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1

Fast method for quantum mechanical molecular dynamics

NASA Astrophysics Data System (ADS)

As the processing power available for scientific computing grows, first-principles Born-Oppenheimer molecular dynamics simulations are becoming increasingly popular for the study of a wide range of problems in materials science, chemistry, and biology. Nevertheless, the computational cost of Born-Oppenheimer molecular dynamics still remains prohibitively large for many potential applications. Here we show how to avoid a major computational bottleneck: the self-consistent-field optimization prior to force calculations. The optimization-free quantum mechanical molecular dynamics method gives trajectories that are almost indistinguishable from an “exact” microcanonical Born-Oppenheimer molecular dynamics simulation even when low-prefactor linear scaling sparse matrix algebra is used. Our findings show that the computational gap between classical and quantum mechanical molecular dynamics simulations can be significantly reduced.

Niklasson, Anders M. N.; Cawkwell, Marc J.

2012-11-01

2

Quantum mechanics/molecular mechanics restrained electrostatic potential fitting.

We present a quantum mechanics/molecular mechanics (QM/MM) method to evaluate the partial charges of amino acid residues for use in MM potentials based on their protein environment. For each residue of interest, the nearby residues are included in the QM system while the rest of the protein is treated at the MM level of theory. After a short structural optimization, the partial charges of the central residue are fit to the electrostatic potential using the restrained electrostatic potential (RESP) method. The resulting charges and electrostatic potential account for the individual environment of the residue, although they lack the transferable nature of library partial charges. To evaluate the quality of the QM/MM RESP charges, thermodynamic integration is used to measure the pKa shift of the aspartic acid residues in three different proteins, turkey egg lysozyme, beta-cryptogein, and Thioredoxin. Compared to the AMBER ff99SB library values, the QM/MM RESP charges show better agreement between the calculated and experimental pK(a) values for almost all of the residues considered. PMID:24176005

Burger, Steven K; Schofield, Jeremy; Ayers, Paul W

2013-12-01

3

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

4

A theoretical study of the molecular mechanism of the thymidylate synthase-catalyzed reaction has been carried out using hybrid quantum mechanics\\/molecular mechanics methods. We have examined all of the stationary points (reactants, intermediates, transition structures, and products) on the multidimensional potential energy surfaces for the multistep enzymatic process. The characterization of these relevant structures facilitates the gaining of insight into the

Natalia Kanaan; Sergio Martí; Vicent Moliner; Amnon Kohen

2007-01-01

5

Human immunodeficiency virus (HIV)-1 integrase (IN) is an attractive target for development of acquired immunodeficiency syndrome chemotherapy. In this study, conventional and coupled quantum mechanical and molecular mechanical (QM/MM) molecular dynamics (MD) simulations of HIV-1 IN complexed with 5CITEP (IN-5CITEP) were carried out. In addition to differences in the bound position of 5CITEP, significant differences at the two levels of theory were observed in the metal coordination geometry and the areas involving residues 116–119 and 140–166. In the conventional MD simulation, the coordination of Mg2+ was found to be a near-perfect octahedral geometry whereas a distorted octahedral complex was observed in QM/MM. All of the above reasons lead to a different pattern of protein-ligand salt link formation that was not observed in the classical MD simulation. Furthermore to provide a theoretical understanding of inhibition mechanisms of 5CITEP and its derivative (DKA), hybrid QM/MM MD simulations of the two complexes (IN-5CITEP and IN-DKA) have been performed. The results reveal that areas involving residues 60–68, 116–119, and 140–149 were substantially different among the two systems. The two systems show similar pattern of metal coordination geometry, i.e., a distorted octahedron. In IN-DKA, both OD1 and OD2 of Asp-64 coordinate the Mg2+ in a monodentate fashion whereas only OD1 is chelated to the metal as observed in IN-5CITEP. The high potency of DKA as compared to 5CITEP is supported by a strong salt link formed between its carboxylate moiety and the ammonium group of Lys-159. Detailed comparisons between HIV-1 IN complexed with DKA and with 5CITEP provide information about ligand structure effects on protein-ligand interactions in particular with the Lys-159. This is useful for the design of new selective HIV-1 IN inhibitors.

Nunthaboot, Nadtanet; Pianwanit, Somsak; Parasuk, Vudhichai; Ebalunode, Jerry O.; Briggs, James M.; Kokpol, Sirirat

2007-01-01

6

Drug-Target Binding Investigated by Quantum Mechanical/Molecular Mechanical (QM/MM) Methods

NASA Astrophysics Data System (ADS)

Many important drugs, also used in the clinics, exert their function by binding covalently to their targets. Understanding their action requires quantum mechanical simulations. Here, after briefly reviewing few basic concepts of thermodynamics and kinetics of drug-target binding, we summarize principles and applications of Car-Parrinello quantum mechanics/molecular mechanics (QM/MM) simulations. From this discussion, this approach emerges as a computational methodology particularly well suited to investigate covalent binding in systems of pharmacological relevance.

Rothlisberger, U.; Carloni, P.

7

NASA Astrophysics Data System (ADS)

A quantum mechanics/molecular mechanics molecular dynamics simulation was performed for liquid water to investigate structural and dynamical properties of this peculiar liquid. The most important region containing a central reference molecule and all nearest surrounding molecules (first coordination shell) was treated by Hartree-Fock (HF), post-Hartree-Fock [second-order Møller-Plesset perturbation theory (MP2)], and hybrid density functional B3LYP [Becke's three parameter functional (B3) with the correlation functional of Lee, Yang, and Parr (LYP)] methods. In addition, another HF-level simulation (2HF) included the full second coordination shell. Site to site interactions between oxygen-oxygen, oxygen-hydrogen, and hydrogen-hydrogen atoms of all ab initio methods were compared to experimental data. The absence of a second peak and the appearance of a shoulder instead in the gO-O graph obtained from the 2HF simulation is notable, as this feature has been observed so far only for pressurized or heated water. Dynamical data show that the 2HF procedure compensates some of the deficiency of the HF one-shell simulation, reducing the difference between correlated (MP2) and HF results. B3LYP apparently leads to too rigid structures and thus to an artificial slow down of the dynamics.

Xenides, Demetrios; Randolf, Bernhard R.; Rode, Bernd M.

2005-05-01

8

NASA Astrophysics Data System (ADS)

A quantum mechanical/molecular mechanical aerosol model is developed to describe the interaction between gas phase molecules and atmospheric particles. The model enables the calculation of interaction energies and time-dependent properties. We use the model to investigate how a succinic acid molecule interacts with an aqueous particle. We show how the interaction energies and linear response properties (excitation energies, transition moments, and polarizabilities) depend on the distance between aerosol particle and molecule and on their relative orientation. The results are compared with those obtained previously using a dielectric continuum model [Sloth et al., J. Phys. Chem. (submitted)].

Sloth, Marianne; Bilde, Merete; Mikkelsen, Kurt V.

2003-06-01

9

A combined quantum mechanical/molecular mechanical/continuum (QM/MMpol/C) style method is developed for time-dependent density functional theory (TDDFT, including long-range corrected TDDFT) method, induced dipole polarizable force field, and induced surface charge continuum model. Induced dipoles and induced charges are included in the TDDFT equations to solve for the transition energies, relaxed density, and transition density. Analytic gradient is derived and implemented for geometry optimization and molecular dynamics simulation. QM/MMpol/C style DFT and TDDFT methods are used to study the hydrogen bonding of the photoactive yellow protein chromopore in ground state and excited state. PMID:24006973

Thellamurege, Nandun M; Cui, Fengchao; Li, Hui

2013-08-28

10

NASA Astrophysics Data System (ADS)

A combined quantum mechanical/molecular mechanical/continuum (QM/MMpol/C) style method is developed for time-dependent density functional theory (TDDFT, including long-range corrected TDDFT) method, induced dipole polarizable force field, and induced surface charge continuum model. Induced dipoles and induced charges are included in the TDDFT equations to solve for the transition energies, relaxed density, and transition density. Analytic gradient is derived and implemented for geometry optimization and molecular dynamics simulation. QM/MMpol/C style DFT and TDDFT methods are used to study the hydrogen bonding of the photoactive yellow protein chromopore in ground state and excited state.

Thellamurege, Nandun M.; Cui, Fengchao; Li, Hui

2013-08-01

11

A simple quantum mechanical/molecular mechanical (QM/MM) model for methanol

NASA Astrophysics Data System (ADS)

Mixed quantum mechanical/molecular mechanical (QM/MM) models, in which one part of a system is treated at an ab initio level while the rest is described by an empirical force field, are becoming increasingly popular. In this Letter, we describe a simple QM/MM model for methanol (CH 3OH) in which the OH constitutes the ab initio region and is treated within a density functional representation, while the methyl group, the MM region, is treated using the AMBER force field. The model is used to study the structure of the bulk liquid and is shown to compare favorably with the experimental structure.

Morrone, Joseph A.; Tuckerman, Mark E.

2003-03-01

12

The Role of Gln61 in HRas GTP Hydrolysis: A Quantum Mechanics/Molecular Mechanics Study

Activation of the water molecule involved in GTP hydrolysis within the HRas?RasGAP system is analyzed using a tailored approach based on hybrid quantum mechanics/molecular mechanics (QM/MM) simulation. A new path emerges: transfer of a proton from the attacking water molecule to a second water molecule, then a different proton is transferred from this second water molecule to the GTP. Gln61 will stabilize the transient OH? and H3O+ molecules thus generated. This newly proposed mechanism was generated by using, for the first time to our knowledge, the entire HRas-RasGAP protein complex in a QM/MM simulation context. It also offers a rational explanation for previous experimental results regarding the decrease of GTPase rate found in the HRas Q61A mutant and the increase exhibited by the HRas Q61E mutant.

Martin-Garcia, Fernando; Mendieta-Moreno, Jesus Ignacio; Lopez-Vinas, Eduardo; Gomez-Puertas, Paulino; Mendieta, Jesus

2012-01-01

13

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

2011-06-15

14

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

15

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

16

The extent to which accuracy of electric charges plays a role in protein-ligand docking is investigated through development of a docking algorithm, which incorporates quantum mechanical/molecular mechanical (QM/MM) calculations. In this algorithm, fixed charges of ligands obtained from force field parameterization are replaced by QM/MM calculations in the protein environment, treating only the ligands as the quantum region. The algorithm is tested on a set of 40 cocrystallized structures taken from the Protein Data Bank (PDB) and provides strong evidence that use of nonfixed charges is important. An algorithm, dubbed “Survival of the Fittest” (SOF) algorithm, is implemented to incorporate QM/MM charge calculations without any prior knowledge of native structures of the complexes. Using an iterative protocol, this algorithm is able in many cases to converge to a nativelike structure in systems where redocking of the ligand using a standard fixed charge force field exhibits nontrivial errors. The results demonstrate that polarization effects can play a significant role in determining the structures of protein-ligand complexes, and provide a promising start towards the development of more accurate docking methods for lead optimization applications.

CHO, ART E.; GUALLAR, VICTOR; BERNE, BRUCE J.; FRIESNER, RICHARD

2014-01-01

17

Quantum mechanics/molecular mechanics study of oxygen binding in hemocyanin.

We report a combined quantum mechanics/molecular mechanics (QM/MM) study on the mechanism of reversible dioxygen binding in the active site of hemocyanin (Hc). The QM region is treated by broken-symmetry density functional theory (DFT) with spin projection corrections. The X-ray structures of deoxygenated (deoxyHc) and oxygenated (oxyHc) hemocyanin are well reproduced by QM/MM geometry optimizations. The computed relative energies strongly depend on the chosen density functional. They are consistent with the available thermodynamic data for oxygen binding in hemocyanin and in synthetic model complexes when the BH&HLYP hybrid functional with 50% Hartree-Fock exchange is used. According to the QM(BH&HLYP)/MM results, the reaction proceeds stepwise with two sequential electron transfer (ET) processes in the triplet state followed by an intersystem crossing to the singlet product. The first ET step leads to a nonbridged superoxo CuB(II)-O2(•-) intermediate via a low-barrier transition state. The second ET step is even more facile and yields a side-on oxyHc complex with the characteristic Cu2O2 butterfly core, accompanied by triplet-singlet intersystem crossing. The computed barriers are very small so that the two ET processes are expected to very rapid and nearly simultaneous. PMID:24762083

Saito, Toru; Thiel, Walter

2014-05-15

18

Large scale simulation of quantum-mechanical molecular dynamics for nano-polycrystalline diamond

Quantum-mechanical molecular-dynamics simulations are carried out to explore possible precursor states of nano-polycrystalline diamond, a novel ultra-hard material produced directly from graphite. Large-scale simulation with 105 atoms is realized by using the 'order-N' simulation code 'ELSES' (http:\\/\\/www.elses.jp). The simulation starts with a diamond structure that contains initial structural defects and results in a mixture of graphite(sp2)-like and diamond(sp3)-like regions as

Takeo Hoshi; Toshiaki Iitaka; Maria Fyta

2010-01-01

19

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

20

Quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations were performed to investigate the methylation of 6-mercaptopurine catalyzed by thiopurine S-methyltransferase. Several setups with different tautomeric forms and orientations of the substrate were considered. It is found that, with the orientation in chain A of the X-ray structure, the substrate can form an ideal near-attack configuration for the methylation reaction, which may take place after the deprotonation of the substrate by the conserved residue Asp23 through a water chain. The potential of mean force (PMF) of the methyl-transfer step for the most favorable pathway is 19.6 kcal/mol, which is in good agreement with the available experimental rate constant data. PMID:21615136

Pan, Xiao-Liang; Cui, Feng-Chao; Liu, Jing-Yao

2011-06-23

21

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

22

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.

23

We have investigated the protonation state and photoabsorption spectrum of Schiff-base (SB) nitrogen bound 11-cis-retinal in human blue and mouse UV cone visual pigments as well as in bovine rhodopsin by hybrid quantum mechanical\\/molecular mechanical (QM\\/MM) calculations. We have employed both multireference (MRCISD+Q, MR-SORCI+Q, and MR-DDCI2+Q) and single reference (TD-B3LYP and RI-CC2) QM methods. The calculated ground-state and vertical excitation

Ahmet Altun; Shozo Yokoyama; Keiji Morokuma

2009-01-01

24

To investigate the structural and dynamical properties of the tetraamminezinc(ii) complex (Zn-tetraamine) in aqueous solution, ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulation was performed for 50 ps at the Hartree-Fock (HF) level of theory. A predominant 4-coordinate solvation structure with a maximum probability of the Zn-N distance at approximately 2.1 A was observed, which seems to be involved in the associative mode of water exchange reactions to produce a short-lived, 5-coordinated trigonal bipyramidal structure. Several sets of structural and dynamical parameters such as radial distribution functions (RDF), coordination number distributions (CND), angular distributions (ADF), ligands' mean residence times (MRT) and ion-ligand stretching frequencies have been evaluated in order to get an in depth knowledge of the physical and chemical properties of the tetraamminezinc(ii) complex in aqueous solution. A comparative study of the tetraamminezinc(ii) complex with previously published mono-, di- and triamminezinc(ii) complexes has been also performed, which yielded significant insights into the complex properties as a function of an increasing number of first-shell ammonia ligands. PMID:20544098

Qaiser Fatmi, M; Hofer, Thomas S; Rode, Bernd M

2010-09-01

25

The mechanism of DNA cytosine-5-methylation catalyzed by the bacterial M.HhaI enzyme has been considered as a stepwise nucleophilic addition of Cys-81-S? to cytosine C6 followed by C5 nucleophilic replacement of the methyl of S-adenosyl-l-methionine to produce 5-methyl-6-Cys-81-S-5,6-dihydrocytosine. In this study, we show that the reaction is concerted from a series of energy calculations by using the quantum mechanical/molecular mechanical hybrid method. Deprotonation of 5-methyl-6-Cys-81-S-5,6-dihydrocytosine and expulsion of Cys-81-S? provides the product DNA 5-methylcytosine. A required base catalyst for this deprotonation is not available as a member of the active site structure. A water channel between the active site and bulk water allows entrance of solvent to the active site. Hydroxide at 10?7 mole fraction (pH = 7) is shown to be sufficient for the required catalysis. We also show that Glu-119-CO2H can divert the reaction by protonating cytosine N3 when Cys-81-S? attacks cytosine, to form the 6-Cys-81-S-3-hydrocytosine. The reactants and 6-Cys-81-S-3-hydrocytosine product are in rapid equilibrium, and this explains the observed hydrogen exchange of cytosine with solvent.

Zhang, Xiaodong; Bruice, Thomas C.

2006-01-01

26

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

Carbamate and urea derivatives are important classes of fatty acid amide hydrolase (FAAH) inhibitors that carbamoylate the active-site nucleophile Ser241. In the present work, the reactivation mechanism of carbamoylated FAAH is investigated by means of a quantum mechanics/molecular mechanics (QM/MM) approach. The potential energy surfaces for decarbamoylation of FAAH covalent adducts, deriving from the O-aryl carbamate URB597 and from the N-piperazinylurea JNJ1661610, were calculated and compared to that for deacylation of FAAH acylated by the substrate oleamide. Calculations show that a carbamic group bound to Ser241 prevents efficient stabilization of transition states of hydrolysis, leading to large increments in the activation barrier. Moreover, the energy barrier for the piperazine carboxylate was significantly lower than that for the ciclohexyl carbamate derived from URB597. This is consistent with experimental data showing slowly reversible FAAH inhibition for the N-piperazinylurea inhibitor and irreversible inhibition for URB597.

Lodola, Alessio; Capoferri, Luigi; Rivara, Silvia; Tarzia, Giorgio; Piomelli, Daniele; Mulholland, Adrian; Mor, Marco

2013-01-01

28

A combined quantum mechanical/molecular mechanical/continuum (QM/MM/C) style second order Møller-Plesset perturbation theory (MP2) method that incorporates induced dipole polarizable force field and induced surface charge continuum solvation model is established. The Z-vector method is modified to include induced dipoles and induced surface charges to determine the MP2 response density matrix, which can be used to evaluate MP2 properties. In particular, analytic nuclear gradient is derived and implemented for this method. Using the Assisted Model Building with Energy Refinement induced dipole polarizable protein force field, the QM/MM/C style MP2 method is used to study the hydrogen bonding distances and strengths of the photoactive yellow protein chromopore in the wild type and the Glu46Gln mutant. PMID:24811633

Thellamurege, Nandun M; Si, Dejun; Cui, Fengchao; Li, Hui

2014-05-01

29

In recent years, the design of artificial metalloenzymes obtained by the insertion of homogeneous catalysts into biological macromolecules has become a major field of research. These hybrids, and the corresponding X-ray structures of several of them, are offering opportunities to better understand the synergy between organometallic and biological subsystems. In this work, we investigate the resting state and activation process of a hybrid inspired by an oxidative haemoenzyme but presenting an unexpected reactivity and structural features. An extensive series of quantum mechanics/molecular mechanics calculations show that the resting state and the activation processes of the novel enzyme differ from naturally occurring haemoenzymes in terms of the electronic state of the metal, participation of the first coordination sphere of the metal and the dynamic process. This study presents novel insights into the sensitivity of the association between organometallic and biological partners and illustrates the molecular challenge that represents the design of efficient enzymes based on this strategy. PMID:24829279

Ortega-Carrasco, Elisabeth; Lledós, Agustí; Maréchal, Jean-Didier

2014-07-01

30

NASA Astrophysics Data System (ADS)

A combined quantum mechanical/molecular mechanical/continuum (QM/MM/C) style second order Møller-Plesset perturbation theory (MP2) method that incorporates induced dipole polarizable force field and induced surface charge continuum solvation model is established. The Z-vector method is modified to include induced dipoles and induced surface charges to determine the MP2 response density matrix, which can be used to evaluate MP2 properties. In particular, analytic nuclear gradient is derived and implemented for this method. Using the Assisted Model Building with Energy Refinement induced dipole polarizable protein force field, the QM/MM/C style MP2 method is used to study the hydrogen bonding distances and strengths of the photoactive yellow protein chromopore in the wild type and the Glu46Gln mutant.

