and quantum cryptography. PMID:17780511

Tesche, C

2000-10-27

299

Statistical Mechanics of Quantum Integrable Systems  

NASA Astrophysics Data System (ADS)

Recent developments in statistical mechanics of quantum integrable systems are reviewed. Those studies are fundamental and have a renewed interest related to newly developing fields such as atomic Bose-Einstein condensations, photonic crystals and quantum computations. After a brief summary of the basic concepts and methods, the following three topics are discussed. First, by the thermal Bethe ansatz (TBA), a hard-core Bose gas is exactly solved. The model includes fully the effect of excluded volume and is identified to be a c=1 conformal field theory. Second, the cluster expansion method based on the periodic boundary condition for the Bethe wave function, which we call the Bethe ansatz cluster expansion (BACE) method, is developed for a ?-function gas and the XXX Heisenberg chain. This directly proves the TBA and reveals intrinsic properties of quantum integrable systems. Third, for a ?-function gas, the integral equations for the distribution functions of the quasi-momentum and the quasi-particle energy are solved in the form of power series. In the weak coupling case, the results reproduce those of Bogoliubov theory.

Wadati, Miki; Kato, Go; Iida, Toshiaki

300

Supersymmetric quantum mechanics and its applications  

SciTech Connect

The Hamiltonian in Supersymmetric Quantum Mechanics is defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of the component parts that constitute the supersymmetric system are explored. The implications of supersymmetry for the solutions of the Schroedinger equation, the Dirac equation, the inverse scattering theory and the multi-soliton solutions of the KdV equation are examined. Applications to scattering problems in Nuclear Physics with specific reference to singular potentials which arise from considerations of supersymmetry will be discussed.

Sukumar, C.V. [Wadham College, University of Oxford, Oxford OX1 3PN (United Kingdom)

2004-12-23

301

BiHermitian supersymmetric quantum mechanics  

NASA Astrophysics Data System (ADS)

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].

Zucchini, Roberto

2007-04-01

302

Hidden geometric character of relativistic quantum mechanics  

NASA Astrophysics Data System (ADS)

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 4×4 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 4×4 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.

Almeida, José B.

2007-01-01

303

Position-dependent noncommutativity in quantum mechanics  

SciTech Connect

The model of the position-dependent noncommutativity in quantum mechanics is proposed. We start with given commutation relations between the operators of coordinates [x-circumflex{sup i},x-circumflex{sup j}]={omega}{sup ij}(x-circumflex), 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 obeys 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 noncommutativity.

Gomes, M.; Kupriyanov, V. G. [Instituto de Fisica, Universidade de Sao Paulo (Brazil)

2009-06-15

304

Landau Problem in Noncommutative Quantum Mechanics  

Microsoft Academic Search

The Landau problem in non-commutative quantum mechanics (NCQM) is studied.\\u000aFirst by solving the Schr$\\\\ddot{o}$dinger equations on noncommutative(NC) space\\u000awe obtain the Landau energy levels and the energy correction that is caused by\\u000aspace-space noncommutativity. Then we discuss the noncommutative phase space\\u000acase, namely, space-space and momentum-momentum non-commutative case, and we\\u000aget the explicit expression of the Hamiltonian as well

Sayipjamal Dulat; Kang Li

2008-01-01

305

Topological Solution of Bohmian Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The topological solutions of the De Broglie-Bohm quantum mechanics are presented. Starting from the Schrödinger equation for one particle system and ?-mapping topological current theory, the trajectory of the particle is derived explicitly, and can be used as the world line of the particle. The world line is just at the zero point of the wave function and it is shown that the vorticity of the world line can be expressed by Hopf index and Brouwer degree. The evolution of the world line at the bifurcation point is given.

Shi, Xuguang; Yu, Ming; Duan, Yishi

306

Perspectives: Quantum Mechanics on Phase Space  

NASA Astrophysics Data System (ADS)

The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical particle model descriptions exhibiting either Galileian or Lorentzian symmetry. The structures of fundamental importance are the relevant (Lie) groups of symmetries and their homogeneous (and associated) spaces that, in the situations of interest, also possess Hamiltonian structures. Comments are made on the relation between the theory outlined and a recent paper by Carmeli, Cassinelli, Toigo, and Vacchini.

Brooke, J. A.; Schroeck, F. E.

2005-11-01

307

Formulation, interpretation and application of non-commutative quantum mechanics  

NASA Astrophysics Data System (ADS)

In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on positive operator valued measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non-commutativity are identified.

Scholtz, F. G.; Gouba, L.; Hafver, A.; Rohwer, C. M.

2009-05-01

308

Super classical quantum mechanics: The best interpretation of nonrelativistic quantum mechanics  

NASA Astrophysics Data System (ADS)

It has been shown that Newtonian classical mechanics (NCM) suffers from several kinds of chaotic indeterminacies. That means, a large set of problems treated with NCM gives results which are in wild disagreement with observation. In the present paper, these shortcomings are repaired in a simple, obvious, and essentially unique manner. The NCM theory is thereby transformed into a new theory which is fully equivalent to the Heisenberg, Schrödinger, and Dirac nonrelativistic quantum mechanics, with the vital addition of Born's probabilistic interpretation of the wave function built in from the start. I call this new theory ``super classical quantum mechanics'' (SCQM). Using Ehrenfest's theorem of 1927, the classical limit of the new theory, SCQM, is seen to give exactly the results expected of the repaired Newtonian theory of classical mechanics.

Lamb, Willis E.

2001-04-01

309

Loop transfer matrix and loop quantum mechanics  

NASA Astrophysics Data System (ADS)

The gonihedric model of random surfaces on a 3d euclidean lattice has equivalent representation in terms of transfer matrix K(Qi,Qf) which describes the propagation of loops Q. We extend the previous construction of loop transfer matrix to the case of non-zero self-intersection coupling constant kappa. We introduce loop generalization of Fourier transformation which allows to diagonalize transfer matrices depending on symmetric difference of loops and express all eigenvalues of 3d loop transfer matrix through the correlation functions of the corresponding 2d statistical system. The loop Fourier transformation allows to carry out analogy with quantum mechanics of point particles, to introduce conjugate momentum loop P and to define loop quantum mechanics. We also consider transfer matrix on 4d lattice which describes propagation of memebranes. This transfer matrix can also be diagonalized by using generalized Fourier transformation, and all its eigenvalues are equal to the correlation functions of the corresponding 3d statistical system. Particularly the free energy of the 4d membrane system is equal to the free energy of 3d gonihedric system of loops.

Savvidy, George K.

2000-09-01

310

Molecular model with quantum mechanical bonding information.  

PubMed

The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules. PMID:21894893

Bohórquez, Hugo J; Boyd, Russell J; Matta, Chérif F

2011-09-06

311

Attaching Theories of Consciousness to Bohmian Quantum Mechanics  

Microsoft Academic Search

The de Broglie-Bohm theory of quantum mechanics (here simply called Bohmian\\u000aMechanics or BM) [1-10] is an augmentation of ``bare'' quantum mechanics (the\\u000abare theory being given by an algebra of operators and a quantum state that\\u000asets the expectation values of these operators) that includes a definite\\u000ahistory or Bohmian trajectory. This definite trajectory gives BM a somewhat\\u000amore

Don N. Page

1995-01-01

312

Probability in the formalism of quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

The methods of Born and Einstein are used to obtain the probability density in the formalism of quantum mechanics on phase space. The resulting probability leads to a contextual measurement scheme. The Wigner representation, the Husimi representation and the mass shell representation are discussed from the point of view of quantum mechanics on phase space. We also give ramifications for paradoxes in standard quantum mechanics.

Schroeck, Franklin E., Jr.

2012-02-01

313

Mind, Matter and Quantum Mechanics (2nd edition)  

Microsoft Academic Search

Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried

G Mahler

2004-01-01

314

BOOK REVIEW: Mind, Matter and Quantum Mechanics (2nd edition)  

Microsoft Academic Search

Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried

H. P. Stapp

2004-01-01

315

INTRODUCTION TO RELATIVISTIC QUANTUM MECHANICS AND THE DIRAC EQUATION  

Microsoft Academic Search

The development of quantum mechanics is presented from a his- torical perspective. The principles of special relativity are reviewed. Relativis- tic quantum mechanics is developed, including the Klein-Gordon equation and up to the Dirac equation. Near the end of the 19th century, physicists were confident in their view of the world. Newton's mechanics had explained the dynamics of everything from

JACOB E. SONE

316

Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics  

NASA Astrophysics Data System (ADS)

We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.

Jakši?, V.; Ogata, Y.; Pillet, C.-A.; Seiringer, R.

2012-07-01

317

On phase-space representations of quantum mechanics  

NASA Astrophysics Data System (ADS)

We discuss a class of representations of quantum mechanics which uses functions defined on a parameter space to represent observable quantities. We show that infinitesimal canonical transformations could be used to introduce a phase-space-like structure consistent with the requirements of quantum mechanics. The resulting family of phase-space representations of quantum mechanics contains many well-known representations as special cases, e.g., the Weyl-Wigner-Moyal, normal and antinormal one. It is also flexible enough to represent, e.g., /PT-symmetric theories, introduced recently within the context of non-Hermitian quantum mechanics.

Wlodarz, J. J.

2001-07-01

318

Lyapunov exponent in quantum mechanics. A phase-space approach  

NASA Astrophysics Data System (ADS)

Using the symplectic tomography map, both for the probability distributions in classical phase-space and for the Wigner functions of its quantum counterpart, we discuss a notion of Lyapunov exponent for quantum dynamics. Because the marginal distributions, obtained by the tomography map, are always well-defined probabilities, the correspondence between classical and quantum notions is very clear. Then we also obtain the corresponding expressions in Hilbert space. Some examples are worked out. Classical and quantum exponents are seen to coincide for local and non-local time-dependent quadratic potentials. For non-quadratic potentials classical and quantum exponents are different and some insight is obtained on the taming effect of quantum mechanics on classical chaos. A detailed analysis is made for the standard map. Providing an unambiguous extension of the notion of Lyapunov exponent to quantum mechanics, the method that is developed is also computationally efficient in obtaining analytical results for the Lyapunov exponent, both classical and quantum.

Man'ko, V. I.; Vilela Mendes, R.

2000-11-01

319

Exponential complexity and ontological theories of quantum mechanics  

SciTech Connect

Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We consider the general class of ontological theories describing a quantum system by a set of variables with Markovian (either deterministic or stochastic) evolution. We provide proof that the number of continuous variables cannot be smaller than 2N-2, N being the Hilbert-space dimension. Thus, any ontological Markovian theory of quantum mechanics requires a number of variables which grows exponentially with the physical size. This result is relevant also in the framework of quantum Monte Carlo methods.

Montina, A. [Dipartimento di Fisica, Universita di Firenze, Via Sansone 1, 50019 Sesto Fiorentino (Italy)

2008-02-15

320

Paul A.M. Dirac's The Principles of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Paul A.M. Dirac’s book, The Principles of Quantum Mechanics, summarized the foundations of a new science, much of which was his own creation. It expressed the spirit of the new quantum mechanics, creating a descriptive language that we still use. I discuss the successive editions of Dirac’s book and their critical reception, noting changes, especially in the formulation of the general theory and in its treatment of relativistic quantum theory and quantum electrodynamics. In the case of the later editions, I discuss Dirac’s negative attitude toward renormalized quantum electrodynamics.

Brown, Laurie M.

2006-12-01

321

Measurement theory and stochastic differential equations in quantum mechanics  

NASA Astrophysics Data System (ADS)

Continuous (in time) measurements can be introduced in quantum mechanics by using operation-valued measures and quantum stochastic calculus. In this paper quantum stochastic calculus is used for showing the connections between measurement theory and open-system theory. In particular, it is shown how continuous measurements are strictly related to the concept of output channels, introduced in the framework of quantum stochastic differential equations by Gardiner and Collet.

Barchielli, Alberto

1986-09-01

322

Causal Quantum Mechanics Treating Position and Momentum Symmetrically  

NASA Astrophysics Data System (ADS)

De Broglie and Bohm formulated a causal quantum mechanics with a phase space density whose integral over momentum reproduces the position probability density of the usual statistical quantum theory. We propose a causal quantum theory with a joint probability distribution such that the separate probability distributions for position and momentum agree with the usual quantum theory. Unlike the Wigner distribution the suggested distribution is positive-definite and obeys the Liouville condition.