Thellamurege, Nandun M.; Si, Dejun; Cui, Fengchao; Li, Hui

2014-05-01

31

NASA Astrophysics Data System (ADS)

We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical (QM)-molecular-mechanical (MM) calculations. To remedy the nonphysical QM/MM Coulomb interaction at short distances arising from a point electrostatic potential (ESP) charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge and describe the effect of a s-wave expansion, extended over the covalent radius rc, of the MM atom. The resulting potential describes that, at short distances, large scale cancellation of Coulomb interaction arises intrinsically from the localized expansion of the MM point charge and the potential self-consistently reduces to 1/rc at zero distance providing a renormalization to the Coulomb energy near interatomic separations. Employing this renormalized Hamiltonian, we developed an interface between the Car-Parrinello molecular-dynamics program and the classical molecular-dynamics simulation program Groningen machine for chemical simulations. With this hybrid code we performed QM/MM calculations on water dimer, imidazole carbon monoxide (CO) complex, and imidazole-heme-CO complex with CO interacting with another imidazole. The QM/MM results are in excellent agreement with experimental data for the geometry of these complexes and other computational data found in literature.

Biswas, P. K.; Gogonea, V.

2005-10-01

32

We present a series of capping-potentials designed as link atoms to saturate dangling bonds at the quantum/classical interface within density functional theory-based hybrid QM/MM calculations. We aim at imitating the properties of different carbon-carbon bonds by means of monovalent analytic pseudopotentials. These effective potentials are optimized such that the perturbations of the quantum electronic density are minimized. This optimization is based on a stochastic scheme, which helps to avoid local minima trapping. For a series of common biomolecular groups, we find capping-potentials that outperform the more common hydrogen-capping in view of structural and spectroscopic properties. To demonstrate the transferability to complex systems, we also benchmark our potentials with a hydrogen-bonded dimer, yielding systematic improvements in structural and spectroscopic parameters. PMID:22149779

Ihrig, Arvid Conrad; Schiffmann, Christoph; Sebastiani, Daniel

2011-12-01

33

In this work we have investigated the first hyperpolarizability of pNA in 1,4-dioxane solution using a quantum mechanics/molecular mechanics (QM/MM) model. The particular model adopted is the recently developed discrete solvent reaction field (DRF) model. The DRF model is a polarizable QM/MM model in which the QM part is treated using time-dependent density-functional theory and local-field effects are incorporated. This allows for direct computation of molecular effective properties which can be compared with experimental results. The solvation shift for the first hyperpolarizability is calculated to be 30% which is in good agreement with the experimental results. However, the calculated values, both in the gas phase and in solution, are by a factor of 2 larger than the experimental ones. This is in contrast to the calculation of the first hyperpolarizability for several small molecules in the gas phase where fair agreement is found with experimental. The inclusion of local-field effects in the calculations was found to be crucial and neglecting them led to results which are significantly larger. To test the DRF model the refractive index of liquid 1,4-dioxane was also calculated and found to be in good agreement with experiment. PMID:16229570

Jensen, Lasse; van Duijnen, Piet Th

2005-08-15

34

NASA Astrophysics Data System (ADS)

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

2009-04-01

35

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

We have investigated the protonation state and photoabsorption spectrum of Schiff-base (SB) nitrogen bound 11-cis-retinal in human blue and mouse UV cone visual pigments as well as in bovine rhodopsin by hybrid quantum mechanical/molecular mechanical (QM/MM) calculations. We have employed both multireference (MRCISD+Q, MR-SORCI+Q, and MR-DDCI2+Q) and single reference (TD-B3LYP and RI-CC2) QM methods. The calculated ground-state and vertical excitation energies show that UV-sensitive pigments have deprotonated SB nitrogen, while violet-sensitive pigments have protonated SB nitrogen, in agreement with some indirect experimental evidence. A significant blue shift of the absorption maxima of violet-sensitive pigments relative to rhodopsins arises from the increase in bond length alternation of the polyene chain of 11-cis-retinal induced by polarizing fields of these pigments. The main counterion is Glu113 in both violet-sensitive vertebrate pigments and bovine rhodopsin. Neither Glu113 nor the remaining pigment has a significant influence on the first excitation energy of 11-cis-retinal in the UV-sensitive pigments that have deprotonated SB nitrogen. There is no charge transfer between the SB and beta-ionone terminals of 11-cis-retinal in the ground and first excited states. PMID:19630373

Altun, Ahmet; Yokoyama, Shozo; Morokuma, Keiji

2009-10-29

37

NASA Astrophysics Data System (ADS)

We have investigated the protonation state and photoabsorption spectrum of Schiff-base (SB) nitrogen bound 11-cis-retinal in human blue and mouse UV cone visual pigments as well as in bovine rhodopsin by hybrid quantum mechanical/molecular mechanical (QM/MM) calculations. We have employed both multireference (MRCISD+Q, MR-SORCI+Q, and MR-DDCI2+Q) and single reference (TD-B3LYP and RI-CC2) QM methods. The calculated ground-state and vertical excitation energies show that UV-sensitive pigments have deprotonated SB nitrogen, while violet-sensitive pigments have protonated SB nitrogen, in agreement with some indirect experimental evidence. A significant blue shift of the absorption maxima of violet-sensitive pigments relative to rhodopsins arises from the increase in bond length alternation of the polyene chain of 11-cis-retinal induced by polarizing fields of these pigments. The main counterion is Glu113 in both violet-sensitive vertebrate pigments and bovine rhodopsin. Neither Glu113 nor the remaining pigment has a significant influence on the first excitation energy of 11-cis-retinal in the UV-sensitive pigments that have deprotonated SB nitrogen. There is no charge transfer between the SB and ?-ionone terminals of 11-cis-retinal in the ground and first excited states.

Altun, Ahmet; Yokoyama, Shozo; Morokuma, Keiji

2009-07-01

38

We have investigated the protonation state and photoabsorption spectrum of Schiff-base (SB) nitrogen bound 11-cis-retinal in human blue and mouse UV cone visual pigments as well as in bovine rhodopsin by hybrid quantum mechanical/molecular mechanical (QM/MM) calculations. We have employed both multireference (MRCISD+Q, MR-SORCI+Q, and MR-DDCI2+Q) and single reference (TD-B3LYP and RI-CC2) QM methods. The calculated ground-state and vertical excitation energies show that UV-sensitive pigments have deprotonated SB nitrogen, while violet-sensitive pigments have protonated SB nitrogen, in agreement with some indirect experimental evidence. A significant blue shift of the absorption maxima of violet-sensitive pigments relative to rhodopsins arises from the increase in bond length alternation of the polyene chain of 11-cis-retinal induced by polarizing fields of these pigments. The main counterion is Glu113 in both violet-sensitive vertebrate pigments and bovine rhodopsin. Neither Glu113 nor the remaining pigment has a significant influence on the first excitation energy of 11-cis-retinal in the UV-sensitive pigments that have deprotonated SB nitrogen. There is no charge transfer between the SB and ?-ionone terminals of 11-cis-retinal in the ground and first excited states.

Altun, Ahmet; Yokoyama, Shozo; Morokuma, Keiji

2009-01-01

39

Recent computer simulations of the cysteine nucleophilic attack on propanal in human mitochondrial Aldehyde Dehydrogenase (ALDH2) yielded an unexpected result; the chemically reasonable formation of a dead-end cysteine-cofactor adduct when NAD+ was in the “hydride transfer” position. More recently, this adduct found independent crystallographic support in work on formyltetrahydrofolate dehydrogenase, work which further found evidence of the same adduct on re-examination of deposited electron densities of ALDH2. Although the experimental data showed this adduct was reversible, several mechanistic questions arise from the fact that it forms at all. Here, we present results from further Quantum Mechanical/Molecular Mechanical (QM/MM) simulations toward understanding the mechanistic implications of adduct formation. These simulations revealed that formation of the oxyanion thiohemiacetal intermediate only when the nicotinamide ring of NAD+ is oriented away from the active site, contrary to prior arguments. In contrast, and in seeming paradox, when NAD is oriented to receive the hydride, disassociation of the oxyanion intermediate to form the dead-end adduct is more thermodynamically-favored than maintaining the oxyanion intermediate necessary for catalysis to proceed. However, this disassociation to the adduct could be avoided through proton transfer from the enzyme to the intermediate. Our results continue to indicate that the unlikely source of this proton is the Cys302 main chain amide.

Wymore, Troy; Deerfield, David W.; Hempel, John

2008-01-01

40

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

41

NASA Astrophysics Data System (ADS)

Energy and free energy barriers for acetaldehyde conversion in aldehyde oxidoreductase are determined for three reaction pathways using quantum mechanical/molecular mechanical (QM/MM) calculations on the solvated enzyme. Ab initio single-point QM/MM energies are obtained at the stationary points optimized at the DFT(B3LYP)/MM level. These ab initio calculations employ local correlation treatments [LMP2 and LCCSD(T0)] in combination with augmented triple- and quadruple-zeta basis sets, and the final coupled cluster results include MP2-based corrections for basis set incompleteness and for the domain approximation. Free energy perturbation (FEP) theory is used to generate free energy profiles at the DFT(B3LYP)/MM level for the most important reaction steps by sampling along the corresponding reaction paths using molecular dynamics. The ab initio and FEP QM/MM results are combined to derive improved estimates of the free energy barriers, which differ from the corresponding DFT(B3LYP)/MM energy barriers by about 3 kcal mol-1. The present results confirm the qualitative mechanistic conclusions from a previous DFT(B3LYP)/MM study. Most favorable is a three-step Lewis base catalyzed mechanism with an initial proton transfer from the cofactor to the Glu869 residue, a subsequent nucleophilic attack that yields a tetrahedral intermediate (IM2), and a final rate-limiting hydride transfer. The competing metal center activated pathway has the same final step but needs to overcome a higher barrier in the initial step on the route to IM2. The concerted mechanism has the highest free energy barrier and can be ruled out. While confirming the qualitative mechanistic scenario proposed previously on the basis of DFT(B3LYP)/MM energy profiles, the present ab initio and FEP QM/MM calculations provide corrections to the barriers that are important when aiming at high accuracy.

Dieterich, Johannes M.; Werner, Hans-Joachim; Mata, Ricardo A.; Metz, Sebastian; Thiel, Walter

2010-01-01

42

We report a combined quantum mechanical/molecular mechanical (QM/MM) study of the effect of mutations of the Phe434 residue in the active site of cyclohexanone monooxygenase (CHMO) on its enantioselectivity toward 4-hydroxycyclohexanone. In terms of our previously established model of the enzymatic Baeyer-Villiger reaction, enantioselectivity is governed by the preference toward the equatorial ((S)-selectivity) or axial ((R)-selectivity) conformation of the substituent at the C4 carbon atom of the cyclohexanone ring in the Criegee intermediate and the subsequent rate-limiting transition state for migration (TS2). We assess the enantiopreference by locating all relevant TS2 structures at the QM/MM level. In the wild-type enzyme we find that the axial conformation is energetically slightly more stable, thus leading to a small excess of (R)-product. In the Phe434Ser mutant, there is a hydrogen bond between the serine side chain and the equatorial substrate hydroxyl group that is retained during the whole reaction, and hence there is pronounced reverse (S)-enantioselectivity. Another mutant, Phe434Ile, is shown to preserve and enhance the (R)-selectivity. All these findings are in accordance with experiment. The QM/MM calculations allow us to explain the effect of point mutations on CHMO enantioselectivity for the first time at the molecular level by an analysis of the specific interactions between substrate and active-site environment in the TS2 structures that satisfy the basic stereoelectronic requirement of anti-periplanarity for the migrating ?-bond. PMID:23600847

Polyak, Iakov; Reetz, Manfred T; Thiel, Walter

2013-05-01

43

NASA Astrophysics Data System (ADS)

The nudged elastic band (NEB) and string methods are widely used to obtain the reaction path of chemical reactions and phase transitions. In these methods, however, it is difficult to define an accurate Lagrangian to generate the conservative forces. On the other hand, the constrained optimization with locally updated planes (CO-LUP) scheme defines target function properly and suitable for micro-iteration optimizations in quantum mechanical/molecular mechanical (QM/MM) systems, which uses the efficient second order QM optimization. However, the method does have problems of inaccurate estimation of reactions and inappropriate accumulation of images around the energy minimum. We introduce three modifications into the CO-LUP scheme to overcome these problems: (1) An improved tangent estimation of the reaction path, which is used in the NEB method, (2) redistribution of images using an energy-weighted interpolation before updating local tangents, and (3) reduction of the number of constraints, in particular translation/rotation constraints, for improved convergence. First, we test the method on the isomerization of alanine dipeptide without QM/MM calculation, showing that the method is comparable to the string method both in accuracy and efficiency. Next, we apply the method for defining the reaction paths of the rearrangement reaction catalyzed by chorismate mutase (CM) and of the phosphoryl transfer reaction catalyzed by cAMP-dependent protein kinase (PKA) using generalized hybrid orbital QM/MM calculations. The reaction energy barrier of CM is in high agreement with the experimental value. The path of PKA reveals that the enzyme reaction is associative and there is a late transfer of the substrate proton to Asp 166, which is in agreement with the recently published result using the NEB method.

Jung, Jaewoon; Re, Suyong; Sugita, Yuji; Ten-no, Seiichiro

2013-01-01

44

A combination of the polarizable continuum model (PCM) and the hybrid quantum mechanics\\/molecular mechanics (QM\\/MM) methodology, PCM-MM\\/QM, is used to include the solute electronic polarization and then study the solvent effects on the low-lying n-->pi* excitation energy and the 15N nuclear magnetic shielding of pyrazine and pyridazine in aqueous environment. The results obtained with PCM-MM\\/QM are compared with two other

Vinícius Manzoni; Marcelo L. Lyra; Kaline Coutinho; Sylvio Canuto

2011-01-01

45

Glycosaminoglycans (GAGs) play an important role in many biological processes in the extracellular matrix. In a theoretical approach, structures of monosaccharide building blocks of natural GAGs and their sulfated derivatives were optimized by a B3LYP6311ppdd//B3LYP/6-31+G(d) method. The dependence of the observed conformational properties on the applied methodology is described. NMR chemical shifts and proton-proton spin-spin coupling constants were calculated using the GIAO approach and analyzed in terms of the method's accuracy and sensitivity towards the influence of sulfation, O1-methylation, conformations of sugar ring, and ? dihedral angle. The net sulfation of the monosaccharides was found to be correlated with the 1H chemical shifts in the methyl group of the N-acetylated saccharides both theoretically and experimentally. The ? dihedral angle conformation populations of free monosaccharides and monosaccharide blocks within polymeric GAG molecules were calculated by a molecular dynamics approach using the GLYCAM06 force field and compared with the available NMR and quantum mechanical data. Qualitative trends for the impact of sulfation and ring conformation on the chemical shifts and proton-proton spin-spin coupling constants were obtained and discussed in terms of the potential and limitations of the computational methodology used to be complementary to NMR experiments and to assist in experimental data assignment.

Samsonov, Sergey A.; Riemer, Thomas; Huster, Daniel; Pisabarro, M. Teresa

2014-01-01

46

GHMP kinases are a group of structurally related small molecule kinases. They have been found in all kingdoms of life and are mostly responsible for catalyzing the ATP-dependent phosphorylation of intermediary metabolites. Although the GHMP kinases are of clinical, pharmaceutical, and biotechnological importance, the mechanism of GHMP kinases is controversial. A catalytic base mechanism was suggested for mevalonate kinase that has a structural feature of the ?-phosphate of ATP close to an aspartate residue; however, for one GHMP family member, homoserine kinase, where the residue acting as general base is absent, a direct phosphorylation mechanism was suggested. Furthermore, it was proposed by some authors that all the GHMP kinases function by a similar mechanism. This controversy in mechanism has limited our ability to exploit these enzymes as drug targets and in biotechnology. Here the phosphorylation reaction mechanism of the human galactokinase, a member of the GHMP kinase family, was investigated using molecular dynamics simulations and density functional theory-based quantum mechanics/molecular mechanics calculations (B3LYP-D/AMBER99). The reaction coordinates were localized by potential energy scan using an adiabatic mapping method. Our results indicate that a highly conserved Glu174 captures Arg105 in the proximity of the ?-phosphate of ATP, forming a H-bond network; therefore, the mobility of ATP in the large oxyanion hole is restricted. Arg228 functions to stabilize the negative charge developed at the ?,?-bridging oxygen of the ATP during bond cleavage. The reaction occurs via a direct phosphorylation mechanism, and the Asp186 in the proximity of ATP does not directly participate in the reaction pathway. Because Arg228 is not conserved among GHMP kinases, reagents which form interactions with Arg228, and therefore can interrupt its function in phosphorylation, may be developed into potential selective inhibitors for galactokinase. PMID:23786354

Huang, Meilan; Li, Xiaozhou; Zou, Jian-Wei; Timson, David J

2013-07-16

47

Because of the increasing resistance of malaria parasites to antimalarial drugs, the lack of highly effective vaccines, and an inadequate control of mosquito vectors, the problem is growing, especially in the developing world. New approaches to drug development are consequently required. One of the proteases involved in the degradation of human hemoglobin is named falcipain-2 (FP2), which has emerged as a promising target for the development of novel antimalarial drugs. However, very little is known about the inhibition of FP2. In this paper, the inhibition of FP2 by the epoxysuccinate E64 has been studied by molecular dynamics (MD) simulations using hybrid AM1d/MM and M06-2X/MM potentials to obtain a complete picture of the possible free energy reaction paths. A thorough analysis of the reaction mechanism has been conducted to understand the inhibition of FP2 by E64. According to our results, the irreversible attack of Cys42 on E64 can take place on both carbon atoms of the epoxy ring because both processes present similar barriers. While the attack on the C2 atom presents a slightly smaller barrier (12.3 vs 13.6 kcal mol(-1)), the inhibitor-protein complex derived from the attack on C3 appears to be much more stabilized. In contrast to previous hypotheses, our results suggest that residues such as Gln171, Asp170, Gln36, Trp43, Asn81, and even His174 would be anchoring the inhibitor in a proper orientation for the reaction to take place. These results may be useful for the rational design of new compounds with higher inhibitory activity. PMID:24811524

Arafet, Kemel; Ferrer, Silvia; Martí, Sergio; Moliner, Vicent

2014-05-27

48

We report a combined quantum mechanics/molecular mechanics (QM/MM) study to determine the protein-ligand interaction energy between CDK2 (cyclin-dependent kinase 2) and five inhibitors with the N2-substituted 6-cyclohexylmethoxypurine scaffold. The computational results in this work show that the QM/MM interaction energy is strongly correlated to the biological activity and can be used as a predictor, at least within a family of substrates. A detailed analysis of the protein-ligand structures obtained from molecular dynamics simulations shows specific interactions within the active site that, in some cases, have not been reported before to our knowledge. The computed interaction energy gauges the strength of protein-ligand interactions. Finally, energy decomposition and multiple regression analyses were performed to check the contribution of the electrostatic and van der Waals energies to the total interaction energy and to show the capabilities of the computational model to identify new potent inhibitors.

Alzate-Morales, Jans H.; Contreras, Renato; Soriano, Alejandro; Tunon, Inaki; Silla, Estanislao

2007-01-01

49

We have established a quantum mechanics (QM)/molecular mechanics (MM) hybrid method for calculating the Raman spectra of protein-bound cofactors using the ?-subunit of C-phycocyanin containing a phycocyanobilin (PCB) chromophore as a test case. The PCB cofactor was described with density functional theory, whereas the protein matrix was treated with the CHARMM force field. The Hessian matrix of the QM region was built by taking into account bonded and nonbonded interactions with the protein environment and projected onto the internal coordinate space. Force constants were scaled with a global set of scaling factors, and the Raman intensities were computed using a finite-field method combined with a fourth-order differentiation algorithm for the calculation of the polarizability derivatives. In general, the QM/MM results provided a substantially improved description of the experimental resonance Raman (RR) spectra of the protein-bound cofactor compared to QM calculations of isolated PCB models in vacuo. The results allow the assessment of the effect of the protein-cofactor interactions on the RR spectra and reveal the potential and limitations of QM calculations on isolated tetrapyrroles for determining the chromophore structures in the various species and states of phytochromes for which three-dimensional structures are not available.

Mroginski, Maria Andrea; Mark, Franz; Thiel, Walter; Hildebrandt, Peter

2007-01-01

50

The catalytic mechanism of MsrA in Mycobacterium tuberculosis, in which S-methionine sulfoxide (Met-O) is reduced to methionine (Met), has been investigated using docking, molecular dynamics (MD) simulations, and ONIOM (quantum mechanics/molecular mechanics) methods. In addition, the roles of specific active site residues, including an aspartyl (Asp87) near the recycling cysteine, tyrosyls (Tyr44 and Tyr92), and glutamyl (Glu52), have been examined, as well as the general effects of the protein and active site on the nature and properties of mechanistic intermediates. The mechanism is initiated by the transfer of a proton from the catalytic cysteine's thiol (Cys13SH) via a bridging water to the R group carboxylate of Glu52. The now anionic sulfur of Cys13 nucleophilically attacks the substrate's sulfur with concomitant transfer of a proton from Glu52 to the sulfoxide oxygen, generating a sulfurane. The active site enhances the proton affinity of the sulfurane oxygen, which can readily accept a proton from the phenolic hydroxyls of Tyr44 or Tyr92 to give a sulfonium cation. Subsequently, Asp87 and the recycling cysteine (Cys154) can facilitate nucleophilic attack of a solvent water at the Cys13S center of the sulfonium to give a sulfenic acid (Cys13SOH) and Met. For the subsequent reduction of Cys13SOH with intramolecular disulfide bond formation, Asp87 can help facilitate nucleophilic attack of Cys154S at the sulfur of Cys13SOH by deprotonating its thiol. This reduction is found likely to occur readily upon suitable positioning of the active site hydrogen bond network and the sulfur centers of both Cys13 and Cys154. The calculated rate-limiting barrier is in good agreement with experiment. PMID:23418817

Dokainish, Hisham M; Gauld, James W

2013-03-12

51

AlkB repair enzymes are important nonheme iron enzymes that catalyse the demethylation of alkylated DNA bases in humans, which is a vital reaction in the body that heals externally damaged DNA bases. Its mechanism is currently controversial and in order to resolve the catalytic mechanism of these enzymes, a quantum mechanics/molecular mechanics (QM/MM) study was performed on the demethylation of the N1-methyladenine fragment by AlkB repair enzymes. Firstly, the initial modelling identified the oxygen binding site of the enzyme. Secondly, the oxygen activation mechanism was investigated and a novel pathway was found, whereby the catalytically active iron(IV)–oxo intermediate in the catalytic cycle undergoes an initial isomerisation assisted by an Arg residue in the substrate binding pocket, which then brings the oxo group in close contact with the methyl group of the alkylated DNA base. This enables a subsequent rate-determining hydrogen-atom abstraction on competitive ?-and ?-pathways on a quintet spin-state surface. These findings give evidence of different locations of the oxygen and substrate binding channels in the enzyme and the origin of the separation of the oxygen-bound intermediates in the catalytic cycle from substrate. Our studies are compared with small model complexes and the effect of protein and environment on the kinetics and mechanism is explained.

Quesne, Matthew G; Latifi, Reza; Gonzalez-Ovalle, Luis E; Kumar, Devesh; de Visser, Sam P

2014-01-01

52

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

2013-09-11

53

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

54

Chagas' disease, also known as American trypanosomiasis, is a lethal, chronic disease that currently affects more than 10 million people in Central and South America. The trans-sialidase from Trypanosoma cruzi (T. cruzi, TcTS) is a crucial enzyme for the survival of this parasite: sialic acids from the host are transferred to the cell surface glycoproteins of the trypanosome, thereby evading the host's immune system. On the other hand, the sialidase of T. rangeli (TrSA), which shares 70% sequence identity with TcTS, is a strict hydrolase and shows no trans-sialidase activity. Therefore, TcTS and TrSA represent an excellent framework to understand how different catalytic activities can be achieved with extremely similar structures. By means of combined quantum mechanics-molecular mechanics (QM/MM, SCC-DFTB/Amberff99SB) calculations and umbrella sampling simulations, we investigated the hydrolysis mechanisms of TcTS and TrSA and computed the free energy profiles of these reactions. The results, together with our previous computational investigations, are able to explain the catalytic mechanism of sialidases and describe how subtle differences in the active site make TrSA a strict hydrolase and TcTS a more efficient trans-sialidase. PMID:24814976

Bueren-Calabuig, Juan A; Pierdominici-Sottile, Gustavo; Roitberg, Adrian E

2014-06-01

55

We have developed a hybrid approach based on a combination of integral equation theory of molecular liquids and QM\\/MM methodology in NorthWest computational Chemistry (NWChem) software package. We have split the evaluations into consequent QM\\/MM and statistical mechanics calculations based on the one-dimensional reference interaction site model, which allows us to reduce signicantly the time of computation. The method complements

Gennady N. Chuev; Marat Valiev; Marina V. Fedotova

2012-01-01

56

Quantum Mechanical/Molecular Mechanical (QM/MM) geometry optimizations of the X-ray crystal structures of PDE10-AMP (PDB code 2OUN) and PDE10-GMP (PDB code 2OUQ) complexes have been performed to characterize the state of the AMP and GMP products, respectively. Results show that only one phosphate oxygen atom (O1) is protonated for both AMP and GMP product complexes. In addition, the QM/MM calculations have resolved the orientation of the amide group of Gln726 in PDE10-GMP which was in conflict with the assignment of the guanine group of GMP in the X-ray crystal structure. Calculations reveal that the amide oxygen and nitrogen atom of Gln726 are rotated 180° resulting in two strong hydrogen bonds formed between the amide group of Gln726 and guanine group of GMP. Binding free energy calculations for both QM/MM optimized structures confirm the new conformational assignment of Gln726 in PDE10-GMP. The calculated binding free energy of the rotated structure is ~22 kcal/mol lower than the X-ray crystal assignment. The lower energy is mainly derived from the formation of two hydrogen bonds between the amide group of Gln726 and guanine group of GMP. This implies that the orientation of the amide oxygen and nitrogen atoms in PDE10-AMP is different from PDE10-GMP. Finally, our results help to understand why PDE10 can hydrolyze both cAMP and cGMP.

Lu, Haiting; Goren, Alan C.; Zhan, Chang-Guo

2010-01-01

57

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

58

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

59

The authors present a method based on a linear response theory that allows one to optimize the geometries of quantum mechanical/molecular mechanical (QM/MM) systems on the free energy surfaces. Two different forms of linear response free energy functionals are introduced, and electronic wave functions of the QM region, as well as the responses of electrostatic and Lennard-Jones potentials between QM and MM regions, are self-consistently determined. The covariant matrix relating the QM charge distribution to the MM response is evaluated by molecular dynamics (MD) simulation of the MM system. The free energy gradients with respect to the QM atomic coordinates are also calculated using the MD trajectory results. They apply the present method to calculate the free energy profiles of Menshutkin-type reaction of NH3 with CH3Cl and Claisen rearrangement of allyl vinyl ether in aqueous solution. For the Menshutkin reaction, the free energy profile calculated with the modified linear response free energy functional is in good agreement with that by the free energy perturbation calculations. They examine the nonequilibrium solvation effect on the transmission coefficient and the kinetic isotope effect for the Claisen rearrangement. PMID:17444719

Higashi, Masahiro; Hayashi, Shigehiko; Kato, Shigeki

2007-04-14

60

NASA Astrophysics Data System (ADS)

The authors present a method based on a linear response theory that allows one to optimize the geometries of quantum mechanical/molecular mechanical (QM/MM) systems on the free energy surfaces. Two different forms of linear response free energy functionals are introduced, and electronic wave functions of the QM region, as well as the responses of electrostatic and Lennard-Jones potentials between QM and MM regions, are self-consistently determined. The covariant matrix relating the QM charge distribution to the MM response is evaluated by molecular dynamics (MD) simulation of the MM system. The free energy gradients with respect to the QM atomic coordinates are also calculated using the MD trajectory results. They apply the present method to calculate the free energy profiles of Menshutkin-type reaction of NH3 with CH3Cl and Claisen rearrangement of allyl vinyl ether in aqueous solution. For the Menshutkin reaction, the free energy profile calculated with the modified linear response free energy functional is in good agreement with that by the free energy perturbation calculations. They examine the nonequilibrium solvation effect on the transmission coefficient and the kinetic isotope effect for the Claisen rearrangement.

Higashi, Masahiro; Hayashi, Shigehiko; Kato, Shigeki

2007-04-01

61

NASA Astrophysics Data System (ADS)

A new method called adaptive force matching (AFM) has been developed that is capable of producing high quality force fields for condensed phase simulations. This procedure involves the parametrization of force fields to reproduce ab initio forces obtained from condensed phase quantum-mechanics/molecular-mechanics (QM/MM) calculations. During the procedure, the MM part of the QM/MM is iteratively improved so as to approach ab initio quality. In this work, the AFM method has been tested to parametrize force fields for liquid water so that the resulting force fields reproduce forces calculated using the ab initio MP2 and the Kohn-Sham density functional theory with the Becke-Lee-Yang-Parr (BLYP) and Becke three-parameter LYP (B3LYP) exchange correlation functionals. The AFM force fields generated in this work are very simple to evaluate and are supported by most molecular dynamics (MD) codes. At the same time, the quality of the forces predicted by the AFM force fields rivals that of very expensive ab initio calculations and are found to successfully reproduce many experimental properties. The site-site radial distribution functions (RDFs) obtained from MD simulations using the force field generated from the BLYP functional through AFM compare favorably with the previously published RDFs from Car-Parrinello MD simulations with the same functional. Technical aspects of AFM such as the optimal QM cluster size, optimal basis set, and optimal QM method to be used with the AFM procedure are discussed in this paper.

Akin-Ojo, Omololu; Song, Yang; Wang, Feng

2008-08-01

62

We have developed a hybrid approach based on a combination of integral equation theory of molecular liquids and QM/MM methodology in NorthWest computational Chemistry (NWChem) software package. We have split the evaluations into conse- quent QM/MM and statistical mechanics calculations based on the one-dimensional reference interaction site model, which allows us to reduce signicantly the time of computation. The method complements QM/MM capabilities existing in the NWChem package. The accuracy of the presented method was tested through com- putation of water structure around several organic solutes and their hydration free energies. We have also evaluated the solvent effect on the conformational equilibria. The applicability and limitations of the developed approach are discussed.

Chuev, Gennady N.; Valiev, Marat; Fedotova, Marina V.

2012-04-10

63

NASA Astrophysics Data System (ADS)

In the present work, we have performed quantum chemical calculations to determine preferable species among the ionic complexes that are present in ambient water due to the autodissociation of water molecule. First, we have formulated the relative population of the hydrated complexes with respect to the bare ion (H3O+ or OH-) in terms of the solvation free energies of the relevant molecules. The solvation free energies for various ionic species (H3O+, H5O2+, H7O3+, H9O4+ or OH-, H3O2-, H5O3-, H7O4-, H9O5-), categorized as proton or hydroxide ion in solution, have been computed by employing the QM/MM-ER method recently developed by combining the quantum mechanical/molecular mechanical (QM/MM) approach with the theory of energy representation (ER). Then, the computed solvation free energies have been used to evaluate the ratio of the populations of the ionic complexes to that of the bare ion (H3O+ or OH-). Our results suggest that the Zundel form, i.e., H5O2+, is the most preferable in the solution among the cationic species listed above though the Eigen form (H9O4+) is very close to the Zundel complex in the free energy, while the anionic fragment from water molecules mostly takes the form of OH-. It has also been found that the loss of the translational entropy of water molecules associated with the formation of the complex plays a role in determining the preferable size of the cluster.

Takahashi, Hideaki; Ohno, Hajime; Yamauchi, Toshihiko; Kishi, Ryohei; Furukawa, Shin-Ichi; Nakano, Masayoshi; Matubayasi, Nobuyuki

2008-02-01

64

The (23)Na quadrupolar coupling constant of the Na(+) ion in aqueous solution has been predicted using molecular dynamics simulations and hybrid quantum mechanics/molecular mechanics methods for the calculation of electric field gradients. The developed computational approach is generally expected to provide reliable estimates of the quadrupolar coupling constants of monoatomic species in condensed phases, and we show here that intermolecular polarization and non-electrostatic interactions are of crucial importance as they result in a 100% increased quadrupolar coupling constant of the ion as compared to a simpler pure electrostatic picture. These findings question the reliability of the commonly applied classical Sternheimer approximation for the calculations of the electric field gradient. As it can be expected from symmetry considerations, the quadrupolar coupling constants of the 5- and 6-coordinated Na(+) ions in solution are found to differ significantly. PMID:23247548

Aidas, K?stutis; Ågren, Hans; Kongsted, Jacob; Laaksonen, Aatto; Mocci, Francesca

2013-02-01

65

In this review paper, we will give an overview of recent theoretical studies on the catalytic cycle(s) of NOS (nitric oxide synthase) enzymes and in particular on the later stages of these cycles where experimental work is difficult due to the short lifetime of intermediates. NOS enzymes are vital for human health and are involved in the biosynthesis of toxic nitric oxide. Despite many experimental efforts in the field, the catalytic cycle of this important enzyme is still surrounded by many unknowns and controversies. Our theoretical studies were focused on the grey zones of the catalytic cycle, where intermediates are short-lived and experimental detection is impossible. Thus combined QM/MM (quantum mechanics/molecular mechanics) as well as DFT (density functional theory) studies on NOS enzymes and active site models have established a novel mechanism of oxygen activation and the conversion of L-arginine into N(omega)-hydroxo-arginine. Although NOS enzymes show many structural similarities to cytochrome P450 enzymes, it has long been anticipated that therefore they should have a similar catalytic cycle where molecular oxygen binds to a haem centre and is converted into an Fe(IV)-oxo haem(+*) active species (Compound I). Compound I, however, is elusive in the cytochrome P450s as well as in NOS enzymes, but indirect experimental evidence on cytochrome P450 systems combined with theoretical modelling have shown it to be the oxidant responsible for hydroxylation reactions in cytochrome P450 enzymes. By contrast, in the first catalytic cycle of NOS it has been shown that Compound I is first reduced to Compound II before the hydroxylation of arginine. Furthermore, substrate arginine in NOS enzymes appears to have a dual function, namely first as a proton donor in the catalytic cycle to convert the ferric-superoxo into a ferric-hydroperoxo complex and secondly as the substrate that is hydroxylated in the process leading to N(omega)-hydroxo-arginine. PMID:19290865

de Visser, Sam P

2009-04-01

66

Since Vogt's discovery of A(3)-retinal or 3-hydroxyretinal in insects in 1983 and Matsui's discovery of A(4)-retinal or 4-hydroxyretinal in firefly squid in 1988, hydroxyretinal-protein interactions mediating vision have remained largely unexplored. In the present study, A(3)- and A(4)-retinals are theoretically incorporated into squid and bovine visual pigments by use of the hybrid quantum mechanics/molecular mechanics [SORCI+Q//B3LYP/6-31G(d):Amber96] method, and insights into structure, enantioselectivity, and spectroscopy are gathered and presented for the first time. Contrary to general perception, our findings rule out the formation of a hydrogen bond between the hydroxyl-bearing ?-ionone ring portion of retinal and opsin. Compared to A(1)-pigments, A(3)- and A(4)-pigments exhibit slightly blue-shifted absorption maxima due to increase in bond-length alternation of the hydroxyretinal. We suggest that (i) the binding site of firefly squid (Watasenia scintillans) opsin is very similar to that of the Japanese common squid (Todarodes pacificus) opsin; (ii) the molecular mechanism of spectral tuning in small white butterflies involve sites S116 and T185 and breaking of a hydrogen bond between sites E180 and T185; and finally (iii) A(3)-retinal may have occurred during the conversion of A(1)- to A(2)-retinal and insects may have acquired them, in order to absorb light in the blue-green wavelength region and to speed up the G-protein signaling cascade. PMID:22087641

Sekharan, Sivakumar; Yokoyama, Shozo; Morokuma, Keiji

2011-12-29

67

The present work addresses the solvatochromic shift of phenol blue (PB) dye. For this purpose the results of Car-Parrinello molecular dynamics (CPMD) simulations for PB in gas phase are compared with results obtained for PB in water from CPMD hybrid quantum mechanics-molecular mechanics (CPMD-QM/MM) calculations. The absorption spectra were obtained using the intermediate neglect of differential overlap/spectroscopic-configuration interaction (INDO/CIS) method and were calculated for a multitude of configurations of the trajectory. The calculated lambda(max) for PB in gas phase was found to be about 535 nm, which is considerably lower than the lambda(max) reported for PB in nonpolar solvents. Different solvation shells for PB in water have been defined based on the solute-all-atoms and solvent center of mass radial distribution function (g(r(X-O))). The electronic excitation energies for PB computed in the presence of solvent molecules in an increasing number of solvation shells were calculated in a systematic way to evaluate their contributions to the solvatochrmic shift. The inclusion of solvent molecules in the hydration shell yields a lambda(max) of 640 nm, which contributes to almost 78% of the solvatochromic shift. The inclusion of solvent molecules up to 10 A in the g(r(X-O)) rdf yields a lambda(max) of 670 nm which is in good agreement with the experimentally reported value of 654-684 nm. Overall, the present study suggests that the combined CPMD-QM/MM and INDO-CIS approach can be used successfully to model solvatochromic shifts of organic dye molecules. PMID:20572722

Murugan, N Arul; Jha, Prakash Chandra; Rinkevicius, Z; Ruud, Kenneth; Agren, Hans

2010-06-21

68

NASA Astrophysics Data System (ADS)

The present work addresses the solvatochromic shift of phenol blue (PB) dye. For this purpose the results of Car-Parrinello molecular dynamics (CPMD) simulations for PB in gas phase are compared with results obtained for PB in water from CPMD hybrid quantum mechanics-molecular mechanics (CPMD-QM/MM) calculations. The absorption spectra were obtained using the intermediate neglect of differential overlap/spectroscopic-configuration interaction (INDO/CIS) method and were calculated for a multitude of configurations of the trajectory. The calculated ?max for PB in gas phase was found to be about 535 nm, which is considerably lower than the ?max reported for PB in nonpolar solvents. Different solvation shells for PB in water have been defined based on the solute-all-atoms and solvent center of mass radial distribution function (g(rX-O)). The electronic excitation energies for PB computed in the presence of solvent molecules in an increasing number of solvation shells were calculated in a systematic way to evaluate their contributions to the solvatochrmic shift. The inclusion of solvent molecules in the hydration shell yields a ?max of 640 nm, which contributes to almost 78% of the solvatochromic shift. The inclusion of solvent molecules up to 10 A? in the g(rX-O) rdf yields a ?max of 670 nm which is in good agreement with the experimentally reported value of 654-684 nm. Overall, the present study suggests that the combined CPMD-QM/MM and INDO-CIS approach can be used successfully to model solvatochromic shifts of organic dye molecules.

Murugan, N. Arul; Jha, Prakash Chandra; Rinkevicius, Z.; Ruud, Kenneth; A?Gren, Hans

2010-06-01

69

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 D2O and H2O 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.