Roy, S. M.; Singh, Virendra

323

Moyal quantum mechanics: The semiclassical Heisenberg dynamics  

SciTech Connect

The Moyal description of quantum mechanics, based on the Wigner--Weyl isomorphism between operators and symbols, provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in {h_bar} and so presents a preferred foundation for semiclassical analysis. Its semiclassical expansion ``coefficients,`` acting on symbols that represent observables, are simple, globally defined (phase space) differential operators constructed in terms of the classical flow. The first of two presented methods introduces a cluster-graph expansion for the symbol of an exponentiated operator, which extends Groenewold`s formula for the Weyl product of two symbols and has {h_bar} as its natural small parameter. This Poisson bracket based cluster expansion determines the Jacobi equations for the semiclassical expansion of ``quantum trajectories.`` Their Green function solutions construct the regular {h_bar}{down_arrow}0 asymptotic series for the Heisenberg--Weyl evolution map. The second method directly substitutes such a series into the Moyal equation of motion and determines the {h_bar} coefficients recursively. In contrast to the WKB approximation for propagators, the Heisenberg--Weyl description of evolution involves no essential singularity in {h_bar}, no Hamilton--Jacobi equation to solve for the action, and no multiple trajectories, caustics, or Maslov indices. {copyright} 1995 Academic Press, Inc.

Osborn, T.A.; Molzahn, F.H. [Department of Physics, University of Manitoba, Winnipeg, MB, R3T 2N2 (Canada)

1995-07-01

324

Momentum diffusion of the quantum kicked rotor: Comparison of Bohmian and standard quantum mechanics  

Microsoft Academic Search

Momentum diffusion of the quantum kicked rotor is studied with both de Broglie–Bohm and standard approach to quantum mechanics. The Schrödinger equation is solved exactly for the case of quantum resonance and an analytical expression is given for the momentum diffusion. Numerical solutions for both resonance and nonresonance are obtained. We obtain agreement between the two approaches only when the

Yindong Zheng; Donald H. Kobe

2007-01-01

325

Sedeonic Generalization of Relativistic Quantum Mechanics  

NASA Astrophysics Data System (ADS)

We represent sixteen-component values "sedeons," generating associative noncommutative space-time algebra. We demonstrate a generalization of relativistic quantum mechanics using sedeonic wave functions and sedeonic space-time operators. It is shown that the sedeonic second-order equation for the sedeonic wave function, obtained from the Einstein relation for energy and momentum, describes particles with spin 1/2. We showed that the sedeonic second-order wave equation can be reformulated in the form of the system of the first-order Maxwell-like equations for the massive fields. We proposed the sedeonic first-order equations analogous to the Dirac equation, which differ in space-time properties and describe several types of massive and massless particles. In particular we proposed four different equations, which could describe four types of neutrinos.

Mironov, Victor L.; Mironov, Sergey V.

326

Auxiliary nRules of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Standard quantum mechanics makes use of four auxiliary rules that allow the Schrödinger solutions to be related to laboratory experience - such as the Born rule that connects square modulus to probability. These rules (here called the sRules) lead to some unacceptable results. They do not allow the primary observer to be part of the system. They do not allow individual observations (as opposed to ensembles) to be part of the system. They make a fundamental distinction between microscopic and macroscopic things, and they are ambiguous in their description of secondary observers such as Schrödinger's cat. The nRules are an alternative set of auxiliary rules that avoid the above difficulties. In this paper we look at a wide range of representative experiments showing that the nRules adequately relate the Schrödinger solutions to empirical experience.

Mould, Richard A.

2006-01-01

327

Quantum mechanics without an equation of motion  

SciTech Connect

We propose a formulation of quantum mechanics for a finite level system whose potential function is not realizable and/or analytic solution of the wave equation is not feasible. The system's wavefunction is written as an infinite sum in a complete set of square integrable functions. Interaction in the theory is introduced in function space by a real finite tridiagonal symmetric matrix. The expansion coefficients of the wavefunction satisfy a three-term recursion relation incorporating the parameters of the interaction. Information about the structure and dynamics of the system is contained in the scattering matrix, which is defined in the usual way. The bound state energy spectrum (system's structure) is finite. Apart from the 2M- 1 dimensionless parameters of the interaction matrix, whose rank is M, the theory has one additional scale parameter. In the development, we utilize the kinematic tools of the J-matrix method.

Alhaidari, A. D. [Saudi Center for Theoretical Physics, Jeddah 21438 (Saudi Arabia)

2011-06-15

328

Supersymmetric quantum mechanics for string-bits  

SciTech Connect

The authors develop possible versions of supersymmetric single particle quantum mechanics, with application to superstring-bit models in view. The authors focus principally on space dimensions d = 1,2,4,8, the transverse dimensionalities of superstring in 3, 4, 7, 10 space-time dimensions. These are the cases for which classical superstring makes sense, and also the values of d for which Hooke`s force law is compatible with the simplest superparticle dynamics. The basic question they address is: when is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string-bits that do not fall off with distance will almost certainly destroy cluster decomposition. They show that the answer is affirmative for d = 1,2, negative for d = 8, and so far inconclusive for d = 4.

Thorn, C.B. [Univ. of Florida, Gainesville, FL (United States). Dept. of Physics

1997-08-01

329

Twist deformation of rotationally invariant quantum mechanics  

SciTech Connect

Noncommutative quantum mechanics in 3D is investigated in the framework of an abelian Drinfeld twist which deforms a given Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential), and the Coulomb potential.

Chakraborty, B. [S.N. Bose National Center for Basic Sciences, JD Block, Sector III, Salt-Lake, Kolkata-700098 (India); Kuznetsova, Z. [UFABC, Rua Catequese 242, Bairro Jardim, cep 09090-400, Santo Andre (Brazil); Toppan, F. [CBPF, Rua Dr. Xavier Sigaud 150, cep 22290-180, Rio de Janeiro (Brazil)

2010-11-15

330

Deformation quantization of noncommutative quantum mechanics  

NASA Astrophysics Data System (ADS)

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantization. In this paper, we investigate the basic aspects of deformation quantization for noncommutative quantum mechanics (NCQM). We first prove some general relations of the Weyl correspondence in non-commuting phase-space. Then we derive explicit form of the Wigner Function (WF) for NCQM starting from fundamental principle of the Weyl correspondence, and show that it satisfies a generalized lowast-genvalue equation. We also demonstrate that the new WFs possess orthonormality and completeness, so they can be used as a basis to expand all phase-space functions. Some example is discussed to support our results.

Jing, Sicong; Zuo, Fen; Heng, Taihua

2004-10-01

331

New methods for quantum mechanical reaction dynamics  

SciTech Connect

Quantum mechanical methods are developed to describe the dynamics of bimolecular chemical reactions. We focus on developing approaches for directly calculating the desired quantity of interest. Methods for the calculation of single matrix elements of the scattering matrix (S-matrix) and initial state-selected reaction probabilities are presented. This is accomplished by the use of absorbing boundary conditions (ABC) to obtain a localized (L{sup 2}) representation of the outgoing wave scattering Green`s function. This approach enables the efficient calculation of only a single column of the S-matrix with a proportionate savings in effort over the calculation of the entire S-matrix. Applying this method to the calculation of the initial (or final) state-selected reaction probability, a more averaged quantity, requires even less effort than the state-to-state S-matrix elements. It is shown how the same representation of the Green`s function can be effectively applied to the calculation of negative ion photodetachment intensities. Photodetachment spectroscopy of the anion ABC{sup -} can be a very useful method for obtaining detailed information about the neutral ABC potential energy surface, particularly if the ABC{sup -} geometry is similar to the transition state of the neutral ABC. Total and arrangement-selected photodetachment spectra are calculated for the H{sub 3}O{sup -} system, providing information about the potential energy surface for the OH + H{sub 2} reaction when compared with experimental results. Finally, we present methods for the direct calculation of the thermal rate constant from the flux-position and flux-flux correlation functions. The spirit of transition state theory is invoked by concentrating on the short time dynamics in the area around the transition state that determine reactivity. These methods are made efficient by evaluating the required quantum mechanical trace in the basis of eigenstates of the Boltzmannized flux operator.

Thompson, W.H. [Univ. of California, Berkeley, CA (United States). Dept. of Chemistry]|[Lawrence Berkeley Lab., CA (United States)

1996-12-01

332

Two-dimensional quantum mechanical modeling of nanotransistors  

Microsoft Academic Search

Quantization in the inversion layer and phase coherent transport are anticipated to have significant impact on device performance in ``ballistic'' nanoscale transistors. While the role of some quantum effects have been analyzed qualitatively using simple one-dimensional ballistic models, two-dimensional (2D) quantum mechanical simulation is important for quantitative results. In this paper, we present a framework for 2D quantum mechanical simulation

A. Svizhenko; M. P. Anantram; T. R. Govindan; B. Biegel; R. Venugopal

2002-01-01

333

Property Definiteness in Quantum Mechanics: Modal Interpretations.  

NASA Astrophysics Data System (ADS)

Recently, several writers have independently proposed similar solutions to the quantum-mechanical measurement problem. This dissertation examines the conception of physical properties implicit in these proposals, which are known as modal interpretations of quantum mechanics. The dissertation focuses on Richard Healey's interpretation, which I regard as the most promising of the proposals. Chapter One reviews the measurement problem and the way in which modal interpretations address the problem. Chapter Two discusses certain mathematical theorems that impose strict limits on the number of properties that a system can possess at any instant. I examine a number of inferences that interpreters have drawn from these theorems, and argue that some of these inferences are misguided. This discussion leads to the recognition that, despite overarching similarities between Healey's interpretations and several of the other modal interpretations, the interpretations differ in fundamental respects. Chapter Three presents several desiderata on the set of properties possessed by a quantum system at an instant. One of these desiderata concerns the relation between a system's properties and the properties of that system's subsystems. To borrow Frank Arntzenius's illustration, the desideratum demands, for instance, that the left-hand leaf of a table be green if and only if the table has a green left-hand leaf. Unfortunately, most modal interpretations fail to satisfy this demand. Using mathematical arguments, I show that Healey's interpretation satisfies the demand. Chapter Four turns to a problematic feature of Healey's interpretation, namely its violation of a desideratum called Property Intersection. Property Intersection demands that if a variable's value is restricted to a set Delta and is also restricted to a set Gamma, then the value is restricted to the intersection of Delta and Gamma. I propose two strategies for amending Healey's interpretation so that it respects Property Intersection, but I find both of these strategies unsatisfactory, since each creates new problems. I then consider several possible reasons for imposing Property Intersection as a requirement, and I argue that none of these reasons is compelling; thus, I claim, Healey's violation of Property Intersection is defensible.

Reeder, Nicholas Lee

334

Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems  

ERIC Educational Resources Information Center

|In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…

Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih

2009-01-01

335

In Defense of a Heuristic Interpretation of Quantum Mechanics  

ERIC Educational Resources Information Center

Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…

Healy, Eamonn F.

2010-01-01

336

On the End of a Quantum Mechanical Romance  

Microsoft Academic Search

Comparatively recent advances in quantum measurement theory suggest that the decades-old flirtation between quantum mechanics and the philosophy of mind is about to end. Various approaches to what I have elsewhere dubbed 'interactive decoherence' promise to remove the conscious observer from the phenomenon of state vector reduction. The mechanisms whereby decoherence occurs suggest, on the one hand, that consciousness per

Gregory R. Mulhauser

1995-01-01

337

Quantum mechanics needs no consciousness (and the other way around)  

Microsoft Academic Search

It has been suggested that consciousness plays an important role in quantum mechanics as it is necessary for the collapse of wave function during the measurement. Furthermore, this idea has spawned a symmetrical proposal: a possibility that quantum mechanics explains the emergence of consciousness in the brain. Here we formulated several predictions that follow from this hypothetical relationship and that

Shan Yu; Danko Nikolic

2010-01-01

338

Quantum Mechanics and Consciousness: A Causal Correspondence Theory  

Microsoft Academic Search

We may suspect that quantum mechanics and consciousness are re- lated, but the details are not at all clear. In this paper, I suggest how the mind and brain might fit together intimately while still maintaining dis- tinct identities. The connection is based on the correspondence of similar functions in both the mind and the quantum-mechanical brain.

I. J. Thompson

339

On a generalization of quantum mechanics of biquaternions  

SciTech Connect

A generalization of the quantum mechanical formalism by biquaternions is proposed. By a direct example, it is evidenced that such a generalization explains in an algebraic manner the {open_quotes}wave packet reduction{close_quotes} of quantum mechanics. 8 refs.