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

2013-01-01

70

A combination of the polarizable continuum model (PCM) and the hybrid quantum mechanics/molecular mechanics (QM/MM) methodology, PCM-MM/QM, is used to include the solute electronic polarization and then study the solvent effects on the low-lying n??(?) excitation energy and the (15)N nuclear magnetic shielding of pyrazine and pyridazine in aqueous environment. The results obtained with PCM-MM/QM are compared with two other procedures, i.e., the conventional PCM and the iterative and sequential QM/MM (I-QM/MM). The QM calculations are made using density functional theory in the three procedures. For the excitation energies, the time-dependent B3LYP/6-311+G(d) model is used. For the magnetic shielding, the B3LYP/aug-pcS2(N)/pcS2(C,O,H) is used with the gauge-including atomic orbitals. In both cases, i.e., PCM-MM/QM and I-QM/MM, that use a discrete model of the solvent, the solute is surrounded by a first shell of explicit water molecules embedded by an electrostatic field of point charges for the outer shells. The best results are obtained including 28 explicit water molecules for the spectral calculations and 9 explicit water molecules for the magnetic shielding. Using the PCM-MM/QM methodology the results for the n??(?) excitation energies of pyridazine and pyrazine are 32,070 ± 80 cm(-1) and 32,675 ± 60 cm(-1), respectively, in good agreement with the corresponding I-MM/QM results of 32,540 ± 80 cm(-1) and 32,710 ± 60 cm(-1) and the experimental results of 33,450-33,580 cm(-1) and 32,700-33,300 cm(-1). For the (15)N magnetic shielding, the corresponding numbers for the gas-water shifts obtained with PCM-MM/QM are 47.4 ± 1.3 ppm for pyridazine and 19.7 ± 1.1 ppm for pyrazine, compared with the I-QM/MM values of 53.4?±?1.3 ppm and 19.5 ± 1.2 ppm and the experimental results of 42-54 ppm and 17-22 ppm, respectively. The agreement between the two procedures is found to be very good and both are in agreement with the experimental values. PCM-MM/QM approach gives a good solute polarization and could be considered in obtaining reliable results within the expected QM/MM accuracy. With this electronic polarization, the solvent effects on the electronic absorption spectra and the (15)N magnetic shielding of the diazines in water are well described by using only an electrostatic approximation. Finally, it is remarked that the experimental and theoretical results suggest that the (15)N nuclear magnetic shielding of any diazine has a clear dependence with the solvent polarity but not directly with the solute-solvent hydrogen bonds. PMID:22010694

Manzoni, Vinícius; Lyra, Marcelo L; Coutinho, Kaline; Canuto, Sylvio

2011-10-14

71

NASA Astrophysics Data System (ADS)

A combination of the polarizable continuum model (PCM) and the hybrid quantum mechanics/molecular mechanics (QM/MM) methodology, PCM-MM/QM, is used to include the solute electronic polarization and then study the solvent effects on the low-lying n-->?* excitation energy and the 15N nuclear magnetic shielding of pyrazine and pyridazine in aqueous environment. The results obtained with PCM-MM/QM are compared with two other procedures, i.e., the conventional PCM and the iterative and sequential QM/MM (I-QM/MM). The QM calculations are made using density functional theory in the three procedures. For the excitation energies, the time-dependent B3LYP/6-311+G(d) model is used. For the magnetic shielding, the B3LYP/aug-pcS2(N)/pcS2(C,O,H) is used with the gauge-including atomic orbitals. In both cases, i.e., PCM-MM/QM and I-QM/MM, that use a discrete model of the solvent, the solute is surrounded by a first shell of explicit water molecules embedded by an electrostatic field of point charges for the outer shells. The best results are obtained including 28 explicit water molecules for the spectral calculations and 9 explicit water molecules for the magnetic shielding. Using the PCM-MM/QM methodology the results for the n-->?* excitation energies of pyridazine and pyrazine are 32 070 +/- 80 cm-1 and 32 675 +/- 60 cm-1, respectively, in good agreement with the corresponding I-MM/QM results of 32 540 +/- 80 cm-1 and 32 710 +/- 60 cm-1 and the experimental results of 33 450-33 580 cm-1 and 32 700-33 300 cm-1. For the 15N magnetic shielding, the corresponding numbers for the gas-water shifts obtained with PCM-MM/QM are 47.4 +/- 1.3 ppm for pyridazine and 19.7 +/- 1.1 ppm for pyrazine, compared with the I-QM/MM values of 53.4 +/- 1.3 ppm and 19.5 +/- 1.2 ppm and the experimental results of 42-54 ppm and 17-22 ppm, respectively. The agreement between the two procedures is found to be very good and both are in agreement with the experimental values. PCM-MM/QM approach gives a good solute polarization and could be considered in obtaining reliable results within the expected QM/MM accuracy. With this electronic polarization, the solvent effects on the electronic absorption spectra and the 15N magnetic shielding of the diazines in water are well described by using only an electrostatic approximation. Finally, it is remarked that the experimental and theoretical results suggest that the 15N nuclear magnetic shielding of any diazine has a clear dependence with the solvent polarity but not directly with the solute-solvent hydrogen bonds.

Manzoni, Vinícius; Lyra, Marcelo L.; Coutinho, Kaline; Canuto, Sylvio

2011-10-01

72

The formation of Compound I (Cpd I), the active species of the enzyme chloroperoxidase (CPO), was studied using QM/MM calculation. Starting from the substrate complex with hydrogen peroxide, FeIII-HOOH, we examined two alternative mechanisms on the three lowest spin-state surfaces. The calculations showed that the preferred pathway involves heterolytic O-O cleavage that proceeds via the iron hydroperoxide species, i.e., Compound 0 (Cpd 0), on the doublet-state surface. This process is effectively concerted, with a barrier of 12.4 kcal/mol, and is catalyzed by protonation of the distal OH group of Cpd 0. By comparison, the path that involves a direct O-O cleavage from FeIII-HOOH is less favored. A proton coupled electron transfer (PCET) feature was found to play an important role in the mechanism nascent from Cpd 0. Initially, the O-O cleavage progresses in a homolytic sense, but as soon as the proton is transferred to the distal OH, it triggers an electron transfer from the heme-oxo moiety to form water and Cpd I. This study enables us to generalize the mechanisms of O-O activation, elucidated so far by QM/MM calculations, for other heme enzymes, e.g., cytochrome P450cam, horseradish peroxidase (HRP), nitric oxide synthase (NOS), and heme oxygenase (HO). Much like for CPO, in the cases of P450 and HRP, the PCET lowers the barrier below the purely homolytic cleavage alternative (in our case, the homolytic mechanism is calculated directly from FeIII-HOOH). By contrast, the absence of PCET in HO, along with the robust water cluster, prefers a homolytic cleavage mechanism. PMID:18597525

Chen, Hui; Hirao, Hajime; Derat, Etienne; Schlichting, Ilme; Shaik, Sason

2008-08-01

73

Quantum and molecular mechanics calculations for the Diels-Alder reactions of cyclopentadiene with 1,4-naphthoquinone, methyl vinyl ketone, and acrylonitrile have been carried out at the vacuum-water interface and in the gas phase. In conjunction with previous studies of these cycloadditions in dilute solution, a more complete picture of aqueous environmental effects emerges with implications for the origin of observed rate accelerations using heterogeneous aqueous suspensions, "on water" conditions. The pure TIP4P water slab maintains the bulk density and hydrogen-bonding properties in central water layers. The bulk region merges to vacuum over a ca. 5 A band with progressive diminution of the density and hydrogen bonding. The relative free energies of activation and transition structures for the reactions at the interface are found to be intermediate between those calculated in the gas phase and in bulk water; i.e., for the reaction with 1,4-naphthoquinone, the DeltaDeltaG(++) values relative to the gas phase are -3.6 and -7.3 kcal/mol at the interface and in bulk water, respectively. Thus, the results do not support the notion that a water surface is more effective than bulk water for catalysis of such pericyclic reactions. The trend is in qualitative agreement with expectations based on density considerations and estimates of experimental rate constants for the gas phase, a heterogeneous aqueous suspension, and a dilute aqueous solution for the reaction of cyclopentadiene with methyl vinyl ketone. Computed energy pair distributions reveal a uniform loss of 0.5-1.0 hydrogen bond for the reactants and transition states in progressing from bulk water to the vacuum-water interface. Orientational effects are apparent at the surface; e.g., the carbonyl group in the methyl vinyl ketone transition structure is preferentially oriented into the surface. Also, the transition structure for the 1,4-naphthoquinone case is buried more in the surface, and the free energy of activation for this reaction is most similar to the result in bulk water. PMID:20148559

Thomas, Laura L; Tirado-Rives, Julian; Jorgensen, William L

2010-03-10

74

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

75

Naturally occurring intrastrand oxidative cross-link lesions have proven to be a potent source of endogenous DNA damage. Among the variety of lesions that can be formed and have been identified, G[8-5]C damage (in which the C8 atom of a guanine is covalently bonded to the C5 atom of a nearby cytosine belonging to the same strand) occurs with a low incidence yet takes on special importance because of its high mutagenicity. Hybrid Car-Parrinello molecular dynamics simulations, rooted in density functional theory and coupled to molecular mechanics, have been performed to shed light on the cyclization process. The activation free energy of the reacting subsystem embedded in a solvated dodecamer is estimated to be ?12.4 kcal/mol, which is ?3 kcal/mol higher than the value for the prototypical G[8-5m]T lesion inferred employing the same theoretical framework [Garrec, J., Patel, C., Rothlisberger, U., and Dumont, E. (2012) J. Am. Chem. Soc.134, 2111-2119]. This study also situates the G[8-5m]mC lesion at an intermediate activation free energy (?10.5 kcal/mol). The order of reactivity in DNA (T(•) > mC(•) > C(•)) is reversed compared to that in the reacting subsystems in the gas phase (C(•) > mC(•) > T(•)), stressing the crucial role of the solvated B-helix environment. The results of our simulations also characterize a more severe distortion for G[8-5]C than for methylene-bridged intrastrand cross-links. PMID:23256602

Patel, Chandan; Garrec, Julian; Dupont, Céline; Dumont, Elise

2013-01-15

76

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

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

77

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

78

-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

79

NASA Astrophysics Data System (ADS)

Part I. Second Quantization: 1. Elementary quantum mechanics; 2. Identical particles; 3. Second quantization; Part II. Examples: 4. Magnetism; 5. Superconductivity; 6. Superfluidity; Part III. Fields and Radiation: 7. Classical fields; 8. Quantization of fields; 9. Radiation and matter; 10. Coherent states; Part IV. Dissipative Quantum Mechanics: 11. Dissipative quantum mechanics; 12. Transitions and dissipation; Part V. Relativistic Quantum Mechanics: 13. Relativistic quantum mechanics; Index.

Nazarov, Yuli V.; Danon, Jeroen

2013-01-01

80

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

81

NASA Astrophysics Data System (ADS)

Gravity and quantum mechanics tend to stay out of each other's way, but this might change as we devise new experiments to test the applicability of quantum theory to macroscopic systems and larger length scales.

Amelino-Camelia, Giovanni

2014-04-01

82

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

83

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

84

Combined quantum and molecular mechanics (QM/MM).

We describe the current state of the art of mixed quantum mechanics/molecular mechanics (QM/MM) methodology, with a particular focus on modeling of enzymatic reactions. Over the past decade, the effectiveness of these methods has increased dramatically, based on improved quantum chemical methods, advances in the description of the QM/MM interface, and reductions in the cost/performance of computing hardware. Two examples of pharmaceutically relevant applications, cytochrome P450 and class C ?-lactamase, are presented.: PMID:24981493

Friesner, Richard A

2004-12-01

85

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

86

Supersymmetric quantum mechanics.

National Technical Information Service (NTIS)

We summarize recent developments of supersymmetric quantum mechanics. We start from the susy oscillator, mention the factorization schemes and discuss the order of levels of Schroedinger operators as an example. We mention soliton equation and the inverse...

H. Grosse

1989-01-01

87

The Teaching of Quantum Mechanics

NSDL National Science Digital Library

This website has tips and techniques for teaching quantum mechanics. It presents and outlines central ideas in quantum mechanics and includes descriptions of textbooks and software that can be helpful in quantum classes.

Styer, Dan

2003-10-10

88

Supersymmetry in quantum mechanics

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

89

Quantum mechanics for space applications

This paper is an introduction to the following articles in the scope of quantum mechanics for space study initiated by ESA and lead by ONERA. The context of quantum mechanics for space is summarised, and the fields under development are briefly introduced. Technological applications of quantum mechanics in space are explored and some tests of quantum mechanics are outlined. We

A. Bresson; Y. Bidel; P. Bouyer; B. Leone; E. Murphy; P. Silvestrin

2006-01-01

90

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

91

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

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

94

Biorthogonal quantum mechanics

NASA Astrophysics Data System (ADS)

The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called ‘biorthogonal quantum mechanics’, is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems.

Brody, Dorje C.

2014-01-01

95

NASA Astrophysics Data System (ADS)

The axiomatic way of teaching quantum mechanics (QM) is analyzed in the light of its effectiveness in making students ready to understand and use QM. A more intuitive method of teaching QM is proposed. An outline of how a course implementing that method could be structured is presented.

Deumens, Erik

96

Supersymmetric Quantum Mechanics.

National Technical Information Service (NTIS)

We give a general construction for supersymmetric Hamiltonians in quantum mechanics. We find that N-extended supersymmetry imposes very strong constraints, and for N > 4 the Hamiltonian is integrable. We give a variety of examples, for one-particle and fo...

M. de Crombrugghe V. Rittenberg

1982-01-01

97

Geometrizing Relativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of them in the non-relativistic limit.

Falciano, F. T.; Novello, M.; Salim, J. M.

2010-12-01

98

Feynman's simple quantum mechanics

NASA Astrophysics Data System (ADS)

This sample class presents an alternative to the conventional introduction to quantum mechanics and describes its current use in a credit course. This alternative introduction rests on theory presented in professional and popular writings by Richard Feynman. Feynman showed that Nature gives a simple command to the electron: ``Explore all paths.'' All of nonrelativistic quantum mechanics, among other fundamental results, comes from this command. With a desktop computer the student points and clicks to tell a modeled electron which paths to follow. The computer then shows the results, which embody the elemental strangeness and paradoxical behaviors of the world of the very small. Feynman's approach requires few equations and provides a largely non-mathematical introduction to the wave function of conventional quantum mechanics. Draft software and materials already used for two semesters in an e-mail computer conference credit university course show that Feynman's approach works well with a variety of students. The sample class explores computer and written material and describes the next steps in its development.

Taylor, Edwin F.

1997-03-01

99

Logical foundation of quantum mechanics

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

100

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

101

NASA Astrophysics Data System (ADS)

A human being viewing a defocused television tube with sweep voltages turned off will see point scintillations at sufficiently low intensities. We show that quantum mechanics predicts these scintillations. Furthermore, by assuming a response of the human nervous system of a type not inconsistent with experiment, measurement theory is used to show that these scintillations will be distributed in proportion to the magnitude squared of the electron wave function incident upon the television tube screen. This nervous system response is to break up the wave incident upon a spot on the retina into a number of similar waves transmitted by different nerves to the brain. The number of these waves is proportional to the incident energy density. Since the theory itself predicts the proper probability distribution, it is unnecessary to introduce a postulate for it.

Broyles, A. A.

1984-06-01

102

PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics. PMID:23509390

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

2013-04-28

103

Quantum mechanics without measurements

Many of the conceptual problems students have in understanding quantum\\u000amechanics arise from the way probabilities are introduced in standard\\u000a(textbook) quantum theory through the use of measurements. Introducing\\u000aconsistent microscopic probabilities in quantum theory requires setting up\\u000aappropriate sample spaces taking proper account of quantum incompatibility.\\u000aWhen this is done the Schrodinger equation can be used to calculate\\u000aprobabilities

Robert B. Griffiths

2006-01-01

104

Dissipative Forces and Quantum Mechanics

ERIC Educational Resources Information Center

Shows how to include the dissipative forces of classical mechanics in quantum mechanics by the use of non-Hermetian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. (MLH)

Eck, John S.; Thompson, W. J.

1977-01-01

105

Modern Approach to Quantum Mechanics

NASA Astrophysics Data System (ADS)

Inspired by Richard Feynman and J.J. Sakurai, A Modern Approach to Quantum Mechanics lets professors expose their undergraduates to the excitement and insight of Feynman's approach to quantum mechanics while simultaneously giving them a textbook that is well-ordered, logical, and pedagogically sound. This book covers all the topics that are typically presented in a standard upper-level course in quantum mechanics, but its teaching approach is new: Rather than organizing his book according to the historical development of the field and jumping into a mathematical discussion of wave mechanics, Townsend begins his book with the quantum mechanics of spin. Thus, the first five chapters of the book succeed in laying out the fundamentals of quantum mechanics with little or no wave mechanics, so the physics is not obscured by mathematics. Starting with spin systems gives students something new and interesting while providing elegant but straightforward examples of the essential structure of quantum mechanics. When wave mechanics is introduced later, students perceive it correctly as only one aspect of quantum mechanics and not the core of the subject. Praised for its pedagogical brilliance, clear writing, and careful explanations, this book is destined to become a landmark text.

Townsend, John S.

106

Noncommutative Quantum Mechanics and Quantum Cosmology

NASA Astrophysics Data System (ADS)

We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity between momenta is shown to be relevant. We also discuss some qualitative features of the GQW such as the Berry phase. In the context of quantum cosmology we consider a Kantowski-Sachs cosmological model and obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten (SW) map. The WDW equation is explicitly dependent on the noncommutative parameters, ? and ?. We obtain numerical solutions of the noncommutative WDW equation for different values of the noncommutative parameters. We conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommmutativity can be relevant for a selection of possible initial states for the universe.

Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno

107

Classical and Quantum Mechanical Waves

NSDL National Science Digital Library

This web site consists of lecture notes in classical and quantum mechanical waves. The notes include the basics of classical waves including connections to mechanical oscillators, wave packets, and acoustic and electromagnetic waves. The final section outlines the key concepts of the quantum mechanical wave equation including probability and current, free and bound states, time dependent perturbation theory, and radiation. Visual Python and Maple animations are included for download.

Riley, Lewis

2006-07-22

108

Quantum Mechanics: Ontology Without Individuals

NASA Astrophysics Data System (ADS)

The purpose of the present paper is to consider the traditional interpretive problems of quantum mechanics from the viewpoint of a modal ontology of properties. In particular, we will try to delineate a quantum ontology that (i) is modal, because describes the structure of the realm of possibility, and (ii) lacks the ontological category of individual. The final goal is to supply an adequate account of quantum non-individuality on the basis of this ontology.

da Costa, Newton; Lombardi, Olimpia

2014-03-01

109

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

110

Quantum chemical study of the mechanism of action of vitamin K epoxide reductase (VKOR)

NASA Astrophysics Data System (ADS)

Possible model, but simplistic, mechanisms for the action of vitamin K epoxide reductase (VKOR) are investigated with quantum mechanical methods (B3LYP/6-311G**). The geometries of proposed model intermediates in the mechanisms are energy optimized. Finally, the energetics of the proposed (pseudo-enzymatic) pathways are compared. We find that the several pathways are all energetically feasible. These results will be useful for designing quantum mechanical/molecular mechanical method (QM/MM) studies of the enzymatic pathway once three-dimensional structural data are determined and available for VKOR.

Deerfield, David, II; Davis, Charles H.; Wymore, Troy; Stafford, Darrel W.; Pedersen, Lee G.

111

NSDL National Science Digital Library

This web site outlines a set of undergraduate physics labs that investigate quantum interference and entanglement with photons. The labs are designed for simplicity and low cost. A description of the lab set up, background information, the lab manual, and several articles on both the curriculum development and research performed in the lab are provided.

Galvez, Enrique; Holbrow, Charles

2005-04-16

112

Quantum Mechanics: Fundamentals

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 Whitaker

2004-01-01

113

ERIC Educational Resources Information Center

Discusses the quantum theory of measurement and von Neumann's catastrophe of infinite regression." Examines three ways of escapint the von Neumann catastrophe, and suggests that the solution to the dilemma of inteterminism is a universe in which all possible outcomes of an experiment actually occur. Bibliography. (LC)

DeWitt, Bryce S.

1970-01-01

114

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

115

An Introduction to Quantum Mechanics

NSDL National Science Digital Library

This Ohio State website provides an introduction to the principles of quantum mechanics as a supplement to the "discussion of hydrogen and many-electron orbitals commonly found in general chemistry text books." Users can find informative text and graphics explaining Classical Mechanics, uncertainty, Pauli Principle, stationary states, and much more. Through the tutorial, students can explore how physical objects can be perceived as both particles and waves. With the Macromedia Shockwave plug-in, visitors can hear discussions of the quantum mechanics topics covered.

Hanlin, Heath; Kitagawa, Midori; Lilas, Zil; Mcdonald, Neal; Singer, Sherwin J. (Sherwin Jeffrey), 1954-; Timasheva, Anna

2007-06-12

116

Kowalevski top in quantum mechanics

The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra. -- Highlights: •Quantum spectra of the Kowalevski top are calculated. •Semiclassical quantization is carried out by the EBK formulation. •Quantum states are labeled by the semiclassical integer quantum numbers. •Multiplicity of the classical torus makes the spectra nearly degenerate. •Symmetries, quantum numbers and near-degenerate spectra are closely related.

Matsuyama, A., E-mail: spamatu@ipc.shizuoka.ac.jp

2013-09-15

117

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 18 centres in Japan during 2002 and 2003 from children with RTIs as part of the PROTEKT surveillance programme. A proportion of Haemophilus influenzae isolates was subjected to sequencing analysis of the ftsI gene; phylogenetic relatedness was assessed using multilocus sequence typing. Streptococcus pneumoniae isolates were screened for macrolide-resistance genotype by polymerase chain reaction and serotyped using the capsular swelling method. Susceptibility of isolates to selected antibacterials was performed using CLSI methodology. Results and Discussion Of the 557 H. influenzae isolates collected, 30 (5.4%) were ?-lactamase-positive [BL+], 115 (20.6%) were BL-nonproducing ampicillin-resistant (BLNAR; MIC ? 4 mg/L) and 79 (14.2%) were BL-nonproducing ampicillin-intermediate (BLNAI; MIC 2 mg/L). Dabernat Group III penicillin binding protein 3 (PBP3) amino acid substitutions in the ftsI gene were closely correlated with BLNAR status but phylogenetic analysis indicated marked clonal diversity. PBP mutations were also found among BL+ and BL-nonproducing ampicillin-sensitive isolates. Of the antibacterials tested, azithromycin and telithromycin were the most active against H. influenzae (100% and 99.3% susceptibility, respectively). A large proportion (75.2%) of the 468 S. pneumoniae isolates exhibited macrolide resistance (erythromycin MIC ? 1 mg/L); erm(B) was the most common macrolide resistance genotype (58.8%), followed by mef(A) (37.2%). The most common pneumococcal serotypes were 6B (19.7%), 19F (13.7%), 23F (13.5%) and 6A (12.8%). Telithromycin and amoxicillin-clavulanate were the most active antibacterials against S. pneumoniae (99.8% and 99.6% susceptibility, respectively). Conclusion Approximately one-third of H. influenzae isolates from paediatric patients in Japan are BLNAI/BLNAR, mainly as a result of clonally diverse PBP3 mutations. Together with the continued high prevalence of pneumococcal macrolide resistance, these results may have implications for the clinical management of paediatric RTIs in Japan.

Sunakawa, Keisuke; Farrell, David J

2007-01-01

118

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

119

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

120

NASA Astrophysics Data System (ADS)

Computational characterization of flexible and polar carbohydrates poses a challenge to current methodologies. We explore a reparametrized semi-empirical quantum mechanical approach within the framework of the PM3 model. Based on fitting to 1,2-ethanediol structures and energies, the modified PM3 Hamiltonian, denoted PM3CARB-1, exhibits improved performance in a number of respects. In particular, 1C 4 ring conformers of glucopyranose are now correctly predicted to be higher in energy than 4C 1 structures. Hybrid quantum mechanical/molecular mechanical molecular dynamics simulations of a model disaccharide, using this PM3CARB-1 model, do not exhibit transitions from 4C 1 to 1C 4 structures.

McNamara, Jonathan P.; Muslim, Abdul-Mueed; Abdel-Aal, Hoda; Wang, Hong; Mohr, Matthias; Hillier, Ian H.; Bryce, Richard A.

2004-08-01

121

Faster than Hermitian quantum mechanics.

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

2007-01-26

122

Quantum Mechanics and Physical Reality

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

123

A quantum mechanical twin paradox

When a quantummechanical wavepacket undergoes a series of Galilean boosts, the Schrödinger theory predicts the occurrence of a geometrical phase effect that is an example of Berry's phase (Sagnac's phase). In the present paper the conceptual consequences of this phenomenon are considered, in particular for the status of Galilean invariance in nonrelativistic quantum mechanics, and for the relation between that

Dennis Dieks

1990-01-01

124

A quantum mechanical twin paradox

NASA Astrophysics Data System (ADS)

When a quantummechanical wavepacket undergoes a series of Galilean boosts, the Schrödinger theory predicts the occurrence of a geometrical phase effect that is an example of Berry's phase (Sagnac's phase). In the present paper the conceptual consequences of this phenomenon are considered, in particular for the status of Galilean invariance in nonrelativistic quantum mechanics, and for the relation between that theory and classical physics.

Dieks, Dennis

1990-08-01

125

Fun with Supersymmetric Quantum Mechanics.

National Technical Information Service (NTIS)

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 alpha / for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpo...

B. Freedman F. Cooper

1984-01-01

126

PT-symmetric quantum mechanics

This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition H†=H on the Hamiltonian, where † represents the mathematical operation of complex conjugation and matrix transposition. This conventional Hermiticity condition is sufficient to ensure that the Hamiltonian H has a real spectrum. However, replacing this mathematical condition by the weaker and more physical requirement

Carl M. Bender; Stefan Boettcher; Peter N. Meisinger

1999-01-01

127

NASA Astrophysics Data System (ADS)

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 ?-->0 and successive quantum corrections are related with powers of ?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 ?'s and ? matrices to get relativistic wave equations that can have spins with values up to n/2. We then decompose the ?'s and ?'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)?O(4)?O(3)?O(2), and from it obtain the spin and mass content of our relativistic equation.

Moshinsky, Marcos

1999-03-01

128

Recent computer simulations of the cysteine nucleophilic attack on propanal in human mitochondrial aldehyde dehydrogenase (ALDH2) yielded an unexpected result: the chemically reasonable formation of a dead-end cysteine-cofactor adduct when NAD+ was in the \\

Troy Wymore; David W. Deerfield II; John Hempel

2007-01-01

129

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

130

Quantum mechanics on noncommutative spacetime

We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a nonrelativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note, however, that noncommutative intrinsic dipole moments are not observable in present experiments searching for an electric dipole moment of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moments are thus incorrect.

Calmet, Xavier; Selvaggi, Michele [Service de Physique Theorique, CP225 Boulevard du Triomphe B-1050 Brussels (Belgium)

2006-08-01

131

Supersymmetric quantum mechanics with reflections

NASA Astrophysics Data System (ADS)

We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q ? -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wavefunctions of extended Scarf I potentials with different parameters are presented.

Post, Sarah; Vinet, Luc; Zhedanov, Alexei

2011-10-01

132

Modern Undergraduate Quantum Mechanics Experiments

NSDL National Science Digital Library

The site describes a collection of simplified quantum mechanics experiments developed at Whitman College by Professor Mark Beck. It links to a complete laboratory manual with the following experiments: (1) Spontaneous Parametric Downconversion, (2) Proof of the Existence of Photons, (3) Single Photon Interference, (4) Testing Local Realism Ã la Hardy. The manual also presents documentation for LabView interfaces to the experimental setups. Equipment lists, apparatus pictures, and a collection of links to additional resources is included.

Beck, Mark

2004-07-10

133

Complementarity in Categorical Quantum Mechanics

NASA Astrophysics Data System (ADS)

We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a `point-free' definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.

Heunen, Chris

2012-07-01

134

Faster than Hermitian Quantum Mechanics

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

135

Helping Students Learn Quantum Mechanics for Quantum Computing

NASA Astrophysics Data System (ADS)

Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantum computing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantum computing.

Singh, Chandralekha

2007-01-01

136

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

137

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

138

Epistemic restrictions in Hilbert space quantum mechanics

NASA Astrophysics Data System (ADS)

A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results in quantum information theory. This analysis provides a quantum mechanical understanding of some recent work that shows that certain kinds of quantum behavior are exhibited by a fully classical model if by hypothesis an observer's knowledge of its state is appropriately limited.

Griffiths, Robert B.

2013-10-01

139

Propagators in polymer quantum mechanics

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 ?{sub 0}, the length scale introduced in the polymer dynamics and which plays a role analog of that of Planck length in Quantum Gravity. -- Highlights: •Formulas for propagators of free and particle in a box in polymer quantum mechanics. •Initial conditions, composition and Green’s function character is checked. •Propagators reduce to corresponding Schrödinger ones in an appropriately defined limit. •Results show overall consistency of the polymer framework. •For the particle in a box results are also verified using formula from method of images.

Flores-González, Ernesto, E-mail: eflores@xanum.uam.mx; Morales-Técotl, Hugo A., E-mail: hugo@xanum.uam.mx; Reyes, Juan D., E-mail: jdrp75@gmail.com

2013-09-15

140

Quantum mechanical light harvesting mechanisms in photosynthesis

NASA Astrophysics Data System (ADS)

More than 10 million billion photons of light strike a leaf each second. Incredibly, almost every red-coloured photon is captured by chlorophyll pigments and initiates steps to plant growth. Last year we reported that marine algae use quantum mechanics in order to optimize photosynthesis [1], a process essential to its survival. These and other insights from the natural world promise to revolutionize our ability to harness the power of the sun. In a recent review [2] we described the principles learned from studies of various natural antenna complexes and suggested how to utilize that knowledge to shape future technologies. We forecast the need to develop ways to direct and regulate excitation energy flow using molecular organizations that facilitate feedback and control--not easy given that the energy is only stored for a billionth of a second. In this presentation I will describe new results that explain the observation and meaning of quantum-coherent energy transfer. [4pt] [1] Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer, and Gregory D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature 463, 644-648 (2010).[0pt] [2] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro and Rienk van Grondelle, ``Lessons from nature about solar light harvesting'' Nature Chem. 3, 763-774 (2011).

Scholes, Gregory

2012-02-01

141

Quantum Mechanical Approximations in Quantum Field Theory.

National Technical Information Service (NTIS)

Some cooperative, coherent effects in quantum field theory, such as spontaneous symmetry violation, bound states, and entrapment of various excitations, can be exposed only by approximation procedures which do not rely on analyticity or regularity in the ...

R. Jackiw

1975-01-01

142

Can quantum mechanics help distributed computing?

We present a brief survey of results where quantum information processing is useful to solve distributed computation tasks. We describe problems that are impossible to solve using classical resources but that become feasible with the help of quantum mechanics. We also give examples where the use of quantum information significantly reduces the need for communication. The main focus of the

Anne Broadbent; Alain Tapp

2008-01-01

143

Are All Probabilities Fundamentally Quantum Mechanical?

The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated that all probabilities may be fundamentally quantum mechanical in the sense that they may all be derived from the corresponding amplitudes. The classical coin-toss and the quantum

Rajat Kumar Pradhan

2011-01-01

144

Causality and Probability in Quantum Mechanics

NASA Astrophysics Data System (ADS)

This paper critically examines the view of quantum mechanics that emerged shortly after the introduction of quantum mechanics and that has been widespread ever since. Although N. Bohr, P. A. M. Dirac, and W. Heisenberg advanced this view earlier, it is best exemplified by J. von Neumann's argument in Mathematical Foundations of Quantum Mechanics (1932) that the transformation of ``a [quantum] state ... under the action of an energy operator ... is purely causal,'' while, ``on the other hand, the state ... which may measure a [given] quantity ... undergoes in a measurement a non-casual change.'' Accordingly, while the paper discusses all four of these arguments, it will especially focus on that of von Neumann. The paper also offers an alternative, noncausal, view of the quantum-mechanical situation and considers the differences between the ensemble and the Bayesian approaches to quantum mechanics from this perspective.

Plotnitsky, Arkady

2009-03-01

145

Quantum mechanics of Proca fields

We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries.

Zamani, Farhad [Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159 (Iran, Islamic Republic of); Mostafazadeh, Ali [Department of Mathematics, Koc University, Rumelifeneri Yolu, Sariyer, Istanbul 34450 (Turkey)

2009-05-15

146

Quantum mechanics: A new chapter?

NASA Astrophysics Data System (ADS)

We review the conceptual problems in quantum mechanics on a fundamental level. It is shown that the proposed model of extended electrons and a clear understanding of rotations in three dimensional space solve a large part of these problems, in particular the problems related to the ontological status and physical meaning of wavefunctions. It also solves the problem of non-locality. The experimental results obtained in Yves Couder's group and theoretical results by Gerdard Grössing indicate that the wave-like distribution of trajectories of electrons in interference experiments are most likely due to the quantized interactions leading to a discrete set of transferred momenta. A separate experimental confirmation of this interpretation for double-slit interferometry of photons has been given by the group of Steinberg.

Hofer, Werner A.

2012-12-01

147

Kindergarten Quantum Mechanics: Lecture Notes

These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns 'doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I which subsumes my Logic of Entanglement. For a survey on the 'what', the 'why' and the 'hows' I refer to a previous set of lecture notes. In a last section we provide some pointers to the body of technical literature on the subject.

Coecke, Bob [Oxford University Computing Laboratory, Wolfson Building, Parks rd, OX1 3QD Oxford (United Kingdom)

2006-01-04

148

Kindergarten Quantum Mechanics: Lecture Notes

NASA Astrophysics Data System (ADS)

These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in [3, 4]) which subsumes my Logic of Entanglement [11]. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes [12, 13]. In a last section we provide some pointers to the body of technical literature on the subject.

Coecke, Bob

2006-01-01

149

Thermodynamic integration from classical to quantum mechanics.

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. PMID:22168684

Habershon, Scott; Manolopoulos, David E

2011-12-14

150

The Quantum Mechanical Many-Body Problem.

National Technical Information Service (NTIS)

A wide variety of quantum mechanical many-body problems were investigated. The two significant accomplishments of this research are as follows: The development of DCF (dynamical characteristic function) method for treating the statistical mechanics of qua...

A. E. Glassgold

1969-01-01

151

On a realistic interpretation of quantum mechanics

The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This opens the door for an interpretation that, while respecting the indeterministic nature of quantum mechanics, allows to speak of definite values for all

Arnold Neumaier

1999-01-01

152

Quantum Mechanics and physical calculations

NASA Astrophysics Data System (ADS)

We suggest to realize the computer simulation and calculation by the algebraic structure built on the basis of the logic inherent to processes in physical systems (called physical computing). We suggest a principle for the construction of quantum algorithms of neuroinformatics of quantum neural networks. The role of academician Sahakyan is emphasized in the development of quantum physics in Armenia.

Karayan, H. S.

2014-03-01

153

Polymer quantum mechanics and its continuum limit

A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.

Corichi, Alejandro [Instituto de Matematicas, Unidad Morelia, Universidad Nacional Autonoma de Mexico, UNAM-Campus Morelia, A. Postal 61-3, Morelia, Michoacan 58090 (Mexico); Departamento de Gravitacion y Teoria de Campos, Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, Mexico D.F. 04510 (Mexico); Institute for Gravitational Physics and Geometry, Physics Department, Pennsylvania State University, University Park, Pennsylvania 16802 (United States); Vukasinac, Tatjana [Facultad de Ingenieria Civil, Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Michoacan 58000 (Mexico); Zapata, Jose A. [Instituto de Matematicas, Unidad Morelia, Universidad Nacional Autonoma de Mexico, UNAM-Campus Morelia, A. Postal 61-3, Morelia, Michoacan 58090 (Mexico)

2007-08-15

154

Quantum mechanics of open systems

NASA Astrophysics Data System (ADS)

In quantum mechanics, there is a set of problems where the system of interest interacts with another system, usually called "environment". This interaction leads to the exchange of energy and information and makes the dynamics of the system of interest essentially non-unitary. Such problems often appeared in condensed matter physics and attracted much attention after recent advances in nanotechnology. As broadly posed as they are, these problems require a variety of different approaches. This thesis is an attempt to examine several of these approaches in applications to different condensed matter problems. The first problem concerns the so-called "Master equation" approach which is very popular in quantum optics. I show that analytic properties of environmental correlators lead to strong restrictions on the applicability of the approach to the strong-coupling regime of interest in condensed matter physics. In the second problem, I use path integrals to treat the localization of particles on attractive short-range potentials when the environment produces an effective viscous friction force. I find that friction changes drastically the localization properties and leads to much stronger localization in comparison to the non-dissipative case. This has implications for the motion of heavy particles in fermionic liquids and, as will be argued below, is also relevant to the problem of high-temperature superconductivity. Finally, the third problem deals with the interplay of geometric phases and energy dissipation which occurs in the motion of vortices in superconductors. It is shown that this interplay leads to interesting predictions for vortex tunneling in high-temperature superconductors which have been partially confirmed by experiments.

Melikidze, Akakii

155

Nonlinear quantum mechanics: Results and open questions

NASA Astrophysics Data System (ADS)

About 15 years ago, we (Heinz-Dietrich Doebner and I) proposed a special type of nonlinear modification of the usual Schrödinger time-evolution equation in quantum mechanics. Our equation was motivated by certain unitary representations of the group of diffeomorphisms of physical space, in the framework of either nonrelativistic local current algebra or quantum Borel kinematics. Subsequently, we developed this and related approaches to nonlinearity in quantum mechanics considerably further, to incorporate theories of measurement, groups of nonlinear gauge transformations, symmetry and invariance properties, unification of a large family of nonlinear perturbations, and possible physical contexts for quantum nonlinearity. Some of our results and highlights of some open questions are summarized.

Goldin, G. A.

2008-05-01

156

The electron hole transfer (HT) properties of DNA are substantially affected by thermal fluctuations of the pi stack structure. Depending on the mutual position of neighboring nucleobases, electronic coupling V may change by several orders of magnitude. In the present paper, we report the results of systematic QM\\/molecular dynamic (MD) calculations of the electronic couplings and on-site energies for the

Alexander A. Voityuk

2008-01-01

157

Emergence of classical theories from quantum mechanics

NASA Astrophysics Data System (ADS)

Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's "first kind of dynamics", and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.

Hájí?ek, P.

2012-05-01

158

Quantum mechanics, CPT violation, and neutral kaons

NASA Astrophysics Data System (ADS)

The neutral kaon system offers a unique possibility to perform fundamental tests of the basic principles of quantum mechanics and of CPT symmetry. The most recent limits obtained by the KLOE experiment at the DA?NE e+e- collider on several kinds of possible decoherence and CPT violation mechanisms, which in some cases might be justified in a quantum gravity framework, are reviewed. No deviation from the expectations of quantum mechanics and CPT symmetry is observed, while the precision of the measurements, in some cases, reaches the interesting Planck scale region. Finally, prospects for this kind of experimental studies at KLOE-2 are presented.

Domenico, Antonio Di

2012-03-01

159

ADDENDUM: Chaos in Bohmian quantum mechanics

In our recently published paper 'Chaos in Bohmian quantum mechanics' we criticized a paper by Parmenter and Valentine (1995 Phys. Lett. A 201 1), because the authors made an incorrect calculation of the Lyapunov exponent in the case of Bohmian orbits in a quantum system of two uncoupled harmonic oscillators. After our paper was published, we became aware of an

C. Efthymiopoulos; G. Contopoulos

2006-01-01

160

Improving Student Understanding of Quantum Mechanics

NASA Astrophysics Data System (ADS)

We are investigating the difficulties that students have in learning upper-level quantum mechanics and designing quantum interactive learning tutorials (QuILTs). Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. The preliminary results from the QuILTs are promising. Coauthors: Mario Belloni and Wolfgang Christian, Davidson College.

Singh, Chandralekha

2006-04-01

161

Student difficulties in learning quantum mechanics

NSDL National Science Digital Library

Reports on a preliminary project that uses a phenomenographic approach to explore the ways in which a small number of fundamental ideas are conceptualized by students who are judged to have mastered quantum mechanics material.

Johnston, Ian D.; Crawford, K.; Fletcher, P. R.

2006-06-19

162

Student Difficulties in Learning Quantum Mechanics.

ERIC Educational Resources Information Center

Reports on a preliminary project that uses a phenomenographic approach to explore the ways in which a small number of fundamental ideas are conceptualized by students who are judged to have mastered quantum mechanics material. (DDR)

Johnston, I. D.; Crawford, K.; Fletcher, P. R.

1998-01-01

163

Quantum mechanical stabilization of Minkowski signature wormholes

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

164

SSQM (Supersymmetric Quantum Mechanics) and Nonlinear Equations.

National Technical Information Service (NTIS)

The method for obtaining the superpartner potential in the supersymmetric quantum mechanics (SSQM) is discussed in connection with the nonlinear equations and the reflectionless potentials. The correspondence between a new class of the soliton solutions t...