Conte, E. [Inst. of Cybernetics, San Marino (Italy)

1993-06-01

340

Using a Computer-Rich Curriculum to Teach Quantum Mechanics  

NSDL National Science Digital Library

This site is the notes for a seminar on the use of java applets in quantum mechanics pedagogy. Applets are included that cover basic quantum mechanics, hydrogenic and two-particle systems, and some simulation techniques. Time dependent results are stressed.

Belloni, Mario; Carroll, Meghan

2004-03-10

341

New Potentials for Old: The Darboux Transformation in Quantum Mechanics  

ERIC Educational Resources Information Center

|The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics

Williams, Brian Wesley; Celius, Tevye C.

2008-01-01

342

Categorization of Quantum Mechanics Problems by Professors and Students  

ERIC Educational Resources Information Center

|We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…

Lin, Shih-Yin; Singh, Chandralekha

2010-01-01

343

Design and Validation of the Quantum Mechanics Conceptual Survey  

ERIC Educational Resources Information Center

|The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included…

McKagan, S. B.; Perkins, K. K.; Wieman, C. E.

2010-01-01

344

Developing and Evaluating Animations for Teaching Quantum Mechanics Concepts  

ERIC Educational Resources Information Center

|In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantum mechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantum mechanics concepts. They focus on known areas of student difficulty and misconceptions by…

Kohnle, Antje; Douglass, Margaret; Edwards, Tom J.; Gillies, Alastair D.; Hooley, Christopher A.; Sinclair, Bruce D.

2010-01-01

345

In Defense of a Heuristic Interpretation of Quantum Mechanics  

ERIC Educational Resources Information Center

|Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…

Healy, Eamonn F.

2010-01-01

346

Phase Space Correspondence between Classical Optics and Quantum Mechanics  

Microsoft Academic Search

The paper scrutinizes both the similarities and the differences between the classical optics and quantum mechanical theories in phase space, especially between the Wigner distribution functions defined in the respective phase spaces. Classical optics is able to provide an understanding of either the corpuscular or wave aspects of quantum mechanics, reflected in phase space through the classical limit of the

Daniela Dragoman

2004-01-01

347

Predicting crystal structure by merging data mining with quantum mechanics  

Microsoft Academic Search

Modern methods of quantum mechanics have proved to be effective tools to understand and even predict materials properties. An essential element of the materials design process, relevant to both new materials and the optimization of existing ones, is knowing which crystal structures will form in an alloy system. Crystal structure can only be predicted effectively with quantum mechanics if an

Christopher C. Fischer; Kevin J. Tibbetts; Dane Morgan; Gerbrand Ceder

2006-01-01

348

On the representation of quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

It is shown that Hilbert-space quantum mechanics can be represented on phase space in the sense that the density operators can be identified with phase-space densities and the observables can be described by functions on phase space. In particular, we consider phase-space representations of quantum mechanics which are related to certain joint position-momentum observables.

Stulpe, Werner

1992-09-01

349

Quantum Mechanics from Periodic Dynamics: the bosonic case  

SciTech Connect

Enforcing the periodicity hypothesis of the 'old' formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a deterministic field theory. A novel interpretation of the AdS/CFT conjecture is discussed.

Dolce, Donatello [Johannes-Gutenberg Universitaet, D-55099 Mainz (Germany)

2010-05-04

350

Linear Logic for Generalized Quantum Mechanics  

Microsoft Academic Search

Quantum logic is static, describing automata having uncertain states but no state transitions and no Heisenberg uncertainty tradeo. We cast Girard's linear logic in the role of a dynamic quantum logic, regarded as an extension of quantum logic with time nonstandardly interpreted over a domain of linear automata and their dual linear schedules. In this extension the uncertainty tradeo emerges

Vaughan Pratt

1993-01-01

351

Amplitude Phase-Space Model for Quantum Mechanics  

NASA Astrophysics Data System (ADS)

We show that there is a close relationship between quantum mechanics and ordinary probability theory. The main difference is that in quantum mechanics the probability is computed in terms of an amplitude function, while in probability theory a probability distribution is used. Applying this idea, we then construct an amplitude model for quantum mechanics on phase space. In this model, states are represented by amplitude functions and observables are represented by functions on phase space. If we now postulate a conjugation condition, the model provides the same predictions as conventional quantum mechanics. In particular, we obtain the usual quantum marginal probabilities, conditional probabilities and expectations. The commutation relations and uncertainty principle also follow. Moreover Schrödinger's equation is shown to be an averaged version of Hamilton's equation in classical mechanics.

Gudder, Stanley P.

1985-04-01

352

Quantum Mechanics as Quantum Information (and only a little more)  

Microsoft Academic Search

In this paper, I try once again to cause some good-natured trouble. The issue\\u000aremains, when will we ever stop burdening the taxpayer with conferences devoted\\u000ato the quantum foundations? The suspicion is expressed that no end will be in\\u000asight until a means is found to reduce quantum theory to two or three\\u000astatements of crisp physical (rather than

Christopher A. Fuchs

2002-01-01

353

Calendar effects in quantum mechanics in view of interactive holography  

NASA Astrophysics Data System (ADS)

Quantum mechanics in terms of interactive holography appears as `normal' science [1]. With the holography quantum behavior is determined by the interplay of material formations and their conjugate images. To begin with, this effortlessly elucidates the nonlocality in quantum entanglements. Then, it has been shown that Schr"odinger's dynamics for a single particle arises from Bi-Fragmental random walks of the particle itself and its holographic image. For many particles this picture blurs with fragments merging as bosons or fermions. In biomolecules, swapping of particles and their holographic placeholders leads to self-replication of the living matter. Because of broad interpretations of quantum formalism direct experiments attributing it to holography may not be very compelling. The holographic mechanism better reveals as an absolute frame of reference. A number of physical and biological events exhibit annual variations when Earth orbital position changes with respect to the universal holographic mechanism. The well established calendar variations of heart attacks can be regarded as a positive outcome of a generalization of the Michelson experiment, where holography is interferometry and ailing hearts are detectors of pathologically replicated proteins. Also, there have been already observed calendar changes in radioactive decay rates. The same could be expected for various fine quantum experiences, like, e.g., Josephson tunneling. In other words, Quantum Mechanics (February) Quantum Mechanics (August). [1] S. Berkovich, ``A comprehensive explanation of quantum mechanics,'' www.cs.gwu.edu/research/technical-report/170 .

Berkovich, Simon

2013-04-01

354

The Discovery of Quantum Structure and Quantum Mechanic Reinterpretation  

NASA Astrophysics Data System (ADS)

My recent interdisciplinary researches lead me to re-visit the quantum wave-particle duality property. By comparing many of the quantum physics results in scientific literatures I concluded the structure of quantum particle and formulated a new explanation of the wave effect. This discovery is further confirmed by many of the results in other fields. Evident also suggested inside quantum has a not-continuous multi-dimensional space. With this light I formed a hypostasis of space as a not-continuous infinite dimensional space. To proof or disproof this hypostasis I found strong evidences in literature supporting my hypostasis. By evaluating space properties it lead me to the same conclusion of Special Relativity and Uncertainty Principle. Evidence also support quantum is part of space itself and space carries electrical charges on both sides of its dimensional boundaries therefore we can detect the electromagnetic energy in vacuum. These discoveries also give good answers to many of the big questions in science such as gravity, dark energy and space travel.

Zhang, Meggie

2012-10-01

355

Quantum mechanics and the principle of equivalence  

NASA Astrophysics Data System (ADS)

Einstein's principle of equivalence is based on the notion of classical trajectories in spacetime, and the question arises of how this principle applies to quantum particles, especially those in delocalized, highly-non-classical states. I shall describe a quantum version of Galileo's classic experiment, using a model quantum clock to measure the time of flight of a quantum particle in a background gravitational field. Because the particle's mass does not scale out of Schrodinger's equation, unlike in the Newtonian case, conformity with the principle of equivalence is far from obvious and involves some interesting subtleties. It also suggests some new experiments.

Davies, Paul

2007-10-01

356

Testing Quantum Mechanics in High-Energy Physics  

Microsoft Academic Search

In this set of lectures we show that particle physics can also contribute to fundamental questions about quantum mechanics\\u000a (QM) and even shine new light in the fine workings of quantum physics and this at scales of energies which are not available\\u000a for usual quantum systems. In particular the massive meson–antimeson systems are specially suitable as they offer a unique

Beatrix C. Hiesmayr

357

Can you do quantum mechanics without Einstein?  

SciTech Connect

The present form of quantum mechanics is based on the Copenhagen school of interpretation. Einstein did not belong to the Copenhagen school, because he did not believe in probabilistic interpretation of fundamental physical laws. This is the reason why we are still debating whether there is a more deterministic theory. One cause of this separation between Einstein and the Copenhagen school could have been that the Copenhagen physicists thoroughly ignored Einstein's main concern: the principle of relativity. Paul A. M. Dirac was the first one to realize this problem. Indeed, from 1927 to 1963, Paul A. M. Dirac published at least four papers to study the problem of making the uncertainty relation consistent with Einstein's Lorentz covariance. It is interesting to combine those papers by Dirac to make the uncertainty relation consistent with relativity. It is shown that the mathematics of two coupled oscillators enables us to carry out this job. We are then led to the question of whether the concept of localized probability distribution is consistent with Lorentz covariance.

Kim, Y. S. [Department of Physics, University of Maryland, College Park, Maryland 20742 (United States); Noz, Marilyn E. [Department of Radiology, New York University, New York, New York 10016 (United States)

2007-02-21

358

Quantum mechanical studies on model ?-pleated sheets  

PubMed Central

Pauling and Corey proposed a pleated-sheet configuration, now called ?-sheet, as one of the protein secondary structures in addition to ?-helix and ?-sheet. Recently, it has been suggested that ?-sheet is a common feature of amyloidogenic intermediates. We have investigated the stability of anti-parallel ?-sheet and two conformations of ?-sheet in solution phase using the density functional theoretical method. The peptides are modeled as two-strand Acetyl-(Ala)2-N-methylamine. Using stages of geometry optimization and single point energy calculation at B3LYP/cc-pVTZ//B3LYP/6-31G* level and including zero-point energies, thermal, and entropic contribution, we have found that ?-sheet is the most stable conformation, while the ?-sheet proposed by Pauling and Corey has 13.6 kcal/mol higher free energy than the ?-sheet. The ?-sheet that resembles the structure observed in molecular dynamics simulations of amyloidogenic proteins at low pH becomes distorted after stages of geometry optimization in solution. Whether the ?-sheets with longer chains would be increasingly favorable in water relative to the increase in internal energy of the chain needs further investigation. Different from the quantum mechanics results, AMBER parm94 force field gives small difference in solution phase energy between ?-sheet and ?-sheet. The predicted amide I IR spectra of ?-sheet shows the main band at higher frequency than ?-sheet.

Wu, Hao; Canfield, Alana; Adhikari, Jhashanath; Huo, Shuanghong

2009-01-01

359

Quantum mechanical model for Maya Blue  

NASA Astrophysics Data System (ADS)

This work is about Maya Blue (MB), a pigment developed by Mesoamerican civilizations between the 5th and 16th centuries from an aluminosilicate mineral (palygorskite) and an organic dye (indigo). Two different supramolecular quantum-mechanical models afford explanations for the unusual stability of MB based on the oxidation of the indigo molecule during the heating process and its interaction with palygorskite. A model considering indigo derivatives attached to several aluminates shows the principal features of the experimental visible spectrum of MB within the TD-DFT methodology. Another model of an indigo oxidized species confined within an inorganic supramolecular cavity system, that involves about 170 atoms, was calculated after a large configuration interaction of single excited determinants within the NDOL approximation (Montero-Cabrera et al., J Chem Phys, 2007, 127, 145102). It allows a correct reproduction and interpretation of the corresponding spectrum. This second methodology provides the most satisfactory results, being able to manage very big molecular systems at a QM level. Structural explanation for the unusual stability of MB is also provided.

Fuentes, María E.; Peña, Brisa; Contreras, César; Montero, Ana L.; Chianelli, Russell; Alvarado, Manuel; Olivas, Ramón; Rodríguez, Luz M.; Camacho, Héctor; Montero-Cabrera, Luis A.

360

Supersymmetric quantum mechanics for string bits  

SciTech Connect

We develop possible versions of supersymmetric single-particle quantum mechanics, with application to superstring-bit models in view. We focus principally on space dimensions d=1,2,4,8, the transverse dimensionalities of superstring in 3, 4, 6, and 10 space-time dimensions. These are the cases for which {open_quotes}classical{close_quotes} superstring makes sense, and also the values of d for which Hooke{close_quote}s force law is compatible with the simplest superparticle dynamics. The basic question we address is the following: When is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string bits that do not fall off with distance will almost certainly destroy cluster decomposition. We show that the answer is affirmative for d=1,2, negative for d=8, and so far inconclusive for d=4. {copyright} {ital 1997} {ital The American Physical Society}

Thorn, C.B. [Institute for Fundamental Theory, Department of Physics, University of Florida, Gainesville, Florida 32611 (United States)

1997-11-01

361

Implications of quantum theory in the foundations of statistical mechanics  

Microsoft Academic Search

An investigation is made into how the foundations of statistical mechanics are aected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical dierences are identified between classical and

David Wallace

362

"Mysticism" in Quantum Mechanics: The Forgotten Controversy  

ERIC Educational Resources Information Center

This paper argues that a European controversy over a "mystical" hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s--birth of quantum theory--and concluding…

Marin, Juan Miguel

2009-01-01

363

"Mysticism" in Quantum Mechanics: The Forgotten Controversy  

ERIC Educational Resources Information Center

|This paper argues that a European controversy over a "mystical" hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s--birth of quantum theory--and concluding…

Marin, Juan Miguel

2009-01-01

364

Quantum optical test of observation and complementarity in quantum mechanics  

Microsoft Academic Search

Experiments to probe the way in which the measurement process (the presence of a detector) influences the investigated system are proposed and analyzed. These experiments are based on the fact that number states of the radiation field can be generated by the use of a micromaser and cavity quantum electrodynamics. It is shown that which-path (particle) information rules out interference

Marlan O. Scully; Herbert Walther

1989-01-01

365

On the existence of complex spacetime in relativistic quantum mechanics  

Microsoft Academic Search

The infinite dimensional E(?) space, when viewed at large scales, mimics the appearance of a 4-dimensional complex spacetime. The aim of this paper is to prove the existence of such a complex spacetime in our physical world and to show that what the current relativistic quantum mechanics describes is just the quantum phenomena appeared in this 4-dimensional complex spacetime. We

Ciann-Dong Yang

2008-01-01

366

Decoherence, the measurement problem, and interpretations of quantum mechanics  

Microsoft Academic Search

Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their

Maximilian Schlosshauer

2004-01-01

367

Excitation transfer through open quantum networks: a few basic mechanisms  

Microsoft Academic Search

A variety of open quantum networks are currently under intense examination to model energy transport in photosynthetic systems. Here we study the coherent transfer of a quantum excitation over a network incoherently coupled with a structured and small environment that effectively models the photosynthetic reaction center. Our goal is to distill a few basic, possibly universal, mechanisms or \\

Lorenzo Campos Venuti; Paolo Zanardi

2011-01-01

368

Quantum Mechanical Models of Turing Machines That Dissipate No Energy  

Microsoft Academic Search

Quantum mechanical Hamiltonian models of Turing machines are constructed here on a finite lattice of spin- 1\\/2 systems. The models do not dissipate any energy and they operate at the quantum limit in that the system (energy uncertainty)\\/(computation speed) is close to the limit given by the time-energy uncertainty principle.

Paul Benioff

1982-01-01

369

Generalized Lippmann-Schwinger equation in the fractional quantum mechanics  

NASA Astrophysics Data System (ADS)

From the three-dimensional space fractional Schrödinger equation, a generalized Lippmann-Schwinger equation for the fractional quantum mechanics is obtained for both scattering and bound states. We apply the generalized integral equation to study the fractional quantum scattering problem and give the approximate scattering wavefunction of first order and higher orders.

Dong, Jianping

2011-05-01

370

CXXXVI. On the quantum mechanics of helium II  

Microsoft Academic Search

The quantum mechanics of a system of identical interacting particles must lead to the classical hydrodynamic equations of motion at high temperatures, because of the correspondence principle. On the other hand, the behaviour of helium II shows that this is not always the case at low temperatures. In this paperit is shown that' in certain cases the quantum description requires

O. Penrose

1951-01-01

371

OSP Quantum Mechanics: Single Measurments of Spin States Worksheet  

NSDL National Science Digital Library

This set of tutorial worksheets, based on the OSP Quantum Mechanics Simulations, help students explore the measurement of quantum spins. The tutorial starts with an introduction of the physics of spins, and then presents the results of a single measurement on pure, mixed, and superposition states.

Christian, Wolfgang; Belloni, Mario

2010-01-11

372

Solvent effect on the absorption spectra of coumarin 120 in water: A combined quantum mechanical and molecular mechanical study  

NASA Astrophysics Data System (ADS)

The solvent effect on the absorption spectra of coumarin 120 (C120) in water was studied utilizing the combined quantum mechanical/molecular mechanical (QM/MM) method. In molecular dynamics (MD) simulation, a new sampling scheme was introduced to provide enough samples for both solute and solvent molecules to obtain the average physical properties of the molecules in solution. We sampled the structure of the solute and solvent molecules separately. First, we executed a QM/MM MD simulation, where we sampled the solute molecule in solution. Next, we chose random solute structures from this simulation and performed classical MD simulation for each chosen solute structure with its geometry fixed. This new scheme allowed us to sample the solute molecule quantum mechanically and sample many solvent structures classically. Excitation energy calculations using the selected samples were carried out by the generalized multiconfigurational perturbation theory. We succeeded in constructing the absorption spectra and realizing the red shift of the absorption spectra found in polar solvents. To understand the motion of C120 in water, we carried out principal component analysis and found that the motion of the methyl group made the largest contribution and the motion of the amino group the second largest. The solvent effect on the absorption spectrum was studied by decomposing it in two components: the effect from the distortion of the solute molecule and the field effect from the solvent molecules. The solvent effect from the solvent molecules shows large contribution to the solvent shift of the peak of the absorption spectrum, while the solvent effect from the solute molecule shows no contribution. The solvent effect from the solute molecule mainly contributes to the broadening of the absorption spectrum. In the solvent effect, the variation in C-C bond length has the largest contribution on the absorption spectrum from the solute molecule. For the solvent effect on the absorption spectrum from the solvent molecules, the solvent structure around the amino group of C120 plays the key role.

Sakata, Tetsuya; Kawashima, Yukio; Nakano, Haruyuki

2011-01-01

373

Why space has three dimensions: A quantum mechanical explanation  

NASA Astrophysics Data System (ADS)

The theoretical physics of a quantum mechanical model of space, relativistic quantum holography, is described. It specifies three dimensions, such as is validated by the nature of our spatial experience, but where additionally, quantum non-locality, which Feynman described as the only mystery of quantum theory, is made manifest by means of observable phase relationships. For example, synchronicity between events, and other phenomena such as are described by the geometric/Berry phase, etc., which are outside the bounds of classical explanation. It can therefore be hypothesized: a) that we live in a entirely quantum mechanical world/universe and not a classical mechanical one (where quantum phenomena are confined to the microscopic scale) as is the current generally held scientific view, b) that three spatial dimensions are a fundamental consequence of quantum mechanics, c) that quantum holography is a natural candidate to explain quantum gravity, such that mass/inertia concerns not the eigenvalues of some operator, but rather the observable gauge invariant phases of a state vector, postulated to be that of the universe itself, as a whole, and d) that this model provides a natural explanation in terms of relativistic quantum signal processing of any each individual's perception and cognition will be of a three dimensional world, defined similarly in relation to each individual's quantum state vector, describing its mind/body and associated gauge invariant phases or mindset, which have observable consequences, such that mental processes and events can cause neural events and processes! These testable hypotheses, if validated, will have profound implications for our understanding, radically changing our scientific perspective on the world, as we enter the new millennium. .

Marcer, Peter; Schempp, Walter

2000-05-01

374

Testing Quantum Mechanics in High-Energy Physics  

NASA Astrophysics Data System (ADS)

In this set of lectures we show that particle physics can also contribute to fundamental questions about quantum mechanics (QM) and even shine new light in the fine workings of quantum physics and this at scales of energies which are not available for usual quantum systems. In particular the massive meson-antimeson systems are specially suitable as they offer a unique laboratory to test various aspects of particle physics (CP violation, CPT violation, etc.) as well as to test the foundations of QM (local realistic theories versus QM, Bell inequalities, decoherence effects, quantum marking and erasure concepts, Bohr's complementary relation, etc.).

Hiesmayr, Beatrix C.

375

Anomalous capacitance-voltage profiles in quantum wells explained by a quantum mechanical model  

Microsoft Academic Search

We have developed a quantum mechanical model for understanding and explaining the capacitance–voltage (C–V) carrier profiles observed in quantum wells (QW). The external field imposed on the QW during C–V profiling changes the carrier distribution of the system. This model considers the effects of field and quantum confinement of the carriers in the well. The results obtained by iterative solutions

Sudakshina Kundu; Dipankar Biswas; Reshmi Datta

1997-01-01

376

Superluminality and the equivalence postulate of quantum mechanics  

NASA Astrophysics Data System (ADS)

An interpretation of the recent results reported by the OPERA collaboration is that neutrinos propagation in vacuum exceeds the speed of light. It has been further been suggested that this interpretation can be attributed to the variation of the particle average speed arising from the Relativistic Quantum Hamilton-Jacobi Equation. I derive an expression for the quantum correction to the instantaneous relativistic velocity in the framework of the relativistic quantum Hamilton-Jacobi equation, which is derived from the equivalence postulate of quantum mechanics. While the quantum correction does indicate deviations from the classical energy-momentum relation, it does not necessarily lead to superluminal speeds. The quantum correction found herein has a non-trivial dependence on the energy and mass of the particle, as well as on distance travelled. I speculate on other possible observational consequences of the equivalence postulate approach.

Faraggi, Alon E.

2012-03-01

377

Adaptive Perturbation Theory: Quantum Mechanics and Field Theory.  

National Technical Information Service (NTIS)

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation theory is that it...

M. Weinstein

2005-01-01

378

Particles, Waves, and the Interpretation of Quantum Mechanics  

ERIC Educational Resources Information Center

Presents an explanation, without mathematical equations, of the basic principles of quantum mechanics. Includes wave-particle duality, the probability character of the wavefunction, and the uncertainty relations. (MLH)

Christoudouleas, N. D.

1975-01-01

379

On the Origin of Probability in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

I give a brief introduction to many worlds or "no wave function collapse" quantum mechanics, suitable for non-specialists. I then discuss the origin of probability in such formulations, distinguishing between objective and subjective notions of probability.

Hsu, Stephen D. H.

380

Why are probabilistic laws governing quantum mechanics and neurobiology?  

NASA Astrophysics Data System (ADS)

We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.

Kröger, Helmut

2005-08-01

381

Quantum dressed classical mechanics: application to non-adiabatic processes  

Microsoft Academic Search

A newly formulated theory for time-dependent molecular quantum mechanics is used to study processes involving more than one potential energy surface. Good agreement with exact numbers is obtained using one trajectory and just two grid points.

Gert D. Billing

2001-01-01

382

Natural cutoffs and Hilbert space representation of quantum mechanics  

NASA Astrophysics Data System (ADS)

We construct a Hilbert space representation of quantum mechanics in the presence of all natural cutoffs encoded in a generalized uncertainty principle (GUP) that admits a minimal measurable length, a minimal measurable momentum and a maximal momentum.

Nozari, Kourosh; Soleymani, Z.

2013-02-01

383

Quantum mechanics helps in learning for more intelligent robot  

Microsoft Academic Search

A learning algorithm based on state superposition principle is presented. The physical implementation analysis and simulated experiment results show that quantum mechanics can give helps in learning for more intelligent robot.

Dao-Yi Dong; Chun-Lin Chen; Zong-Hai Chen; Chen-Bin Zhang

384

Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics  

NASA Astrophysics Data System (ADS)

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10-7 calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.

Goldfarb, Yair; Degani, Ilan; Tannor, David J.

2006-12-01

385

Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics.  