J. Hruby V. G. Makhan'kov

1987-01-01

165

Supersymmetric Quantum Mechanics and New Potentials.

National Technical Information Service (NTIS)

Using the supersymmetric quantum mechanics the following potential are generalized. The particle in the box, Poeschl-Teller and Rosen-Morse. The new potentials are evaluated and their eigenfunctions and spectra are indicated. (Atomindex citation 20:038198...

E. Drigo Filho

1988-01-01

166

Supersymmetric quantum mechanics for string-bits.

National Technical Information Service (NTIS)

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...

C. B. Thorn

1997-01-01

167

Functional integral in supersymmetric quantum mechanics.

National Technical Information Service (NTIS)

The solution of the square root of the Schroedinger equation for the supersymmetric quantum mechanics is expressed in the form of series. The formula may be considered as a functional integral of the chronological exponent of the super-pseudodifferential ...

D. V. Ktitarev

1990-01-01

168

Supersymmetric Quantum Mechanics of the Relativistic Particle.

National Technical Information Service (NTIS)

An alternative formulation for the superparticle in a scalar potential is presented. This method is based on a combination between the ground state wave function representation and supersymmetric quantum mechanics. For the free relativistic particle case,...

J. Gamboa J. Zanelli

1986-01-01

169

Fundamental Quantum Mechanics--A Graphic Presentation

ERIC Educational Resources Information Center

Describes a presentation of basic quantum mechanics for nonscience majors that relies on a computer-generated graphic display to circumvent the usual mathematical difficulties. It allows a detailed treatment of free-particle motion in a wave picture. (MLH)

Wise, M. N.; Kelley, T. G.

1977-01-01

170

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

171

Using Optical Transforms To Teach Quantum Mechanics

Wave-particle duality, the superposition principle, the uncertainty principle, and single-particle interference are the most fundamental quantum mechanical concepts. The purpose of this paper is to demonstrate that these quantum mechanical principles are illuminated by a study of diffraction patterns created with laser light and a variety of two-dimensional masks. The principles of X-ray crystallography are generally taught using the Bragg

Frank Rioux; Brian J. Johnson

172

Noncommutative quantum mechanics from noncommutative quantum field theory.

We derive noncommutative multiparticle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Particles of opposite charges are found to have opposite noncommutativity. As a result, there is no noncommutative correction to the hydrogen atom spectrum at the tree level. We also comment on the obstacles to take noncommutative phenomenology seriously and propose a way to construct noncommutative SU(5) grand unified theory. PMID:11955188

Ho, Pei-Ming; Kao, Hsien-Chung

2002-04-15

173

Macroscopic quantum mechanics in a classical spacetime.

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

2013-04-26

174

BOOK REVIEWS: Quantum Mechanics: Fundamentals

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

Kurt Gottfri; Tung-Mow Yan

2004-01-01

175

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

176

Can quantum mechanics and supersymmetric quantum mechanics be the multidimensional Ermakov theories?

NASA Astrophysics Data System (ADS)

For both the Schrödinger equation in quantum mechanics and the Riccati-type equation satisfied by the superpotential in supersymmetric quantum mechanics, we explicitly show that there exists an Ermakov-type functional invariant with respect to the space variable. An energy-like interpretation is suggested for this invariant.

Kaushal, R. S.; Parashar, D.

1996-02-01

177

Optimal guidance law in quantum mechanics

Following de Broglie’s idea of a pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by the Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle’s motion is just the wavefunction ?(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for ?(t,x), from which quantum operators emerge naturally. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function ?{sup ?}?. -- Highlights: •Treating quantum mechanics as a pursuit-evasion game. •Reveal an interesting analogy between guided flight motion and guided quantum motion. •Solve optimal quantum guidance problem by dynamic programming. •Gives a formal proof of de Broglie–Bohm’s idea of a pilot wave. •The optimal pilot wave is shown to be a wavefunction solved from Schrödinger equation.

Yang, Ciann-Dong, E-mail: cdyang@mail.ncku.edu.tw; Cheng, Lieh-Lieh, E-mail: leo8101@hotmail.com

2013-11-15

178

Emergent quantum mechanics of finances

NASA Astrophysics Data System (ADS)

This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price–time continuum having fractal properties. The main steps of this development are the statistical scaling, the non-differentiability hypothesis, and the equations of motion entailed by this hypothesis. From perspective of the proposed theory the dynamics of S&P500 index are analyzed.

Nastasiuk, Vadim A.

2014-06-01

179

Statistical mechanics based on fractional classical and quantum mechanics

NASA Astrophysics Data System (ADS)

The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.

Korichi, Z.; Meftah, M. T.

2014-03-01

180

Superstrings and the Foundations of Quantum Mechanics

NASA Astrophysics Data System (ADS)

It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell's powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.

't Hooft, Gerard

2014-03-01

181

Superstrings and the Foundations of Quantum Mechanics

NASA Astrophysics Data System (ADS)

It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell's powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.

't Hooft, Gerard

2014-05-01

182

Space and time from quantum mechanics

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

183

Towards polymer quantum mechanics for fermionic systems

NASA Astrophysics Data System (ADS)

Polymer quantum mechanics is based on models that mimic the loop quantization of gravity. It coincides with the results of the standard quantum mechanical treatment for such models when a certain length scale parameter is considered to be small. In this work we present some steps in the construction of the polymer representation of a Fermi oscillator, the fermonic counterpart of the harmonic oscillator. It is suggested that the non regular character of the bosonic polymer representation has as a counterpart the non superanalytic character of the fermonic polymer case. We propose a candidate Hamiltonian operator and investigate and contrast its energy spectrum with the standard one.

García-Chung, Angel A.; Morales-Técotl, Hugo A.; Reyes, Juan D.

2013-07-01

184

Two basic Uncertainty Relations in Quantum Mechanics

NASA Astrophysics Data System (ADS)

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 Schrödinger 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

2011-04-01

185

Relating the Quantum Mechanics of Discrete Systems to Standard Canonical Quantum Mechanics

NASA Astrophysics Data System (ADS)

Standard canonical quantum mechanics makes much use of operators whose spectra cover the set of real numbers, such as the coordinates of space, or the values of the momenta. Discrete quantum mechanics uses only strictly discrete operators. We show how one can transform systems with pairs of integer-valued, commuting operators and , to systems with real-valued canonical coordinates and their associated momentum operators . The discrete system could be entirely deterministic while the corresponding ( p, q) system could still be typically quantum mechanical.

't Hooft, Gerard

2014-04-01

186

Quantum mechanics clearly violates the weak equivalence principle (WEP). This implies that quantum mechanics also violates the strong equivalence principle (SEP), as shown in this paper. Therefore a theory of quantum gravity may not be possible unless it is not based upon the equivalence principle, or if quantum mechanics can change its mass dependence. Neither of these possibilities seem likely

Mario Rabinowitz

2006-01-01

187

Can quantum mechanics fool the cosmic censor?

NASA Astrophysics Data System (ADS)

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.; Richartz, M.; Saa, A.; da Silva, A. R. R.; Vanzella, D. A. T.

2009-05-01

188

Relativistic quantum mechanics of supersymmetric particles

The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gauge sypersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist.

Marc Henneaux; Claudio Teitelboim

1982-01-01

189

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

190

Finite Size Scaling in Quantum Mechanics

The finite size scaling ansatz is combined with the variational method to extract information about critical behavior of quantum Hamiltonians. This approach is based on taking the number of elements in a complete basis set as the size of the system. As in statistical mechanics, the finite size scaling can then be used directly in the Schrodinger equation. This approach

Pablo Serra; Juan Pablo Neirotti; Sabre Kais

1998-01-01

191

Quantum mechanical hamiltonian models of turing machines

Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1\\/2 systems. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configuration states. Both

Paul Benioff

1982-01-01

192

Spacetime Probabilities in Nonrelativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

We demonstrate the existence of spacetime probabilities in nonrelativistic quantum mechanics, that is, quantum mechanical probabilities for a set of alternatives which are associated, not with a surface of constant time, but with spacetime domains with nonzero spatial and temporal width in Newtonian spacetime. We use the criterion that quantum mechanical probabilities can be defined for a set of alternatives if and only if the interference between any two different alternatives vanishes. Although generalized quantum mechanics was formulated on the basis of this criterion, the actual existence of spacetime probabilities has not been known. In this paper we consider a rectangular spacetime domain Omega and introduce a set of spacetime alternatives \\{Yes, No\\}: ``Yes'' is to find a particle in Omega and ``No'' is the complement to ``Yes''. We show that, if the initial amplitude of the particle belongs to a specific class, then the criterion of vanishing interference is met by ``Yes'' and ``No'' and spacetime probabilities can be therefore defined for the set \\{Yes, No\\}. Owing to the property of the initial amplitude belonging to the class, the resultant probabilities are associated with a clear measurement theoretical meaning.

Yamada, N.; Takagi, S.

1992-01-01

193

Understanding Kinetic Energy paradox in Quantum Mechanics

A concept of Kinetic Energy in Quantum Mechanics is analyzed. Kinetic Energy is not zero in many cases where there are no motion and flux. This paradox can be understood, using expansion of the wave function in Fourier integral, that is on the basis of virtual plane waves.

Yuri Kornyushin

2008-01-01

194

Kinetic and electrostatic energies in quantum mechanics

A concept of kinetic energy in quantum mechanics is analyzed. Kinetic energy is a non-zero positive value in many cases of bound states, when a wave function is a real-valued one and there are no visible motion and flux. This can be understood, using expansion of the wave function into Fourier integral, that is, on the basis of virtual plane

Yuri Kornyushin

2008-01-01

195

Application of nonstandard analysis to quantum mechanics

Quantum mechanics is formulated using a nonstandard Hilbert space. The concept of an eigen vector of a linear operator, which applies to standard as well as nonstandard Hilbert spaces, is replaced by the more general concept of an ultra eigen vector, which applies to nonstandard Hilbert spaces alone. Ultra eigen vectors corresponding to all spectral points of internal self?adjoint operators

M. O. Farrukh

1975-01-01

196

Inverse scattering with supersymmetric quantum mechanics

The application of supersymmetric quantum mechanics to the inverse scattering problem is reviewed. The main difference with standard treatments of the inverse problem lies in the simple and natural extension to potentials with singularities at the origin and with a Coulomb behaviour at infinity. The most general form of potentials which are phase-equivalent to a given potential is discussed. The

Daniel Baye; Jean-Marc Sparenberg

2004-01-01

197

Solution for quantum mechanical problem in physics

NASA Astrophysics Data System (ADS)

The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. In this Paper the solution is obtained by Variational Homotopy perturbation method which is coupling of Variational iteration method and Homotopy Perturbation Method. The solution describes how the wave function of a physical system evolves over time.

Daga, Amruta; Pradhan, V. H.

2013-06-01

198

Riemann hypothesis and quantum mechanics

NASA Astrophysics Data System (ADS)

In their 1995 paper, Jean-Benoît Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ?(?), where ? is an inverse temperature. We formulate Riemann hypothesis (RH) as a property of the low-temperature Kubo-Martin-Schwinger (KMS) states of this theory. More precisely, the expectation value of the BC phase operator can be written as \\phi _{\\beta }(q)=N_{q-1}^{\\beta -1} \\psi _{\\beta -1}(N_q), where Nq = ?qk = 1pk is the primorial number of order q and ?b is a generalized Dedekind ? function depending on one real parameter b as \\psi _b (q)=q \\prod _{p \\in {P,}p \\vert q}\\frac{1-1/p^b}{1-1/p}. Fix a large inverse temperature ? > 2. The RH is then shown to be equivalent to the inequality N_q |\\phi _\\beta (N_q)|\\zeta (\\beta -1) \\gt e^\\gamma log log N_q, for q large enough. Under RH, extra formulas for high-temperature KMS states (1.5 < ? < 2) are derived. 'Number theory is not pure Mathematics. It is the Physics of the world of Numbers.' Alf van der Poorten

Planat, Michel; Solé, Patrick; Omar, Sami

2011-04-01

199

Consistent interpretations of quantum mechanics

Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counterexamples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.

Omnes, R. (Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris XI, Batiment 211, 91405 Orsay CEDEX (France))

1992-04-01

200

A probabilistic approach to quantum mechanics based on tomograms

It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation of quantum states. This can be regarded as a classical-like formulation of quantum mechanics which avoids the counterintuitive concepts of wave function

Michele Caponigro; Stefano Mancini; V. I. Man'ko

2006-01-01

201

Quantum mechanical coherence, resonance, and mind

Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.

Stapp, H.P.

1995-03-26

202

The emergent Copenhagen interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR–Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.

Hollowood, Timothy J.

2014-05-01

203

Emerging interpretations of quantum mechanics and recent progress in quantum measurement

NASA Astrophysics Data System (ADS)

The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism).

Clarke, M. L.

2014-01-01

204

1/n expansion in quantum mechanics

The classical approximation (/ell/ = n - 1 /yields/ /infinity/) for the energy /var epsilon/(/sup 0/) and the semiclassical expansion in problems of quantum mechanics are discussed. A recursive method is proposed for calculating the quantum corrections of arbitrary order to /var epsilon/ (/sup 0/), this being valid for both bound and quasistationary states. The generalization of the method to states with an arbitrary number of nodes and the possibility of a more general choice of the parameter of the semiclassical expansion are considered. The method is illustrated by the example of the Yukawa and funnel potentials and for the Stark effect in the hydrogen atom. These examples demonstrate the rapid convergence of the 1/n expansion even for small quantum numbers.

Vainberg, V.M.; Mur, V.D.; Popov, V.S.; Sergeev, A.V.; Shcheblykin, A.V.

1988-09-01

205

Neutrino oscillations: Quantum mechanics vs. quantum field theory

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

206

Applications of computational quantum mechanics

NASA Astrophysics Data System (ADS)

This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts with novel properties. Doping a metal oxide may alter its intrinsic properties drastically. A catalytically non-active material can be activated by doping. In this study, we showed that pure zirconia (ZrO2) has almost no activity in methanol coupling reaction, whereas when it is doped with aluminum, the doped catalyst produces dimethyl ether (DME), which is valuable as an alternative future energy source.

Temel, Burcin

207

Collocation method for fractional quantum mechanics

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

208

Grounding quantum probability in psychological mechanism.

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

209

Diffeomorphism groups and nonlinear quantum mechanics

NASA Astrophysics Data System (ADS)

This talk is dedicated to my friend and collaborator, Prof. Dr. Heinz-Dietrich Doebner, on the occasion of his 80th birthday. I shall review some highlights of the approach we have taken in deriving and interpreting an interesting class of nonlinear time-evolution equations for quantum-mechanical wave functions, with few equations; more detail may be found in the references. Then I shall comment on the corresponding hydrodynamical description.

Goldin, Gerald A.

2012-02-01

210

Hunting for Snarks in Quantum Mechanics

NASA Astrophysics Data System (ADS)

A long-standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger's wave function ? for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school (led by Bohr, Heisenberg and Pauli) holds that ? provides a complete description of a single electron state; hence the probability interpretation of ??* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school (led by Einstein, de Broglie, Bohm and Jaynes) holds that ? represents a statistical ensemble of possible electron states; hence it is an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung (first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in ?. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark!

Hestenes, David

2009-12-01

211

Relativistic non-Hermitian quantum mechanics

NASA Astrophysics Data System (ADS)

We develop relativistic wave equations in the framework of the new non-Hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT-symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that, in particular, the mass matrix be Hermitian also allows for models that have no counterpart in conventional quantum mechanics. For example it is well known that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here, we show that the same quartet of Weyl spinors, when coupled by a non-Hermitian but PT-symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is nonzero. The PT-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a noninteracting theory it violates P and T individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions and are shown to maintain many of the canonical structures from Hermitian field theory, but with new and interesting possibilities permitted by the non-Hermiticity parameter m2.

Jones-Smith, Katherine; Mathur, Harsh

2014-06-01

212

Hunting for Snarks in Quantum Mechanics

A long-standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger's wave function {psi} for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school(led by Bohr, Heisenberg and Pauli) holds that {psi} provides a complete description of a single electron state; hence the probability interpretation of {psi}{psi}* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school(led by Einstein, de Broglie, Bohm and Jaynes) holds that {psi} represents a statistical ensemble of possible electron states; hence it is an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung(first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in {psi}. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark{exclamation_point}.

Hestenes, David [Physics Department, Arizona State University, Tempe, Arizona 85287 (United States)

2009-12-08

213

From Cbits to Qbits: Teaching computer scientists quantum mechanics

NASA Astrophysics Data System (ADS)

A strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory. Although the article as a whole addresses teachers of physics well versed in quantum mechanics, the central pedagogical development is addressed directly to computer scientists and mathematicians, with only occasional asides to their teacher. Physicists uninterested in quantum pedagogy may be amused (or irritated) by some of the views of standard quantum mechanics that arise naturally from this unorthodox perspective.

Mermin, N. David

2003-01-01

214

NASA Astrophysics Data System (ADS)

In this article Quantum mechanical (QM) calculations by Density Functional Theory (DFT) have been performed of all amino acids present in bovine insulin. Simulated Raman spectra of those amino acids are compared with their experimental spectra and the major bands are assigned. The results are in good agreement with experiment. We have also verified the DFT results with Quantum mechanical molecular mechanics (QM/MM) results for some amino acids. QM/MM results are very similar with the DFT results. Although the theoretical calculation of individual amino acids are feasible, but the calculated Raman spectrum of whole protein molecule is difficult or even quite impossible task, since it relies on lengthy and costly quantum-chemical computation. However, we have tried to simulate the Raman spectrum of whole protein by adding the proportionate contribution of the Raman spectra of each amino acid present in this protein. In DFT calculations, only the contributions of disulphide bonds between cysteines are included but the contribution of the peptide and hydrogen bonds have not been considered. We have recorded the Raman spectra of bovine insulin using micro-Raman set up. The experimental spectrum is found to be very similar with the resultant simulated Raman spectrum with some exceptions.

Tah, Bidisha; Pal, Prabir; Roy, Sourav; Dutta, Debodyuti; Mishra, Sabyashachi; Ghosh, Manash; Talapatra, G. B.

2014-08-01

215

In this article Quantum mechanical (QM) calculations by Density Functional Theory (DFT) have been performed of all amino acids present in bovine insulin. Simulated Raman spectra of those amino acids are compared with their experimental spectra and the major bands are assigned. The results are in good agreement with experiment. We have also verified the DFT results with Quantum mechanical molecular mechanics (QM/MM) results for some amino acids. QM/MM results are very similar with the DFT results. Although the theoretical calculation of individual amino acids are feasible, but the calculated Raman spectrum of whole protein molecule is difficult or even quite impossible task, since it relies on lengthy and costly quantum-chemical computation. However, we have tried to simulate the Raman spectrum of whole protein by adding the proportionate contribution of the Raman spectra of each amino acid present in this protein. In DFT calculations, only the contributions of disulphide bonds between cysteines are included but the contribution of the peptide and hydrogen bonds have not been considered. We have recorded the Raman spectra of bovine insulin using micro-Raman set up. The experimental spectrum is found to be very similar with the resultant simulated Raman spectrum with some exceptions. PMID:24747859

Tah, Bidisha; Pal, Prabir; Roy, Sourav; Dutta, Debodyuti; Mishra, Sabyashachi; Ghosh, Manash; Talapatra, G B

2014-08-14

216

Surveying Students' Understanding of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Development of research-based multiple-choice tests about quantum mechanics is important for assessing students' difficulties and for evaluating curricula and pedagogies that strive to reduce the difficulties. We explore the difficulties that the undergraduate and graduate students have with non-relativistic quantum mechanics of one particle in one spatial dimension. We developed a research-based conceptual multiple-choice survey that targets these issues to obtain information about the common difficulties and administered it to more than a hundred students from seven different 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, time-dependence of wavefunction and time-dependence of expectation value. We find that the advanced 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 survey can be administered to assess the effectiveness of various instructional strategies.