PubMed

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity. PMID:17190540

Goldfarb, Yair; Degani, Ilan; Tannor, David J

2006-12-21

386

Quantum Mechanics in Biology: Photoexcitations in DNA  

NASA Astrophysics Data System (ADS)

We consider here the theoretical and quantum chemical description of the photoexcitated states in DNA duplexes. We discuss the motivation and limitations of an exciton model and use this as the starting point for more detailed excited state quantum chemical evaluations. In particular, we focus upon the role of interbase proton transfer between Watson/Crick pairs in localizing an excitation and then quenching it through intersystem crossing and charge transfer.

Bittner, Eric R.; Czader, Arkadiusz

387

Probability in the Many-Worlds Interpretation of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

It is argued that, although in the Many-Worlds Interpretation of quantum mechanics there is no "probability" for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence between an illegitimate question: "What is the probability of an outcome of a quantum measurement?" with a legitimate question: "What is the probability that `I' am in the world corresponding to that outcome?"; (b) A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and (c) Relativistic causality, which together with (b) explain the Born rule of standard quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing probability measure are discussed.

Vaidman, Lev

388

Quantum mechanical version of the classical Liouville theorem  

NASA Astrophysics Data System (ADS)

In terms of the coherent state evolution in phase space, we present a quantum mechanical version of the classical Liouville theorem. The evolution of the coherent state from |z> to |sz - rz*> corresponds to the motion from a point z (q,p) to another point sz - rz* with |s|2 - |r|2 = 1. The evolution is governed by the so-called Fresnel operator U(s,r) that was recently proposed in quantum optics theory, which classically corresponds to the matrix optics law and the optical Fresnel transformation, and obeys group product rules. In other words, we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space, which seems to be a combination of quantum statistics and quantum optics.

Xie, Chuan-Mei; Fan, Hong-Yi

2013-03-01

389

The instrumentalist aspects of quantum mechanics stem from probability theory  

NASA Astrophysics Data System (ADS)

The aim of the article is to argue that the interpretations of quantum mechanics and of probability are much closer than usually thought. Indeed, a detailed analysis of the concept of probability (within the standard frequency interpretation of R. von Mises) reveals that this notion always refers to an observing system. Therefore the instrumentalist aspects of quantum mechanics, and in particular the enigmatic role of the observer in the Copenhagen interpretation, derive from a precise understanding of probability.

Vervoort, Louis

2012-03-01

390

A primer on quantum mechanics and its interpretations  

Microsoft Academic Search

All the concepts and principles necessary to understand quantum mechanics on an initial level are given in a form suitable for the non-expert. The concepts explained include visualizing the wave function, wave-particle duality, the implications of Schrodinger's cat, probability, the uncertainty principle, collapse of the wave function, and others. However, because of the peculiar, non-intuitive nature of quantum mechanics, one

Casey Blood

2010-01-01

391

Interpreting Quantum Mechanics according to a Pragmatist Approach  

NASA Astrophysics Data System (ADS)

The aim of this paper is to show that quantum mechanics can be interpreted according to a pragmatist approach. The latter consists, first, in giving a pragmatic definition to each term used in microphysics, second, in making explicit the functions any theory must fulfil so as to ensure the success of the research activity in microphysics, and third, in showing that quantum mechanics is the only theory which fulfils exactly these functions.

Bächtold, Manuel

2008-09-01

392

Scalable quantum mechanical simulation of large polymer systems  

SciTech Connect

We describe a program for quantum mechanical calculations of very large hydrocarbon polymer systems. It is based on a new algorithmic approach to the quantum mechanical tight binding equations that naturally leads to a very efficient parallel implementation and that scales linearly with respect to the number of atoms. We get both very high single node performance as well as a significant parallel speedup on the SGI Origin 2000 parallel computer.

Goedecker, S. [Max-Planck Institute for Solid State Research, Stuttgart (Germany); Hoisie, A.; Kress, J.; Lubeck, O.; Wasserman, H. [Los Alamos National Lab., NM (United States)

1997-08-01

393

Quantum mechanics and the social sciences: After hermeneutics  

NASA Astrophysics Data System (ADS)

Quantum mechanics is interpreted, in the spirit of Niels Bohr and Werner Heisenberg, as about physical objects in so far as these are revealed by and within the local, social, and historical process of measurement. An analysis of the hermeneutical aspect of quantum mechanical measurement reveals close analogues with the hermeneutical social/historical sciences. The hermeneutical analysis of science requires the move from the epistemological attitude to an ontological one.

Heelan, Patrick A.

1995-04-01

394

Exactly solvable quantum mechanical models with Stückelberg divergences  

Microsoft Academic Search

We consider an exactly solvable quantum mechanical model with an infinite number of degrees of freedom that is an analogue\\u000a of the model of N scalar fields (?\\/N)(?a\\u000a a)2 in the leading order in 1\\/N. The model involves vacuum and S-matrix divergences and also the Stckelberg divergences, which\\u000a are absent in other known renormalizable quantum mechanical models with, divergences (such

O. Yu. Shvedov; Shvedov I

2000-01-01

395

Acoustic Analog to Quantum Mechanical Level-Splitting  

NASA Astrophysics Data System (ADS)

One difficulty in teaching quantum mechanics is the lack of classroom demonstrations. To sidestep this issue, analogies can provide an enlightening alternative. Acoustics governance by the same time-independent wave equation as quantum mechanics supports it use in such analogies. This presentation examines one such analogy for an infinite potential well with a delta potential perturbation. The physical acoustic system consists of continuous sounds waves traveling in a pair of tubes which are separated by a variable diaphragm. The level-splitting nature of the quantum system can be mimicked in the acoustic system.

Hilbert, Shawn

2010-03-01

396

Aspects of relativistic quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

Recent work on formulating relativistic quantum mechanics on stochastic phase spaces is described. Starting with a brief introduction to the mathematical theory of stochastic spaces, an account is given of non-relativistic quantum mechanics on stochastic phase space. The relativistic theory is introduced by constructing certain classes of representations of the Poincaré group on phase space, obtaining thereby both the classical and the quantum dynamics. Applications to the Dirac equation are discussed, and an alternative 2-component equation for a charged spin-1/2 particle, interacting with an external electromagnetic field is studied.

Twareque Ali, S.

397

Foundations of quantum mechanics: The Langevin equations for QM  

NASA Astrophysics Data System (ADS)

Stochastic derivations of the Schrödinger equation are always developed on very general and abstract grounds. Thus, one is never enlightened which specific stochastic process corresponds to some particular quantum mechanical system, that is, given the physical system—expressed by the potential function, which fluctuation structure one should impose on a Langevin equation in order to arrive at results identical to those comming from the solutions of the Schrödinger equation. We show, from first principles, how to write the Langevin stochastic equations for any particular quantum system. We also show the relation between these Langevin equations and those proposed by Bohm in 1952. We present numerical simulations of the Langevin equations for some quantum mechanical problems and compare them with the usual analytic solutions to show the adequacy of our approach. The model also allows us to address important topics on the interpretation of quantum mechanics.

Olavo, L. S. F.; Lapas, L. C.; Figueiredo, A.

2012-05-01

398

Statistical Structures Underlying Quantum Mechanics and Social Science  

NASA Astrophysics Data System (ADS)

Common observations of the unpredictability of human behavior and the influence of one question on the answer to another suggest social science experiments are probabilistic and may be mutually incompatible with one another, characteristics attributed to quantum mechanics (as distinguished from classical mechanics). This paper examines this superficial similarity in depth using the Foulis-Randall Operational Statistics language. In contradistinction to physics, social science deals with complex, open systems for which the set of possible experiments is unknowable and outcome interference is a graded phenomenon resulting from the ways the human brain processes information. It is concluded that social science is, in some ways, “less classical” than quantum mechanics, but that generalized “quantum” structures may provide appropriate descriptions of social science experiments. Specific challenges to extending “quantum” structures to social science are identified.

Wright, Ron

2007-08-01

399

Quantum mechanical states as attractors for Nelson processes  

NASA Astrophysics Data System (ADS)

In this paper we reconsider, in the light of the Nelson stochastic mechanics, the idea originally proposed by Bohm and Vigier that arbitrary solutions of the evolution equation for the probability densities always relax in time toward the quantum mechanical density ¦?¦2 derived from the Schrödinger equation. The analysis of a few general propositions and of some physical examples show that the choice of the L1 metrics and of the Nelson stochastic flux is correct for a particular class of quantum states, but cannot be adopted in general. This indicates that the question if the quantum mechanical densities attract other solution of the classical Fokker-Planck equations associated to the Schrödinger equation is physically meaningful, even if a classical probabilistic model good for every quantum stale is still not available. A few suggestion in this direction are finally discussed.

Petroni, Nicola Cufaro; Guerra, Francesco

1995-02-01

400

Multiple-event probability in general-relativistic quantum mechanics  

SciTech Connect

We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.

Hellmann, Frank [Fakultaet fuer Physik, Ludwig-Maximilians-Universitaet, D-80799 Munich (Germany); Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille (France); Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo [Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille (France)

2007-04-15

401

Electron exchange-correlation in quantum mechanics  

SciTech Connect

It is shown that Fermi-Dirac statistics is guaranteed by the Dirac current, from which spin-dependent quantum velocity fields and spin-dependent quantum trajectories can be inferred. Pauli's exclusion principle is demonstrated using the spin-dependent quantum trajectories. The Dirac current, unlike the Schroedinger current, is nonzero for stationary bound states due to the permanent magnetic moment of the electron. It is of order c{sup 0} in agreement with observation that Fermi-Dirac statistics is independent of electronic velocity. In summary the physical basis for exchange-correlation is found in Dirac's equation, although Schroedinger's equation may be used to evaluate the Dirac current in the nonrelativistic regime of electronic velocity.

Ritchie, B

2009-01-30

402

The Transactional Interpretation of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction: quantum peculiarities; 2. The map vs the territory; 3. The original TI: fundamentals; 4. The new possibilist TI: fundamentals; 5. Challenges, replies, and applications; 6. PTI and relativity; 7. The metaphysics of possibility; 8. PTI and 'spacetime'; 9. Epilogue: more than meets the eye; Appendixes; References; Index.

Kastner, Ruth E.

2012-10-01

403

Classical and Quantum-Mechanical State Reconstruction  

ERIC Educational Resources Information Center

|The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that…

Khanna, F. C.; Mello, P. A.; Revzen, M.

2012-01-01

404

Hidden variables and nonlocality in quantum mechanics  

Microsoft Academic Search

Most physicists hold a skeptical attitude toward a 'hidden variables' interpretation of quantum theory, despite David Bohm's successful construction of such a theory and John S. Bell's strong arguments in favor of the idea. The first reason for doubt concerns certain mathematical theorems (von Neumann's, Gleason's, Kochen and Specker's, and Bell's) which can be applied to the hidden variables issue.

Douglas Lloyd Hemmick

1997-01-01

405

Measuring the quantum mechanical wave function  

Microsoft Academic Search

In the past few years experimenters have learned how to determine the complete quantum state of an ensemble of particles or ® elds which have been prepared according to some unknown procedure. Through these experiments they have answered a question posed by W. Pauli in the 1930s. The methods used involve measuring statistical distributions of a well chosen set of

M. G. RAYMER

1997-01-01

406

Quantum Mechanisms of Electronic Signal Propagation Along a Microtubule  

NASA Astrophysics Data System (ADS)

Evidence has been accumulating for the involvement of quantum coherence and entanglement in light harvesting photosynthetic complexes. This tests the adage that biological systems are too "warm and wet" to support quantum phenomena. Recent advancements in experiment and theory have allowed investigators to probe other warm systems for coherent phenomena including polymer chains, bacteriorhodopsin and ion channels. A debate has raged for over a decade regarding hypothetical quantum coherence/ entanglement in microtubules. Here we theoretically investigate coherent energy transfer in microtubules via dipole excitations coupled to the environment in networks of chromophoric amino acids. We present the spatial structure and Hamiltonian, containing localized site energies and couplings between aromatic amino acids, for the microtubule constituent protein tubulin. Energy transfer is discussed in terms of quantum walk formalism and energy transfer efficiency. Plausibility arguments are presented for the conditions favoring a quantum mechanism of electronic signal propagation along a microtubule.

Craddock, Travis; Friesen, Douglas; Tuszynski, Jack

2011-03-01

407

Quantum mechanics of time travel through post-selected teleportation  

NASA Astrophysics Data System (ADS)

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 on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is inequivalent to Deutsch’s theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum-field theory in curved space-time). We derive the dynamical equations that a chronology-respecting system interacting with a CTC will experience. We discuss the possibility of time travel in the absence of general-relativistic closed-timelike curves, and investigate the implications of P-CTCs for enhancing the power of computation.

Lloyd, Seth; Maccone, Lorenzo; Garcia-Patron, Raul; Giovannetti, Vittorio; Shikano, Yutaka

2011-07-01

408

Assessing Expertise in Quantum Mechanics using Categorization Task  

NSDL National Science Digital Library

We discuss the categorization of 20 quantum mechanics problems by 6 physics professors and 22 undergraduate students from two honors-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty members' categorizations were overall rated better than those of students by three faculty members who evaluated all of the categorizations. But the categories created by faculty members were more diverse compared to the uniformity of the categories they created when asked to categorize introductory mechanics problems.

Lin, Shih-Yin; Singh, Chandralekha

2010-01-19

409

On the phase-space picture of quantum mechanics  

NASA Astrophysics Data System (ADS)

A quantum particle with potential energy V(hat q, t) is considered in the frame of a phase-space picture of the quantum theory, and the interconnection between quantum mechanics and a bar h-dependent extended classical dynamics is analysed. The initial position-space wavefunction determines the initial conditions for a set of Hamilton-like equations that leads up to an ensemble of complex-valued phase-space trajectories. The one-dimensional driven harmonic oscillator is used for illustrating the method, and for generating a complete set of phase-space functions.

Campos, D.

2003-05-01

410

Quantum analysis of a linear dc SQUID mechanical displacement detector  

Microsoft Academic Search

We provide a quantum analysis of a dc SQUID mechanical displacement detector within the subcritical Josephson current regime. A segment of the SQUID loop forms the mechanical resonator and motion of the latter is transduced inductively through changes in the flux threading the loop. Expressions are derived for the detector signal response and noise, which are used to evaluate the

M. P. Blencowe; E. Buks

2007-01-01

411

The Quantum Mechanics of Chemical Reactions Involving Conjugate Double Bonds  

Microsoft Academic Search

The various theories of conjugate double bonds are discussed on the basis of quantum mechanics. The potential energy surfaces for the addition of diatomic molecules to such bonds are calculated by the generalized Heitler-London method. It is shown that various mechanisms are possible for such reactions and that such effects as the steric repulsions of the various inactive groups in

Henry Eyring; Albert Sherman; George E. Kimball

1933-01-01

412

Measurement of time in nonrelativistic quantum and classical mechanics  

Microsoft Academic Search

Possible theoretical frameworks for measurement of (arrival) time in the nonrelativistic quantum mechanics are reviewed. It is argued that the ambiguity between indirect measurements by a suitably introduced time operator and direct measurements by a physical clock particle has a counterpart in the corresponding classical framework of measurement of the Newtonian time based on the Hamiltonian mechanics.

Piret Kuusk; Madis Koiv

2001-01-01

413

Quantum mechanical model for two-state jump Markovian process  

Microsoft Academic Search

A quantum mechanical model is given which is equivalent to the stochastic dephasing subject to the two-state jump Markovian process. The stochastic variable corresponds to a Hermitian operator of a spin-1\\/2 system which is embedded in a thermal reservoir, where the time-evolution of the spin-1\\/2 system is described by the quantum master equation of the Lindblad form.

Masashi Ban; Sachiko Kitajima; Kishiko Maruyama; Fumiaki Shibata

2008-01-01

414

(N+1)-dimensional quantum mechanical model for a closed universe  

Microsoft Academic Search

A quantum mechanical model for an (N+1)-dimensional universe arising from a quantum fluctuation is outlined. (3+1) dimensions are a closed, infinitely expanding universe, and the remaining N-3 dimensions are compact. The (3+1) noncompact dimensions are modeled by quantizing a canonical Hamiltonian description of a homogeneous isotropic universe. It is assumed that gravity and the strong-electroweak (SEW) force had equal strengths

T. R. Mongan

1999-01-01

415

Comment on 'Nonlocality, Counterfactuals and Quantum Mechanics'  

SciTech Connect

A recent proof [H. P. Stapp, Am. J. Phys. 65, 300 (1997)], formulated in the symbolic language of modal logic, claims to show that contemporary quantum theory, viewed as a set of rules that allow us to calculate statistical predictions among certain kinds of observations, cannot be imbedded in any rational framework that conforms to the principles that (1) the experimenters' choices of which experiments they will perform can be considered to be free choices, (2) outcomes of measurements are unique, and (3) the free choices just mentioned have no backward-in-time effects of any kind. This claim is similar to Bell's theorem, but much stronger, because no reality assumption alien to quantum philosophy is used. The paper being commented on [W. Unruh, Phys. Rev. A 59, 126 (1999)] argues that some such reality assumption has been ''smuggled'' in. That argument is examined here and shown, I believe, to be defective.

Stapp, H.P.

1999-04-14

416

Comment on ``Nonlocality, counterfactuals, and quantum mechanics''  

NASA Astrophysics Data System (ADS)

A recent proof [H. P. Stapp, Am. J. Phys. 65, 300 (1997)], formulated in the symbolic language of modal logic, claims to show that contemporary quantum theory, viewed as a set of rules that allow us to calculate statistical predictions among certain kinds of observations, cannot be imbedded in any rational framework that conforms to the principles that (1) the experimenters' choices of which experiments they will perform can be considered to be free choices, (2) outcomes of measurements are unique, and (3) the free choices just mentioned have no backward-in-time effects of any kind. This claim is similar to Bell's theorem, but much stronger, because no reality assumption alien to quantum philosophy is used. The paper being commented on [W. Unruh, Phys. Rev. A 59, 126 (1999)] argues that some such reality assumption has been ``smuggled'' in. That argument is examined here and shown, I believe, to be defective.

Stapp, Henry P.

1999-09-01

417

Entropy Production and Equilibration in Yang-Mills Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Entropy production in relativistic heavy-ion collisions is an important physical quantity for studying the equilibration and thermalization of hot matters of quantum chromodynamics (QCD). To formulate a nontrivial definition of entropy for an isolated quantum system, a certain kind of coarse graining may be applied so that the entropy for this isolated quantum system depends on time explicitly. The Husimi distribution, which is a coarse grained distribution in the phase space, is a suitable candidate for this approach. We proposed a general and systematic method of solving the equation of motion of the Husimi distribution for an isolated quantum system. The Husimi distribution is positive (semi-)definite all over the phase space. In this method, we assume the Husimi distribution is composed of a large number of Gaussian test functions. The equation of motion of the Husimi distribution, formulated as a partial differential equation, can be transformed into a system of ordinary differential equations for the centers and the widths of these Gaussian test functions. We numerically solve the system of ordinary differential equations for the centers and the widths of these test functions to obtain the Husimi distribution as a function of time. To ensure the numerical solutions of the trajectories of the test particles preserve physical conservation laws, we obtain a constant of motion for the quantum system. We constructed a coarse grained Hamiltonian whose expectation value is exactly conserved. The conservation of the coarse grained energy confirms the validity of this method. Moreover, we calculated the time evolution of the coarse grained entropy for a model system (Yang-Mills quantum mechanics). Yang-Mills quantum mechanics is a quantum system whose classical correspondence possesses chaotic behaviors. The numerical results revealed that the coarse grained entropy for Yang-Mills quantum mechanics saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system. Our results confirmed the validity of the framework of first-principle evaluation of the coarse grained entropy growth rate. We show that, in the energy regime under study, the relaxation time for the entropy production in Yang-Mills quantum mechanics is approximately the same as the characteristic time of the system, indicating fast equilibration of the system. Fast equilibration of Yang-Mills quantum mechanics is consistent to current understanding of fast equilibration of hot QCD matter in relativistic heavy-ion collisions.

Tsai, Hung-Ming

418

Quantum Mechanics as a Theory of Probability  

Microsoft Academic Search

We develop and defend the thesis that the Hilbert space formalism of quantum\\u000amechanics is a new theory of probability. The theory, like its classical\\u000acounterpart, consists of an algebra of events, and the probability measures\\u000adefined on it. The construction proceeds in the following steps: (a) Axioms for\\u000athe algebra of events are introduced following Birkhoff and von Neumann.

Itamar Pitowsky

2005-01-01

419

The ‘time of occurrence’ in quantum mechanics  

Microsoft Academic Search

Apart from serving as a parameter in describing the evolution of a system, time appears also as an observable property of\\u000a a system in experiments where one measures ‘the time of occurrence’ of an event associated with the system. However, while\\u000a the observables normally encountered in quantum theory (and characterized by self-adjoint operators or projection-valued measures)\\u000a correspond to instantaneous measurements,

M D Srinivas; R. Vijayalakshmi

1981-01-01

420

PREFACE: Progress in supersymmetric quantum mechanics  

NASA Astrophysics Data System (ADS)

The theory of integrable systems is grounded in the very beginning of theoretical physics: Kepler's system is an integrable system. This field of dynamical systems, where one looks for exact solutions of the equations of motion, has attracted most of the great figures in mathematical physics: Euler, Lagrange, Jacobi, etc. Liouville was the first to formulate the precise mathematical conditions ensuring solvability `by quadrature' of the dynamical equations, and his theorem still lies at the heart of the recent developments. The modern era started about thirty years ago with the systematic formulation of soliton solutions to nonlinear wave equations. Since then, impressive developments arose both for the classical and the quantum theory. Subtle mathematical techniques were devised for the resolution of these theories, relying on algebra (group theory), analysis and algebraic geometry (Riemann theory of surfaces). We therefore clearly see that the theory of integrable systems lies ab initio at a crossing of physics and mathematics, and that the developments of these last thirty years have strengthened this dual character, which makes it into an archetypal domain of mathematical physics. As regards the classical theory, beyond the direct connections to the various domains of classical soliton physics (hydrodynamics, condensed matter physics, laser optics, particle physics, plasma, biology or information coding), one has witnessed in these recent years more unexpected (and for some of them not yet well understood) connections to a priori farther fields of theoretical physics: string theory (through matrix models), topological field theories (two dimensional Yang--Mills, three dimensional Chern--Simons--Witten), or supersymmetric field theories (for instance the correspondence discovered by Seiberg and Witten between classical integrable models and quantum potentials). Quantum integrable theories provide examples of exactly (non perturbatively) solvable physical models. They thus allow one to obtain descriptions of non trivial phenomena such as second order phase transition in condensed systems (spin lattices) and exact solution of relativistic quantum field theories (Sine--Gordon...). On the other hand, they supply an excellent example of fruitful interface between physics and mathematics: the theory of quantum groups (and the germane theory of special functions) is a perfect illustration of this rôle and perspectives of such new developments appear very promising. The purpose of the first RAQIS meeting was to bring together researchers from the various fields of mathematics and physics connected to the theory of quantum integrable systems. This conference was held in the framework of the European TMR network EUCLID `Integrable models and applications: from strings to condensed matter', contract number HPRN-CT-2002-00325. The RAQIS03 meeting took place at the Laboratoire d'Annecy-le-vieux de Physique Théorique (LAPTH, France) from 25 March to 28 March, 2003. The organising committee consisted of Daniel Arnaudon, Jean Avan, Luc Frappat, Éric Ragoucy and Paul Sorba. Financial support was provided by Université de Savoie and CNRS-DRI (Centre National de la Recherche Scientifique, Direction des Relations Internationales). In particular various scientific contacts with several Japanese participants were initiated thanks to the CNRS PICS contract number 911. This special issue of Journal of Physics A: Mathematical and General is dedicated to the subject of the RAQIS03 meeting in Annecy-le-vieux. Most of the contributors to this issue took part in the meeting, but this volume does not aim to be a proceedings in the usual sense of the word: contributions do not necessarily coincide with the reports presented at the meeting, nor are the contributors restricted exclusively to those people that were present. The intention of the special issue is to benefit from the occasion offered by the RAQIS03 meeting to highlight the important new areas in quantum integrability, by collecting together in one single volume a selection of article

Aref'eva, I.; Fernández, D. J.; Hussin, V.; Negro, J.; Nieto, L. M.; Samsonov, B. F.