Singh, Chandralekha; Zhu, Guangtian

2011-03-01

217

Surveying Students' Understanding of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Development of research-based multiple-choice tests about quantum mechanics is important for assessing students' difficulties and for evaluating curricula and pedagogies that strive to reduce the difficulties. We explore the difficulties that the undergraduate and graduate students have with non-relativistic quantum mechanics of one particle in one spatial dimension. We developed a research-based conceptual multiple-choice survey that targets these issues to obtain information about the common difficulties and administered it to more than a hundred students from seven different 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, time-dependence of wavefunction and time-dependence of expectation value. We find that the advanced 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 survey can be administered to assess the effectiveness of various intructional strategies.

Singh, Chandralekha; Zhu, Guangtian

2010-10-01

218

Quantum mechanics with coordinate dependent noncommutativity

NASA Astrophysics Data System (ADS)

Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.

Kupriyanov, V. G.

2013-11-01

219

Quantum mechanics with coordinate dependent noncommutativity

Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.

Kupriyanov, V. G. [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)] [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)

2013-11-15

220

Topological quantum mechanics in 2 + 1 dimensions

The authors show that the classical and quantum covariant dynamics of spinning particles in flat space in 2 + 1 dimensions are derived from a pure Wess-Zumino term written on the space of adjoint orbits of the ISO(2,1) group. Similarly, the dynamics of spinning particles in 2 + 1 de Sitter (anti-de Sitter) space are derived from a Wess-Zumino term on the space of adjoint orbits of SO(3,1)(SO(2,2)). It is shown that a quantum mechanical description of spin is possible in 2 + 1 dimensions without introducing explicit spin degrees of freedom, but at the expense of having a noncommutative space-time geometry.

Skagerstam, B.S. (Inst. of Theoretical Physics, Chalmers Univ. of Technology, S-412 96 Goteborg (SE)); Stern, A. (Dept. of Physics and Astronomy, Univ. of Alabama, Tuscaloosa, AL (US))

1990-04-20

221

Quantum Mechanics à la Langevin and Supersymmetry

NASA Astrophysics Data System (ADS)

We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under ${\\mathcal N}=1$ SUSY, but can be obtained from a, manifestly, supersymmetric expression, upon fixing a local fermionic symmetry, called $\\kappa-$symmetry. The kinetic term for the fermions is a total derivative and can contribute only on the boundaries. We define combinations that scale appropriately, as the lattice spacing is taken to zero and the lattice size to infinity and provide evidence, by numerical simulations, that the correlation functions of the auxiliary field do satisfy Wick's theorem. We show, in particular, that simulations can be carried out using a purely bosonic action. The physical import is that the classical trajectory, $\\phi(\\tau)$, becomes a (chiral) superfield, $(\\phi(\\tau),\\psi_{\\alpha}(\\tau),F(\\tau))$, when quantum fluctuations are taken into account.

Nicolis, S.

222

Quantum mechanical Hamiltonian models of discrete processes

Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement.

Benioff, P.

1981-03-01

223

A fragment-based fractional number of electron (FNE) approach, is developed to study entire electron transfer (ET) processes from the electron donor region to the acceptor region in condensed phase. Both regions are described by the density-fragment interaction (DFI) method while FNE as an efficient ET order parameter is applied to simulate the electron transfer process. In association with the QM/MM energy expression, the DFI-FNE method is demonstrated to describe ET processes robustly with the Ru2+-Ru3+ self-exchange ET as a proof-of-concept example. This method allows for systematic calculations of redox free energies, reorganization energies, and electronic couplings, and the absolute ET rate constants within the Marcus regime.

Zeng, Xiancheng; Hu, Xiangqian; Yang, Weitao

2013-01-01

224

Many-body quantum mechanics as a symplectic dynamical system

An approach is formulated to the problem of obtaining approximate solutions to many-body quantum mechanics. The starting point is the representation of quantum mechanics as Hamiltonian mechanics on a symplectic manifold (phase space). It is shown that Dirac's variation of an action integral provides a natural mechanism for constraining the dynamics to symplectic submanifolds and gives rise to a hierarchy

D. J. Rowe; A. Ryman; G. Rosensteel

1980-01-01

225

The Yukawa potential in semirelativistic formulation via supersymmetry quantum mechanics

NASA Astrophysics Data System (ADS)

We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation (SSE) with the Yukawa potential via the supersymmetric quantum mechanics (SUSYQM) for arbitrary quantum numbers. Useful figures and tables are also included.

Hassanabadi, S.; Ghominejad, M.; Zarrinkamar, S.; Hassanabadi, H.

2013-06-01

226

Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion. PMID:24831528

Suh, J; Weinstein, A J; Lei, C U; Wollman, E E; Steinke, S K; Meystre, P; Clerk, A A; Schwab, K C

2014-06-13

227

Testing Quantum Mechanics on New Ground

NASA Astrophysics Data System (ADS)

Preface; Acknowledgements; 1. Wave-particle duality; 2. Cavity quantum electrodynamics; 3. Quantum nondemolition measurements; 4. Topological phases; 5. Macroscopic quantum coherence; 6. The quantum Zeno paradox; 7. Testing collapse; 8. Macroscopic quantum jumps; 9. Nonlocality; 10. Tunneling times; References; Indexes.

Ghose, Partha

2006-11-01

228

Scattering in PT-symmetric quantum mechanics

A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with Hermiticity, T invariance and PT invariance.

Cannata, Francesco [Istituto Nazionale di Fisica Nucleare, Sezione di Bologna and Dipartimento di Fisica dell' Universita, Via Irnerio 46, I 40126 Bologna (Italy)]. E-mail: Francesco.Cannata@bo.infn.it; Dedonder, Jean-Pierre [GMPIB Universite Paris 7 - Denis-Diderot, 2 Place Jussieu, F-75251, Paris Cedex 05 (France)]. E-mail: dedonder@paris7.jussieu.fr; Ventura, Alberto [Ente Nuove Tecnologie, Energia e Ambiente, Bologna and Istituto Nazionale di Fisica Nucleare, Sezione di Bologna (Italy)]. E-mail: Alberto.Ventura@bologna.enea.it

2007-02-15

229

Improved lattice actions for supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

We analyze the Euclidean version of supersymmetric quantum mechanics on the lattice by means of a numerical path integral. We consider two different lattice derivatives and improve the actions containing them with respect to supersymmetry by systematically adding interaction terms with nonzero extent. To quantize this improvement, we measure boson and fermion masses and Ward identities for the naive as well as the improved models. The masses are degenerate in all models, but the magnitude of the Ward identities decreases significantly for both derivative operators using the improved actions. This is a clear sign that the breaking of supersymmetry due to lattice artifacts is reduced.

Schierenberg, Sebastian; Bruckmann, Falk

2014-01-01

230

The metaphysics of quantum mechanics: Modal interpretations

NASA Astrophysics Data System (ADS)

This dissertation begins with the argument that a preferred way of doing metaphysics is through philosophy of physics. An understanding of quantum physics is vital to answering questions such as: What counts as an individual object in physical ontology? Is the universe fundamentally indeterministic? Are indiscernibles identical? This study explores how the various modal interpretations of quantum mechanics answer these sorts of questions; modal accounts are one of the two classes of interpretations along with so-called collapse accounts. This study suggests a new alternative within the class of modal views that yields a more plausible ontology, one in which the Principle of the Identity of Indisceribles is necessarily true. Next, it shows that modal interpretations can consistently deny that the universe must be fundamentally indeterministic so long as they accept certain other metaphysical commitments: either a perfect initial distribution of states in the universe or some form of primitive dispositional properties. Finally, the study sketches out a future research project for modal interpretations based on developing quantified quantum logic.

Gluck, Stuart Murray

2004-11-01

231

Quantum Superspace, q-EXTENDED Supersymmetry and Parasupersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

We describe q-deformation of the extended supersymmetry and construct q-extended supersymmetric Hamiltonian. For this purpose we formulate q-superspace formalism and construct q-supertransformation group. On this basis q-extended supersymmetric Lagrangian is built. The canonical quantization of this system is considered. The connection with multi-dimensional matrix representations of the parasupersymmetric quantum mechanics is discussed and q-extended supersymmetric harmonic oscillator is considered as a simplest example of the described constructions. We show that extended supersymmetric Hamiltonians obey not only extended SUSY but also the whole family of symmetries (q-extended supersymmetry) which is parametrized by continuous parameter q on the unit circle.

Ilinski, K. N.; Uzdin, V. M.

232

Comment on ``Arrival time in quantum mechanics'' and ``Time of arrival in quantum mechanics''

NASA Astrophysics Data System (ADS)

Contrary to claims contained in papers by Grot, Rovelli, and Tate [Phys. Rev. A 54, 4676 1996)] and Delgado and Muga [Phys. Rev. A 56, 3425 (1997)], the ``time operator,'' which I have constructed [Rep. Math. Phys. 6, 361 (1974)] in an axiomatic way, is a self-adjoint operator existing in a usual Hilbert space of (nonrelativistic or relativistic) quantum mechanics.

Kijowski, Jerzy

1999-01-01

233

Noncommutative quantum mechanics as a gauge theory

The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second-class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system into an Abelian gauge theory exhibiting only first class constraints. The appropriateness of the BFT embedding, as implemented in this work, is verified by showing that there exists a one to one mapping linking the second-class model with the gauge invariant sector of the gauge theory. As is known, the functional quantization of a gauge theory calls for the elimination of its gauge freedom. Then, we have at our disposal an infinite set of alternative descriptions for noncommutative quantum mechanics, one for each gauge. We study the relevant features of this infinite set of correspondences. The functional quantization of the gauge theory is explicitly performed for two gauges and the results compared with that corresponding to the second-class system. Within the operator framework the gauge theory is quantized by using Dirac's method.

Bemfica, F. S.; Girotti, H. O. [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 - Porto Alegre, RS (Brazil)

2009-06-15

234

The formal path integral and quantum mechanics

Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.

Johnson-Freyd, Theo [Department of Mathematics, University of California - Berkeley, 970 Evans Hall, Berkeley, California 94720 (United States)

2010-11-15

235

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

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

236

Mind, Matter and Quantum Mechanics (2nd edition)

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

237

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

238

Relationship between quantum-mechanical systems with and without monopoles

It is shown that the inclusion of the monopole field in the three- and five-dimensional spherically symmetric quantum-mechanical systems, with the addition of the special centrifugal term, leads to the lift of the range of the total and azimuth quantum numbers only. Meanwhile the functional dependence of the energy spectra on quantum numbers does not undergo any changes. We also

Levon Mardoyan; Armen Nersessian; Armen Yeranyan

2007-01-01

239

Induced representations of quantum kinematical algebras and quantum mechanics

NASA Astrophysics Data System (ADS)

Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. In this paper we propose their generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper (Arratia O and del Olmo M A 2001 Preprint math.QA/0110275) to induce representations of quantum bicrossproduct algebras, we construct the representations of the family of standard quantum inhomogeneous algebras U?(iso?(2)). This family contains the quantum Euclidean, Galilei and Poincaré algebras, all of them in (1+1) dimensions. As byproducts we obtain the actions of these quantum algebras on regular co-spaces that are an algebraic generalization of the homogeneous spaces and q-Casimir equations which play the role of q-Schrödinger equations.

Arratia, Oscar; del Olmo, Mariano A.

2002-10-01

240

Quantum Mechanics with Basic Field Theory

NASA Astrophysics Data System (ADS)

Preface; 1. Basic formalism; 2. Fundamental commutator and time evolution of state vectors and operators; 3. Dynamical equations; 4. Free particles; 5. Particles with spin 1/2; 6. Gauge invariance, angular momentum and spin; 7. Stern-Gerlach experiments; 8. Some exactly solvable bound state problems; 9. Harmonic oscillator; 10. Coherent states; 11. Two-dimensional isotropic harmonic oscillator; 12. Landau levels and quantum Hall effect; 13. Two-level problems; 14. Spin 1/2 systems in the presence of magnetic field; 15. Oscillation and regeneration in neutrino and neutral K-mesons as two-level systems; 16. Time-independent perturbation for bound states; 17. Time-dependent perturbation; 18. Interaction of charged particles and radiation in perturbation theory; 19. Scattering in one dimension; 20. Scattering in three dimensions - a formal theory; 21. Partial wave amplitudes and phase shifts; 22. Analytic structure of the S-matrix; 23. Poles of the Green's function and composite systems; 24. Approximation methods for bound states and scattering; 25. Lagrangian method and Feynman path integrals; 26. Rotations and angular momentum; 27. Symmetry in quantum mechanics and symmetry groups; 28. Addition of angular momenta; 29. Irreducible tensors and Wigner-Eckart theorem; 30. Entangled states; 31. Special theory of relativity: Klein Gordon and Maxwell's equation; 32. Klein Gordon and Maxwell's equation; 33. Dirac equation; 34. Dirac equation in the presence of spherically symmetric potentials; 35. Dirac equation in a relativistically invariant form; 36. Interaction of Dirac particle with electromagnetic field; 37. Multiparticle systems and second quantization; 38. Interactions of electrons and phonons in condensed matter; 39. Superconductivity; 40. Bose Einstein condensation and superfluidity; 41. Lagrangian formulation of classical fields; 42. Spontaneous symmetry breaking; 43. Basic quantum electrodynamics and Feynman diagrams; 44. Radiative corrections; 45. Anomalous magnetic moment and Lamb shift; Appendix; References; Index.

Desai, Bipin R.

2009-12-01

241

a Quantum Mechanical Semiconductor Device Simulator.

NASA Astrophysics Data System (ADS)

Semiconductor device simulators have generally been based on either classical or semi-classical approaches. In these approaches, the Poisson's equation is solved with either the current continuity equation or the Boltzmann transport equation. Methods based on quantum mechanics have been generally very computer intensive, and thus until recently not much favored. However, with the availability of faster and more powerful computers this picture is changing. As the physical dimensions of the semiconductor devices are reduced, the assumptions made in the classical and the semi-classical approaches become invalid and the simulation results become inaccurate. For such cases, quantum mechanical concepts must be introduced to provide accurate simulation results. This dissertation presents the proof of concept of a semiconductor device simulator based on the quantum mechanical principals. The simulation technique is based on the self consistent solution of the Poisson's and time independent Schrodinger wave equation for a 1-D finite differenced grid. The applicability of the technique to a 2-D finite differenced grid is also presented. The simulation is performed by first solving for the Fermi energy distribution inside the simulation domain. The initial estimates about the carrier concentrations are developed from the Fermi energy distribution. Based on the carrier concentrations, the potential distribution inside the device is updated using the Poisson's equation. The updated potential distribution is then used in the time independent Schrodinger's equation and the carrier wave vectors are thus determined. The carrier wave vectors, along with appropriate density of state function and distribution function are used to update the carrier concentrations. For the 1-D case, the density of state function is based on a single dimension of a three dimensional volume with the assumption that the density of states is the same for all the three dimensions. The distribution function used is the Fermi-Dirac distribution function. The new carrier concentrations thus computed are then substituted back into the Poisson's equation, and self consistency is obtained when minimum error criteria have been met. The device simulator has the capability of simulating heterojunctions semiconductor devices fabricated from elemental semiconductors such as Si and Ge, as well as binary and tertiary compound semiconductors.

Bhutta, Imran Ahmed

242

Tampering detection system using quantum-mechanical systems

The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.

Humble, Travis S. (Knoxville, TN); Bennink, Ryan S. (Knoxville, TN); Grice, Warren P. (Oak Ridge, TN)

2011-12-13

243

Moyal quantum mechanics: The semiclassical Heisenberg dynamics

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)] [Department of Physics, University of Manitoba, Winnipeg, MB, R3T 2N2 (Canada)

1995-07-01

244

Quantum mechanics and the direction of time

In recent papers the authors have discussed the dynamical properties of large Poincare systems (LPS), that is, nonintegrable systems with a continuous spectrum (both classical and quantum). An interesting example of LPS is given by the Friedrichs model of field theory. As is well known, perturbation methods analytic in the coupling constant diverge because of resonant denominators. They show that this Poincare catastrophe can be eliminated by a natural time ordering of the dynamical states. They obtain then a dynamical theory which incorporates a privileged direction of time (and therefore the second law of thermodynamics). However, it is only in very simple situations that his time ordering can be performed in an extended Hilbert space. In general, they need to go to the Liouville space (superspace) and introduce a time ordering of dynamical states according to the number of particles involved in correlations. This leads then to a generalization of quantum mechanics in which the usual Heisenberg's eigenvalue problem is replaced by a complex eigenvalue problem in the Liouville space.

Hasegawa, H.; Petrosky, T. (Univ. of Texas, Austin (United States)); Prigogine, I. (Univ. of Texas, Austin (United States) International Solvay Inst. for Physics and Chemistry, Brussels (Belgium)); Tasaki, S. (International Solvay Inst. for Physics and Chemistry, Brussels (Belgium))

1991-03-01

245

Quantum mechanics without an equation of motion

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

246

Supersymmetric quantum mechanics and Painlevé equations

NASA Astrophysics Data System (ADS)

In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.

Bermudez, David; Fernández C., David J.

2014-01-01

247

Nonlinear supersymmetric quantum mechanics: concepts and realizations

NASA Astrophysics Data System (ADS)

The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is outlined and different one-dimensional and two-dimensional realizations are described. It is elaborated how the nonlinear SUSY approach provides two new methods of SUSY separation of variables for various two-dimensional models. In the framework of these methods, a partial and/or complete solution of some two-dimensional models becomes possible. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. The emergence of hidden symmetries and spectrum generating algebras is elucidated in the context of the nonlinear SUSY in one-dimensional stationary and non-stationary, as well as in two-dimensional QM.

Andrianov, A. A.; Ioffe, M. V.

2012-12-01

248

Twist deformations of the supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

The mathcal{N} -extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even mathcal{N} one can identify the 1 D mathcal{N} -extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.

Castro, Paulo G.; Chakraborty, Biswajit; Kuznetsova, Zhanna; Toppan, Francesco

2011-06-01

249

Twist deformation of rotationally invariant quantum mechanics

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

250

Quantum mechanical evolution towards thermal equilibrium.

The circumstances under which a system reaches thermal equilibrium, and how to derive this from basic dynamical laws, has been a major question from the very beginning of thermodynamics and statistical mechanics. Despite considerable progress, it remains an open problem. Motivated by this issue, we address the more general question of equilibration. We prove, with virtually full generality, that reaching equilibrium is a universal property of quantum systems: almost any subsystem in interaction with a large enough bath will reach an equilibrium state and remain close to it for almost all times. We also prove several general results about other aspects of thermalization besides equilibration, for example, that the equilibrium state does not depend on the detailed microstate of the bath. PMID:19658469

Linden, Noah; Popescu, Sandu; Short, Anthony J; Winter, Andreas

2009-06-01

251

Relativistic quantum mechanics of supersymmetric particles

NASA Astrophysics Data System (ADS)

The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gauge supersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist. This follows formally from the gauge invariance properties of the action and physically it corresponds to the fact that particles can travel backwards as well as forward in coordinate time. However, appropriate application of path integral techniques yields directly the proper time representation of the Feynman propagator. Next we extend the formalism to systems described by anticommuting variables. This problem presents some difficulty when the dimension of the phase space is odd, because the holomorphic representation does not exist. It is shown, however, that the usual connection between the evolution operator and the path integral still holds provided one indludes in the action the boundary term that makes the classical variational principle well defined. The path integral for the relativistic spinning particle is then evaluated and it is shown to lead directly to a representation for the Feynman propagator in terms of two proper times, one commuting, the other anticommuting, which appear in a symmetric manner. This representation is used to derive scattering amplitudes in an external field. In this step the anticommuting proper time is integrated away and the analysis is carried in terms of one (commuting) proper time only, just as in the spinless case. Finally, some properties of the quantum mechanics of the ghost particles that appear in the path integral for constrained systems are developed in an appendix.