2004-10-01

421

Generalized coherent states under deformed quantum mechanics with maximum momentum  

NASA Astrophysics Data System (ADS)

Following the Gazeau-Klauder approach, we construct generalized coherent states (GCS) as the quantum simulator to examine the deformed quantum mechanics, which exhibits an intrinsic maximum momentum. We study deformed harmonic oscillators and compute their probability distribution and entropy of states exactly. Also, a particle in an infinite potential box is studied perturbatively. In particular, unlike usual quantum mechanics, the present deformed case increases the entropy of the Planck scale quantum optical system. Furthermore, for simplicity, we obtain the modified uncertainty principle (MUP) with the perturbative treatment up to leading order. MUP turns out to increase generally. However, for certain values of ? (a parameter of GCS), it is possible that the MUP will vanish and hence will exhibit the classical characteristic. This is interpreted as the manifestation of the intrinsic high-momentum cutoff at lower momentum in a perturbative treatment. Although the GCS saturates the minimal uncertainty in a simultaneous measurement of physical position and momentum operators, thus constituting the squeezed states, complete coherency is impossible in quantum gravitational physics. The Mandel Q number is calculated, and it is shown that the statistics can be Poissonian and super-/sub-Poissonian depending on ?. The equation of motion is studied, and both Ehrenfest’s theorem and the correspondence principle are recovered. Fractional revival times are obtained through the autocorrelation, and they indicate that the superposition of a classical-like subwave packet is natural in GCS. We also contrast our results with the string-motivated (Snyder) type of deformed quantum mechanics, which incorporates a minimum position uncertainty rather than a maximum momentum. With the advances of quantum optics technology, it might be possible to realize some of these distinguishing quantum-gravitational features within the domain of future experiments.

Ching, Chee Leong; Ng, Wei Khim

2013-10-01

422

A deformation quantization theory for noncommutative quantum mechanics  

SciTech Connect

We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].

Costa Dias, Nuno; Prata, Joao Nuno [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Av. Campo Grande, 376, 1749-024 Lisboa (Portugal) and Grupo de Fisica Matematica, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal); Gosson, Maurice de [NuHAG Fakultaet fuer Mathematik, Universitaet Wien, Wien 1090 (Austria); Luef, Franz [NuHAG Fakultaet fuer Mathematik, Universitaet Wien, Wien 1090 (Austria); Department of Mathematics, UC Berkeley, 847 Evans Hall, Berkeley, California 94720-3840 (United States)

2010-07-15

423

Is the consistent histories approach to quantum mechanics consistent?  

NASA Astrophysics Data System (ADS)

The Consistent Histories (CH) formalism attempts to construct a quantum framework which can be used without the need to introduce observers external to the studied system. The prime motivation in mind is the application of the formalism to the universe as a whole. In order to achieve this, CH maintains that a formulation of quantum mechanics should allow for the assignment of probabilities to alternative histories of a system. Therefore, it provides an observer-independent criterion to decide which sets of histories can be given probabilities and states rules to determine them. The framework establishes that each realm, that is, each set of histories to which probabilities can be assigned, provides a valid quantum-mechanical account of a system. Furthermore, the version of CH first presented in [1, 2] proposes an "evolutionary" explanation of our existence in the universe and of our preference for quasiclassical descriptions of nature. The present work critically evaluates claims to the effect that the formalism offered in [1, 2] solves many interpretational problems in quantum mechanics. In particular, it is pointed out that the interpretation of the proposed framework leaves vague two crucial points, namely, whether realms are fixed or chosen and the link between measurements and histories. The claim of this work is that by doing so, CH overlooks the main interpretational problems of quantum mechanics. Furthermore, we challenge the evolutionary explanation offered and we critically examine the proposed notion of a realm-dependent reality.

Okon, Elias

2013-06-01

424

Quantum measurement I. The measuring process and the interpretation of quantum mechanics  

NASA Astrophysics Data System (ADS)

Quantum mechanics and its interpretation are connected in a manifold way by the measuring process. The measuring apparatus serve as a means for the verification of the theory and are considered as physical objects also subject to the Jaws of this theory. On the basis of this interrelation some parts of the interpretation can be derived from other parts by means of quantum theory. On the other hand there are interpretations which must be excluded on the basis of the quantum theory of measurement.

Mittelstaedt, Peter

1993-10-01

425

Reality in quantum mechanics, Extended Everett Concept, and consciousness  

NASA Astrophysics Data System (ADS)

Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer’s consciousness into the quantum theory of measurements. Most naturally, this is achieved in the framework of Everett’s “many-world interpretation” of quantum mechanics. According to this interpretation, various classical alternatives are perceived by consciousness separately from each other. In the Extended Everett Concept (EEC) proposed by the present author, the separation of the alternatives is identified with the phenomenon of consciousness. This explains the classical character of the alternatives and unusual manifestations of consciousness arising “at the edge of consciousness” (i.e., in sleep or trance) when its access to “other alternative classical realities” (other Everett’s worlds) becomes feasible. Because of reversibility of quantum evolution in EEC, all time moments in the quantum world are equivalent, while the impression of flow of time appears only in consciousness. If it is assumed that consciousness may influence the probabilities of alternatives (which is consistent in case of infinitely many Everett’s worlds), EEC explains free will, “probabilistic miracles” (observing low-probability events), and decreasing entropy in the sphere of life.

Mensky, M. B.

2007-09-01

426

Conceptual and mathematical barriers to students learning quantum mechanics  

NASA Astrophysics Data System (ADS)

Quantum mechanics has revolutionized the way we view the physical world. This theory has required a dramatic revision in the structure of the laws of mechanics governing the behavior of the particles and led to the discovery of macroscopic quantum effects ranging from lasers and superconductivity to neutron stars and radiation from black holes. Though its validity is well confirmed by the experimental evidence available, quantum mechanics remains somewhat of a mystery. The purpose of this study is to identify students' conceptual and mathematical difficulties in learning the core concepts of introductory quantum mechanics, with the eventual goal of developing instructional material to help students with these difficulties. We have investigated student understanding of several core topics in the introductory courses, including quantum measurement, probability, Uncertainty Principle, wave functions, energy eigenstates, recognizing symmetry in physical systems, and mathematical formalism. Student specific difficulties with these topics are discussed throughout this dissertation. In addition, we have studied student difficulties in learning, applying, and making sense out of complex mathematical processes in the physics classroom. We found students' achievement in quantum courses is not independent of their math backgrounds (correlation coefficient 0.547 for P631 and 0.347 for P263). In addition, there is a large jump in the level of mathematics at which one needs to succeed in physics courses after the sophomore level in The Ohio State University's physics curriculum. Many students do not have a functional understanding of probability and its related terminologies. For example, many students confuse the "expectation value" with "probability density" in measurement and some students confuse "probability density" with "probability amplitude" or describe the probability amplitude as a "place" or "area." Our data also suggested that students tend to use classical models when interpreting quantum systems; for example, some students associate a higher energy to a larger amplitude in a wave function. Others, have difficulty differentiating wave functions from energy eigenstates. Furthermore, some students do not use the relationship between the wave function and the wavenumber as a primary resource in for qualitative analysis of wave functions in regions of different potential. Many students have difficulty recognizing mathematical symbols for a given graph and lack the ability to associate the correct functions with their respective graphs. I addition, students do not distinguish an oscillatory function such as e-ix from an exponential decay function such as e-x. The results reported suggest recommendations for further study of student understanding of quantum mechanics and for the development of materials to aid understanding. These recommendations have potentially important implications for the teaching of introductory quantum mechanics and for the development of teaching aids, texts, and technology resources.

Sadaghiani, Homeyra R.

427

Unstable particles in non-relativistic quantum mechanics?  

SciTech Connect

The Schroedinger equation is up-to-a-phase invariant under the Galilei group. This phase leads to the Bargmann's superselection rule, which forbids the existence of the superposition of states with different mass and implies that unstable particles cannot be described consistently in non-relativistic quantum mechanics (NRQM). In this paper we claim that Bargmann's rule neglects physical effects and that a proper description of non-relativistic quantum mechanics requires to take into account this phase through the Extended Galilei group and the definition of its action on spacetime coordinates.

Hernandez-Coronado, H. [Instituto Mexicano del Petroleo, Eje central Lazaro Cardenas 152, 07730, Mexico D.F. (Mexico)

2011-10-14

428

The role of the rigged Hilbert space in quantum mechanics  

NASA Astrophysics Data System (ADS)

There is compelling evidence that, when a continuous spectrum is present, the natural mathematical setting for quantum mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in quantum mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space.

de la Madrid, Rafael

2005-04-01

429

Local observables, nonlocality, and asymptotically separable quantum mechanics  

NASA Astrophysics Data System (ADS)

Quantum mechanics is troubled by the problem of nonlocality inherent in the theory. In a series of papers we explore the possibility of an algebraic formulation of quantum mechanics based on local observables which would incorporate nonlocality when small distances are involved but would be separable at large distances. This paper reviews some of the basic ideas and theories developed recently. These include a unified localization scheme, the introduction of local comoving evolution, local comoving observables, and related conservation laws. Technical considerations and mathematical jargon are kept to a minimum to avoid obscuring physical reasoning.

Wan, K. Kong

1988-09-01

430

Spacetime alternatives in the quantum mechanics of a relativistic particle  

SciTech Connect

Hartle's generalized quantum mechanics formalism is used to examine spacetime coarse grainings, i.e., sets of alternatives defined with respect to a region extended in time as well as space, in the quantum mechanics of a free relativistic particle. For a simple coarse graining and suitable initial conditions, tractable formulas are found for branch wave functions. Despite the nonlocality of the positive-definite version of the Klein-Gordon inner product, which means that nonoverlapping branches are not sufficient to imply decoherence, some initial conditions are found to give decoherence and allow the consistent assignment of probabilities.

Whelan, J.T. (Department of Physics, University of California, Santa Barbara, California 93106-9530 (United States) Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge, CB3 0EH (United Kingdom))

1994-11-15

431

Study on a Possible Darwinian Origin of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

A sketchy subquantum theory deeply influenced by Wheeler's ideas (Am. J. Phys. 51:398-404, 1983) and by the de Broglie-Bohm interpretation (Goldstein in Stanford Encyclopedia of Philosophy, 2006) of quantum mechanics is further analyzed. In this theory a fundamental system is defined as a dual entity formed by bare matter and a methodological probabilistic classical Turing machine. The evolution of the system would be determined by three Darwinian informational regulating principles. Some progress in the derivation of the postulates of quantum mechanics from these regulating principles is reported. The entanglement in a bipartite system is preliminarily considered.

Baladrón, C.

2011-03-01

432

Quantum Magnetomechanics: Ultrahigh-Q-Levitated Mechanical Oscillators  

NASA Astrophysics Data System (ADS)

Engineering nanomechanical quantum systems possessing ultralong motional coherence times allows for applications in precision quantum sensing and quantum interfaces, but to achieve ultrahigh motional Q one must work hard to remove all forms of motional noise and heating. We examine a magneto-meso-mechanical quantum system that consists of a 3D arrangement of miniature superconducting loops which is stably levitated in a static inhomogeneous magnetic field. The motional decoherence is predominantly due to loss from induced eddy currents in the magnetized sphere which provides the trapping field ultimately yielding Q˜109 with motional oscillation frequencies of several hundreds of kilohertz. By inductively coupling this levitating object to a nearby driven flux qubit one can cool its motion very close to the ground state and this may permit the generation of macroscopic entangled motional states of multiple clusters.

Cirio, M.; Brennen, G. K.; Twamley, J.

2012-10-01

433

Quantum Model of Classical Mechanics: Maximum Entropy Packets  

NASA Astrophysics Data System (ADS)

In a previous paper, a statistical method of constructing quantum models of classical properties has been described. The present paper concludes the description by turning to classical mechanics. The quantum states that maximize entropy for given averages and variances of coordinates and momenta are called ME packets. They generalize the Gaussian wave packets. A non-trivial extension of the partition-function method of probability calculus to quantum mechanics is given. Non-commutativity of quantum variables limits its usefulness. Still, the general form of the state operators of ME packets is obtained with its help. The diagonal representation of the operators is found. A general way of calculating averages that can replace the partition function method is described. Classical mechanics is reinterpreted as a statistical theory. Classical trajectories are replaced by classical ME packets. Quantum states approximate classical ones if the product of the coordinate and momentum variances is much larger than Planck constant. Thus, ME packets with large variances follow their classical counterparts better than Gaussian wave packets.

Hájí?ek, P.

2009-09-01

434

Quantum mechanical force field for water with explicit electronic polarization.  

PubMed

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

Han, Jaebeom; Mazack, Michael J M; Zhang, Peng; Truhlar, Donald G; Gao, Jiali

2013-08-01

435

Hilbert space for quantum mechanics on superspace  

NASA Astrophysics Data System (ADS)

In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl2-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.

Coulembier, K.; de Bie, H.

2011-06-01

436

Hilbert space for quantum mechanics on superspace  

SciTech Connect

In superspace a realization of sl{sub 2} is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl{sub 2}-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.

Coulembier, K.; De Bie, H. [Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Krijgslaan 281, 9000 Gent (Belgium)

2011-06-15

437

Quantum Mechanics, Pattern Recognition, and the Mammalian Brain  

NASA Astrophysics Data System (ADS)

Although the usual way of representing Markov processes is time asymmetric, there is a way of describing Markov processes, due to Schrodinger, which is time symmetric. This observation provides a link between quantum mechanics and the layered Bayesian networks that are often used in automated pattern recognition systems. In particular, there is a striking formal similarity between quantum mechanics and a particular type of Bayesian network, the Helmholtz machine, which provides a plausible model for how the mammalian brain recognizes important environmental situations. One interesting aspect of this relationship is that the ``wake-sleep'' algorithm for training a Helmholtz machine is very similar to the problem of finding the potential for the multi-channel Schrodinger equation. As a practical application of this insight it may be possible to use inverse scattering techniques to study the relationship between human brain wave patterns, pattern recognition, and learning. We also comment on whether there is a relationship between quantum measurements and consciousness.

Chapline, George

2008-10-01

438

Surveying students' understanding of quantum mechanics in one spatial dimension  

NSDL National Science Digital Library

We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and administered it to more than 200 students at 10 institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, and the time-dependence of the wavefunction and expectation values. We find that undergraduate and graduate students have many common difficulties with these concepts and that research-based tutorials and peer-instruction tools can significantly reduce these difficulties. The findings also suggest that graduate quantum mechanics courses may not be effective at helping students to develop a better conceptual understanding of these topics, partly because such courses mainly focus on quantitative assessments.

Zhu, Guangtian; Singh, Chandralekha

2012-04-30

439

Semi-spectral Chebyshev method in quantum mechanics  

SciTech Connect

Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in atomic, nuclear and particle physics, astrophysics, quantum chemistry, etc. In recent years, however, an alternative technique based on the semi-spectral methods has focused considerable attention. The purpose of this work is first to provide the necessary tools and subsequently examine the efficiency of this method in quantum mechanical applications. Restricting our interest to time-independent two-body problems, we obtained the continuous and discrete spectrum solutions of the underlying Schroedinger or Lippmann-Schwinger equations in both, the coordinate and momentum space. In all of the numerically studied examples we had no difficulty in achieving the machine accuracy and the semi-spectral method showed exponential convergence combined with excellent numerical stability.

Deloff, A. [Institute for Nuclear Studies, Warsaw (Poland)]. E-mail: deloff@fuw.edu.pl

2007-06-15

440

From principles of mechanics to quantum mechanics - a survey on fuzziness in scientific theories  

Microsoft Academic Search

In this paper we discuss the principles of two fundamental theories of physics: mechanics and quantum mechanics. First, we consider two philosophical positions of the German physicist Heinrich Hertz. He established one of the both in the introduction of his well known Principles of Mechanics. This view - Hertz's \\

Rudolf Seising

2008-01-01

441

Comment on Putnam's ‘Quantum mechanics and the observer’  

Microsoft Academic Search

observables. For the first part, let me roughly repeat Putnam's argument upon which is based his surprising idea - quantum mechanics as a theory of relativity by his example about Schr6dinger's cat. If one regards the cat as an observer and I will assume one can understand this view, not intended by v. Neumann, the cat-system ensemble is mixed and

D. Mayr

1981-01-01

442

Spin and Uncertainty in the Interpretation of Quantum Mechanics.  

ERIC Educational Resources Information Center

Points out that quantum mechanics interpretations, using Heisenberg's Uncertainty Relations for the position and momentum of an electron, have their drawbacks. The interpretations are limited to the Schrodinger theory and fail to take into account either spin or relativity. Shows why spin cannot be ignored. (Author/GA)

Hestenes, David

1979-01-01

443

Efficient Integration of Quantum Mechanical Wave Equations by Unitary Transforms  

NASA Astrophysics Data System (ADS)

The integration of time dependent quantum mechanical wave equations is a fundamental problem in computational physics and computational chemistry. The energy and momentum spectrum of a wave function imposes fundamental limits on the performance of numerical algorithms for this problem. We demonstrate how unitary transforms can help to surmount these limitations.

Bauke, Heiko; Keitel, Christoph H.

2009-08-01

444

PROBABILISTIC THEORIES: WHAT IS SPECIAL ABOUT QUANTUM MECHANICS?  

Microsoft Academic Search

Quantum Mechanics (QM) is a very special probabilistic theory, yet we don't know which operational principles make it so. Here I will analyze the possibility of deriving QM as the mathematical representation of a fair operational framework, i. e. a set of rules which allows the experimenter to make predictions on future events on the basis of suitable tests, e.

GIACOMO MAURO

445

Open Source Physics Curricular Material for Quantum Mechanics  

NSDL National Science Digital Library

The Open Source Physics Curricular Material paper describes the interactive curricular material created as part of the Open Source Physics project for the teaching and learning of quantum mechanics. Here we focus on the measurement and time evolution of two-state superpositions in the context of bound states and spin.

Belloni, Mario; Christian, Wolfgang; Brown, Douglas

2008-05-30

446

Elementary Quantum Mechanics in a High-Energy Process  

ERIC Educational Resources Information Center

|Compares two approaches to strong absorption in elementary quantum mechanics; the black sphere and a model based on the continuum theory of nuclear reactions. Examines the application to proton-antiproton interactions at low momenta and concludes that the second model is the appropriate and simplest to use. (Author/GA)|

Denville, A.; And Others

1978-01-01

447

Overcoming Misconceptions in Quantum Mechanics with the Time Evolution Operator  

ERIC Educational Resources Information Center

|Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of…

Quijas, P. C. Garcia; Aguilar, L. M. Arevalo

2007-01-01

448

The Universal Arrow of Time II: Quantum mechanics case  

Microsoft Academic Search

This paper is a natural continuation of our previous paper arXiv:1011.4173 . We illustrated earlier that in classical Hamilton mechanics, for overwhelming majority of real chaotic macroscopic systems, alignment of their thermodynamic time arrows occurs because of their low interaction. This fact and impossibility to observe entropy decrease at introspection explain the second law of thermodynamics. The situation in quantum

Oleg Kupervasser

2011-01-01

449

Quasi-Hermitian quantum mechanics in phase space  

SciTech Connect

We investigate quasi-Hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact results are easily obtained. We emphasize spatially periodic solutions, compute various distribution functions and phase-space metrics, and explore the relationships between them.

Curtright, Thomas; Veitia, Andrzej [Department of Physics, University of Miami, Coral Gables, Florida 33124 (United States)

2007-10-15

450

Open Source Physics Curricular Material for Quantum Mechanics  

Microsoft Academic Search

Much of the difficulty in learning advanced concepts in quantum mechanics comes from trying to visualize abstract problems. This article addresses the situation with interactive curricular material created as part of the open source physics project. In particular, the authors focus on the measurement and time evolution of two-state superpositions in the context of bound states and spin.

Mario Belloni; Wolfgang Christian; Douglas Brown

2007-01-01

451

The History of Teaching Quantum Mechanics in Greece  

ERIC Educational Resources Information Center

|In this work, our goal is to examine the attitude of the Greek scientific community towards Quantum Mechanics and establish the history of teaching of this theory in Greece. We have examined Physics textbooks written by professors of the University of Athens, as well as records of public speeches, university yearbooks from 1923 to 1970, articles…

Tampakis, Constantin; Skordoulis, Constantin

2007-01-01

452

Quantum mechanical study of Burkholderia cepacia lipase enantioselectivity  

Microsoft Academic Search

Quantum mechanical, semiempirical (AM1) and ab initio (6-31G*) study of the Burkholderia cepacia lipase (BCL) catalysed reactions of the secondary alcohol esterification and its ester hydrolysis is presented. We have selected BCL for our study because of numerous experimental results available, but also because of its broad selectivity and stability that makes it interesting for industrial use. Previously we developed

Sanja Tomi?; Michael Ramek

2006-01-01

453

Absolute Time and Temperature in Quantum and Classical Relativistic Mechanics  

Microsoft Academic Search

We present a relativistic quantum mechanics of a point mass with absolute thermodynamic time and temperature, combined to a single complex parameter of evolution. In this theory, the geometric time is introduced as one of space-time coordinates; it does not coincide with the thermodynamic time on the kinematical level. It is established, that the theory allows a consistent dynamics with

Vadim V. Asadov; Oleg V. Kechkin

2007-01-01

454

Reflection and Self-Monitoring in Quantum Mechanics  

Microsoft Academic Search

An assumed attribute of expert physicists is that they learn readily from their own mistakes. Experts are unlikely to make the same mistakes when asked to solve a problem a second time, especially if they have had access to a correct solution. Here, we discuss a case study in which fourteen advanced undergraduate physics students taking an honors-level quantum mechanics

Andrew Mason; Chandralekha Singh

2009-01-01

455

Quantum-mechanical theory of optomechanical Brillouin cooling  

SciTech Connect

We analyze how to exploit Brillouin scattering of light from sound for the purpose of cooling optomechanical devices and present a quantum-mechanical theory for Brillouin cooling. Our analysis shows that significant cooling ratios can be obtained with standard experimental parameters. A further improvement of cooling efficiency is possible by increasing the dissipation of the optical anti-Stokes resonance.

Tomes, Matthew; Bahl, Gaurav; Carmon, Tal [Department of Electrical Engineering, University of Michigan, Ann Arbor, Michigan 48109 (United States); Marquardt, Florian [Institut fuer Theoretische Physik, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen (Germany); Max Planck Institute for the Science of Light, Guenther-Scharowsky-Strasse 1/Bau 24, D-91058 Erlangen (Germany)

2011-12-15

456

Spin Kinetic Models of Plasmas - Semiclassical and Quantum Mechanical Theory  

SciTech Connect

In this work a recently published semiclassical spin kinetic model, generalizing those of previous authors are discussed. Some previously described properties are reviewed, and a new example illustrating the theory is presented. The generalization to a fully quantum mechanical description is discussed, and the main features of such a theory is outlined. Finally, the main conclusions are presented.

Brodin, Gert; Marklund, Mattias; Zamanian, Jens [Department of Physics, Umeaa University, SE-901 87 Umeaa (Sweden)

2009-11-10

457

Quantum Mechanical Model Of Pulsar Glitches And Gravitational Waves  

Microsoft Academic Search

We present a quantum mechanical model of the timing irregularities (glitches) in pulsars. The model relies on the build up of differential rotation between the stellar crust and the interior superfluid due to the presence of pinned superfluid vortices. We employ the Gross-Pitaevskii equation to model computationally the dynamics of the superfluid condensate. By invoking conservation of angular momentum between

Lila Warszawski; N. G. Berloff; A. Melatos

2009-01-01

458

(N + 1)Dimensional Quantum Mechanical Model for a Closed Universe  

Microsoft Academic Search

A quantum mechanical model for an (N +1)-dimensional universe arising from a quantumfluctuation is outlined. (3 + 1) dimensions are aclosed, infinitely expanding universe, and the remainingN - 3 dimensions are compact. The (3 + 1) noncompact dimensionsare modeled by quantizing a canonical Hamiltoniandescription of a homogeneous isotropic universe. It isassumed that gravity and the strong-electroweak (SEW) force had equal

T. R. Mongan

1999-01-01

459

New approach to separable bounded quantum-mechanical models  

Microsoft Academic Search

We develop an approach to the treatment of separable bounded quantum-mechanical models by the straightforward modification of a successful method for unbounded ones. We apply a new approach to a simple example and show that it provides solutions to both the bounded and unbounded types of models simultaneously.

Francisco M. Fernández

2008-01-01

460

Test of dilute gas approximation in quantum mechanical model  

Microsoft Academic Search

The validity of dilute gas approximation is explored by making use of the large-sized instanton in quantum mechanical model. It is shown that the Euclidean probability amplitude derived through a dilute gas approximation not only cannot explain the result of the linear combination of atomic orbitals approximation, but also does not exhibit a proper limiting case when the size of

D. K. Park; Soo-Young Lee; Jae-Rok Kahng; Sahng-Kyoon Yoo; C. H. Lee; Chang Soo Park; Eui-Soon Yim

1996-01-01