Henneaux, Marc; Teitelboim, Claudio

1982-10-01

252

Relativistic quantum mechanics of supersymmetric particles

The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gauge sypersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist. This follows formally from the gauge invariance properties of the action and physically it corresponds to the fact that particles can travel backwards as well as forward in coordinate time. However, appropriate application of path integral techniques yields directly the proper time representation of the Feynman propagator. Next we extend the formalism to systems described by anticommuting variables. This problem presents some difficulty when the dimension of the phase space is odd, because the holomorphic representation does not exist. It is shown, however, that the usual connection between the evolution operator and the path integral still holds provided one includes in the action the bounary term that makes the classical variational principle well defined. The path integral for the relativistic spinning particle is then evaluated and it is shown to lead directly to a representation for the Feynman propagator in terms of two proper times, one commuting, the other anticommuting, which appear in a symmetric manner. This representation is used to derive scattering amplitudes in an external field. In this step the anticommuting proper time is integrated away and the analysis is carried in terms of one (commuting) proper time only, just as in the spinless case. Finally, some properties of the quantum mechanics of the ghost particles that appear in the path integral for constrained systems are developed in an appendix.

Henneaux, M.; Teitelboim, C.

1982-10-01

253

New methods for quantum mechanical reaction dynamics

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

254

Interactive Quantum Mechanics Exercises for Just-in-Time Teaching

NSDL National Science Digital Library

This is a collection of online curricular material for a one-semester quantum mechanics course. It consists of interactive Java applets, Physlets, for interactive out-of-class exercises. These applets stress the visualization of quantum mechanical concepts for better student understanding. There are also illustrations suitable for both in-class and out-of-class use.

Belloni, Mario; Cain, Laurence; Christian, Wolfgang

2004-04-04

255

Rigorous solution to a quantum statistical mechanical laser model

A quantum mechanical laser model with relaxation and pumping mechanisms is solved rigorously. A basic equation for the density matrix is derived by the damping theory and is transformed into a corresponding c-number equation for a (quasi-) probability density. This is done with the aid of the quantum phase space method. The probability density is expanded in terms of orthogonal

Fumiaki Shibata; Chikako Uchiyama

1995-01-01

256

Inner-Shell Physics after Fifty Years of Quantum Mechanics.

National Technical Information Service (NTIS)

A historical view is given of how the development of quantum mechanics has been affected by the information relating to inner shells, gathered by physicists since the early days of atomic physics, and of the impact of quantum mechanics on the physics of i...

E. Merzbacher

1976-01-01

257

On the End of a Quantum Mechanical Romance

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

258

The Quantum and Fluid Mechanics of Global Warming

Quantum physics and fluid mechanics are the foundation of any understanding of the Earth's climate. In this talk I invoke three well-known aspects of quantum mechanics to explore what will happen as the concentrations of greenhouse gases such as carbon dioxide continue to increase. Fluid dynamical models of the Earth's atmosphere, demonstrated here in live simulations, yield further insight into

Brad Marston

2008-01-01

259

Effect of violation of quantum mechanics on neutrino oscillation

NASA Astrophysics Data System (ADS)

The effect of quantum mechanics violation due to quantum gravity on neutrino oscillation is investigated. It is found that the mechanism introduced by Ellis, Hagelin, Nanopoulos, and Srednicki through the modification of the Liouville equation can affect neutrino oscillation behavior and may be taken as a new solution of the solar neutrino problem.

Liu, Yong; Hu, Liangzhong; Ge, Mo-Lin

1997-11-01

260

Linear Logic for Generalized Quantum Mechanics

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

261

Lectures on Black Hole Quantum Mechanics

NASA Astrophysics Data System (ADS)

The lectures that follow were originally given in 1992, and written up only slightly later. Since then there have been dramatic developments in the quantum theory of black holes, especially in the context of string theory. None of these are reflected here. The concept of quantum hair, which is discussed at length in the lectures, is certainly of permanent interest, and I continue to believe that in some generalized form it will prove central to the whole question of how information is stored in black holes. The discussion of scattering and emission modes from various classes of black holes could be substantially simplified using modern techniques, and from currently popular perspectives the choice of examples might look eccentric. On the other hand fashions have changed rapidly in the field, and the big questions as stated and addressed here, especially as formulated for "real" black holes (nonextremal, in four-dimensional, asymptotically flat space-time, with supersymmetry broken), remain pertinent even as the tools to address them may evolve. The four lectures I gave at the school were based on two lengthy papers that have now been published, "Black Holes as Elementary Particles," Nuclear Physics B380, 447 (1992) and "Quantum Hair on Black Holes," Nuclear Physics B378, 175 (1992). The unifying theme of this work is to help make plausible the possibility that black holes, although they are certainly unusual and extreme states of matter, may be susceptible to a description using concepts that are not fundamentally different from those we use in describing other sorts of quantum-mechanical matter. In the first two lectures I discussed dilaton black holes. The fact that apparently innocuous changes in the "matter" action can drastically change the properties of a black hole is already very significant: it indicates that the physical properties of small black holes cannot be discussed reliably in the abstract, but must be considered with due regard to the rest of physics. (The macroscopic properties of large black holes, in particular those of astrophysical interest, are presumably well described by the familiar Einstein-Maxwell action which governs the massless fields. Heavy fields will at most provide Yukawa tails to the field surrounding the hole.) I will show how perturbations may be set up and analyzed completely, and why doing this is crucial for understanding the semiclassical physics of the hole including the Hawking radiation quantitatively. It will emerge that there is a class of dilaton black holes which behave as rather straightforward elementary particles. In the other two lectures I discussed the issue of hair on black holes, in particular the existence of hair associated with discrete gauge charges and its physical consequences. This hair is particularly interesting to analyze because it is invisible classically and to all order in ?. Its existence shows that black holes can have some "internal" quantum numbers in addition to their traditional classification by mass, charge, and angular momentum. The text that follows, follows the original papers closely.

Wilczek, Frank

262

Mechanics of quantum and Sharvin conductors

NASA Astrophysics Data System (ADS)

Previously, the authors reported direct evidence of channel saturation and conductance quantization in atomic-sized gold constrictions through mechanical perturbation studies, and also showed that peaks in conductance histograms are insufficient in evaluating their mechanical stability [Armstrong , Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.82.195416 82, 195416 (2010)]. In the present study, gold constrictions spanning the range from quantum to semiclassical (Sharvin) conductance regimes are mechanically probed with picolevel resolution in applied force and deformation, along with simultaneous measurements of conductance. While reconfiguration from one constriction size to another is known to occur by apparently random discrete atomic displacements, results reveal a remarkable simplicity—the magnitude of discrete atomic displacements is limited to a small set of values that correspond to elementary slip distances in gold rather than Au-Au interatomic distance. Combined with measurements of the spring constant of constrictions, results reveal two fundamental crossovers in deformation modes with increasing contact diameter—first, from homogeneous shear to defect-mediated deformation at a diameter that is in close agreement with previous predictions [Sørensen , Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.57.3283 57, 3283 (1998)]; and second, the discovery of another crossover marking surface- to volume-dominated deformation. A remarkable modulus enhancement is observed when the size of the constrictions approaches the Fermi wavelength of the electrons, and in the limit of a single-atom constriction it is at least two times that for bulk gold. Results provide atomistic insight into the stability of these constrictions and an evolutionary trace of deformation modes, beginning with a single-atom contact.

Armstrong, Jason N.; Hua, Susan Z.; Chopra, Harsh Deep

2011-06-01

263

On physical and mathematical causality in quantum mechanics

NASA Astrophysics Data System (ADS)

This paper critically examines the view of quantum phenomena that has persisted since the introduction of quantum mechanics and that still remains prevalent in the foundational literature on quantum theory. According to this view, the independent behavior of quantum systems is causal, while the experimentally manifest lack of causality in observable quantum phenomena and, as a result, the probabilistic nature of our predictions concerning these phenomena are due to the disruption of this causal behavior by interfering with it through the measuring process. It appears that this view originates with P. A. M. Dirac and his work on the transformation theory (introduced by him and P. Jordan), which brought together W. Heisenberg's and E. Schrödinger's versions of quantum mechanics within a single scheme. Other founding figures of quantum theory, specifically N. Bohr, W. Heisenberg, and J. von Neumann, also advanced this view and helped to establish its prominence. The paper discusses these arguments and contends them to be insufficient to support the view that the independent behavior quantum systems is physically causal. It suggests that one can meaningfully speak of mathematical causality in quantum theory, and advocates an alternative, physically noncausal, interpretation of quantum mechanics.

Plotnitsky, Arkady

2010-01-01

264

New Formulation of Statistical Mechanics Using Thermal Pure Quantum States

NASA Astrophysics Data System (ADS)

We formulate statistical mechanics based on a pure quantum state, which we call a "thermal pure quantum (TPQ) state". A single TPQ state gives not only equilibrium values of mechanical variables, such as magnetization and correlation functions, but also those of genuine thermodynamic variables and thermodynamic functions, such as entropy and free energy. Among many possible TPQ states, we discuss the canonical TPQ state, the TPQ state whose temperature is specified. In the TPQ formulation of statistical mechanics, thermal fluctuations are completely included in quantum-mechanical fluctuations. As a consequence, TPQ states have much larger quantum entanglement than the equilibrium density operators of the ensemble formulation. We also show that the TPQ formulation is very useful in practical computations, by applying the formulation to a frustrated two-dimensional quantum spin system.

Sugiura, Sho; Shimizu, Akira

2014-03-01

265

Resources Students Use to Understand Quantum Mechanical Operators

NSDL National Science Digital Library

The Paradigms team at Oregon State University has developed a quantum mechanics curriculum aimed at middle division students that begins with a strong emphasis on using operators, matrices and Dirac notation to describe quantum systems. The curriculum begins with spin systems, and this content ordering relies on students being able to understand quantum mechanical operators, eigenstates and quantum measurement without prior instruction on wave functions. We have analyzed classroom and an interview video to identify resources students use when considering these quantum ideas. Identification of such resources will inform introductory curricula that are prerequisite to the quantum Paradigms and inform the development of Paradigms materials that will guide students to use these resources productively.

Gire, Elizabeth; Manogue, Corinne A.

2008-11-04

266

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.

267

Quantum Mechanical Studies of DNA and LNA

Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies of the electrostatic potentials were compared among model oligonucleotides, and it was observed that small structural modifications induce global changes in the molecular structure and surface potentials. Since ligand structure and electrostatic potential complementarity with a receptor is a determinant for the bonding pattern between molecules, minor chemical modifications may have profound changes in the interaction profiles of oligonucleotides, possibly leading to changes in pharmacological properties. The QM modeling data can be used to understand earlier observations of antisense oligonucleotide properties, that is, the observation that small structural changes in oligonucleotide composition may lead to dramatic shifts in phenotypes. These observations should be taken into account in future oligonucleotide drug discovery, and by focusing more on non RNA target interactions it should be possible to utilize the exhibited property diversity of oligonucleotides to produce improved antisense drugs.

Shim, Irene; Lindow, Morten; ?rum, Henrik

2014-01-01

268

NASA Astrophysics Data System (ADS)

The purpose of this study was to construct a valid and reliable multiple-choice achievement test to assess students' understanding of core concepts of introductory quantum mechanics. Development of the Quantum Mechanics Visualization Instrument (QMVI) occurred across four successive semesters in 1999--2001. During this time 213 undergraduate and graduate students attending the Pennsylvania State University (PSU) at University Park and Arizona State University (ASU) participated in this development and validation study. Participating students were enrolled in four distinct groups of courses: Modern Physics, Undergraduate Quantum Mechanics, Graduate Quantum Mechanics, and Chemistry Quantum Mechanics. Expert panels of professors of physics experienced in teaching quantum mechanics courses and graduate students in physics and science education established the core content and assisted in the validating of successive versions of the 24-question QMVI. Instrument development was guided by procedures outlined in the Standards for Educational and Psychological Testing (AERA-APA-NCME, 1999). Data gathered in this study provided information used in the development of successive versions of the QMVI. Data gathered in the final phase of administration of the QMVI also provided evidence that the intended score interpretation of the QMVI achievement test is valid and reliable. A moderate positive correlation coefficient of 0.49 was observed between the students' QMVI scores and their confidence levels. Analyses of variance indicated that students' scores in Graduate Quantum Mechanics and Undergraduate Quantum Mechanics courses were significantly higher than the mean scores of students in Modern Physics and Chemistry Quantum Mechanics courses (p < 0.05). That finding is consistent with the additional understanding and experience that should be anticipated in graduate students and junior-senior level students over sophomore physics majors and majors in another field. The moderate positive correlation coefficient of 0.42 observed between students' QMVI scores and their final course grades was also consistent with expectations in a valid instrument. In addition, the Cronbach-alpha reliability coefficient of the QMVI was found to be 0.82. Limited findings were drawn on students' understanding of introductory quantum mechanics concepts. Data suggested that the construct of quantum mechanics understanding is most likely multidimensional and the Main Topic defined as "Quantum Mechanics Postulates" may be an especially important factor for students in acquiring a successful understanding of quantum mechanics.

Cataloglu, Erdat

269

Testing Quantum Mechanics in High-Energy Physics

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

270

Quantum mechanics model on a Kähler conifold

We propose an exactly solvable model of the quantum oscillator on the class of Kähler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has nonconstant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction

Stefano Bellucci; Armen Nersessian; Armen Yeranyan

2004-01-01

271

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.

Belloni, Mario; Christian, Wolfgang

2010-01-11

272

Possibility of a Geometric Constraint in the Schrödinger Quantum Mechanics

NASA Astrophysics Data System (ADS)

Within the framework of some straightforward mathematical terms it is argued that there exists a space-invariant in the Schrödinger quantum mechanics (SQM). As an alternative to the geometric features of localized nature dictated by the prescribed boundary conditions in a potential problem in SQM, this spatial invariant is expected to account for some global geometric features of the quantum system.

Kaushal, R. S.

273

Optical coupling mechanisms in quantum well infrared photodetectors

Light coupling systems such as gratings are required because Quantum Well Infrared Photodetectors do not respond to normal incident light due to the quantum mechanical selection rules associated with intersubband transitions. The resolution of the photolithography and accuracy of the etching become key issues in producing smaller grating feature sizes especially in shorter wavelengths. An enhancement factor of three due

Sumith Bandara; Sarath Gunapala; John Liu; Winn Hong; Jin Park

274

A Simplified Quantum Mechanical Model of Diatomic Molecules

ERIC Educational Resources Information Center

Introduces a simple one-dimensional model of a diatomic molecule that can explain all the essential features of a real two particle quantum mechanical system and gives quantitative results in fair agreement with those of a hydrogen molecule. (GA)

Nielsen, Lars Drud

1978-01-01

275

Born series and unitarity in noncommutative quantum mechanics

This paper is dedicated to present model independent results for noncommutative quantum mechanics. We determine sufficient conditions for the convergence of the Born series and, in the sequel, unitarity is proved in full generality.

Bemfica, F. S.; Girotti, H. O. [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 - Porto Alegre, Rio Grande do Sul (Brazil)

2008-01-15

276

Quantum Mechanical Balance Equation Approach to Semiconductor Device Simulation.

National Technical Information Service (NTIS)

This research project was focused on the development of a quantum mechanical balance equation based device simulator that can model advanced, compound, submicron devices, under all transport conditions (AC, DC, and transient response). This report documen...

L. L. Cui

1997-01-01

277

Probabilistic Approach to Teaching the Principles of Quantum Mechanics

ERIC Educational Resources Information Center

Approaches the representation of quantum mechanics through Hilbert space postulates. Demonstrates that if the representation is to be accurate, an evolution operator of the form of a Hamiltonian must be used. (CP)

Santos, Emilio

1976-01-01

278

Quantum tic-tac-toe: A teaching metaphor for superposition in quantum mechanics

NASA Astrophysics Data System (ADS)

Quantum tic-tac-toe was developed as a metaphor for the counterintuitive nature of superposition exhibited by quantum systems. It offers a way of introducing quantum physics without advanced mathematics, provides a conceptual foundation for understanding the meaning of quantum mechanics, and is fun to play. A single superposition rule is added to the child's game of classical tic-tac-toe. Each move consists of a pair of marks subscripted by the number of the move (``spooky'' marks) that must be placed in different squares. When a measurement occurs, one spooky mark becomes real and the other disappears. Quantum tic-tac-toe illustrates a number of quantum principles including states, superposition, collapse, nonlocality, entanglement, the correspondence principle, interference, and decoherence. The game can be played on paper or on a white board. A Web-based version provides a refereed playing board to facilitate the mechanics of play, making it ideal for classrooms with a computer projector.

Goff, Allan

2006-11-01

279

Level Comparison Theorems and Supersymmetric Quantum Mechanics.

National Technical Information Service (NTIS)

The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle...

B. Baumgartner H. Grosse A. Martin

1986-01-01

280

Relativistic models of nonlinear quantum mechanics

I present and discuss a class of nonlinear quantum-theory models, based on simple relativistic field theories, in which the parameters depend on the state of the system via expectation values of local functions of the fields.

T. W. B. Kibble

1978-01-01

281

Quantum Mechanics in Biology: Photoexcitations in DNA

\\u000a We consider here the theoretical and quantum chemical description of the photoexcitated states in DNA duplexes. We discuss\\u000a the motivation and limitations of an exciton model and use this as the starting point for more detailed excited state quantum\\u000a chemical evaluations. In particular, we focus upon the role of interbase proton transfer between Watson\\/Crick pairs in localizing\\u000a an excitation and

Eric R. Bittner; Arkadiusz Czader

2009-01-01

282

Mechanism Of The Quantum Speed-up

NASA Astrophysics Data System (ADS)

Bob chooses a function and gives to Alice the black box that computes it. Alice, without knowing Bob's choice, should find a character of the function (e. g. its period) by computing its value for different arguments. There is naturally correlation between Bob's choice and the solution found by Alice. We show that, in quantum algorithms, this correlation becomes quantum. This highlights an overlooked measurement problem: sharing between two completely or partly redundant measurements the determination of completely or partly correlated measurement outcomes. All is like Alice, by reading the solution at the end of the algorithm, contributed to the initial choice of Bob, with half of it in quantum superposition for all the possible ways of taking this half. This contribution, back evolved to before running the algorithm, where Bob's choice is located, becomes Alice knowing in advance half of the choice. The quantum algorithm is the quantum superposition of all the possible ways of taking half of Bob's choice and, given the advanced knowledge of it, classically computing the missing half. The quantum speed-up comes from comparing two classical algorithms, with and without advanced knowledge of half of Bob's choice.

Castagnoli, Giuseppe

2011-11-01

283

Testing quantum mechanics in the neutral kaon system

The neutral kaon system is a sensitive probe of quantum mechanics. We revive a parametrization of non-quantum-mechanical effects that is motivated by considerations of the nature of space-time foam, and show how it can be constrained by new measurements of KL-->2pi and KL,S semileptonic decays at LEAR or a phi factory. Permanent address: Center for Theoretical Physics, Department of Physics,

Jonathan Richard Ellis; Nikolaos E Mavromatos; Dimitri V Nanopoulos

1992-01-01

284

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

285

Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.

Lee, Sang-Bong

1993-09-01

286

Sensible Quantum Mechanics:. are Probabilities Only in the Mind?

NASA Astrophysics Data System (ADS)

Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic except conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued awareness operators. Ratios of the measures for these sets of perceptions can be interpreted as frequency-type probabilities for many actually existing sets. These probabilities generally cannot be given by the ordinary quantum “probabilities” for a single set of alternatives. Probabilism, or ascribing probabilities to unconscious aspects of the world, may be seen to be an aesthemamorphic myth.

Page, Don N.

287

The Use of Quantum Mechanics in the Treatment of Waveguides

NASA Astrophysics Data System (ADS)

In this paper we give a quantum description of guided waves. A Klein-Gordon type equation is derived for wave propagation in an ideal uniform waveguide, and the appropriate quantum-mechanical interpretation is given. Making use of such methods, we give an analysis of guided waves, of inhomogeneously filled waveguides, of waveguide discontinuities, and generally of passive microwave circuits. A spinorial formalism is employed to derive the equivalent Dirac-type equation. The general applicability of the quantum-mechanical concepts to waveguides is also discussed.

Marinescu, N.

288

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

NASA Astrophysics Data System (ADS)

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 to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se, suffers from a very limited understanding that is even more severe than that of quantum mechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces. Quantum mechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space---not unlike the motion of a classical N-particle system in its 6N-dimensional phase-space. Unfortunately, we need an inside and an outside view, we need an external reference frame, we need an observer. This unavoidable partition is the origin of most of the troubles we have with quantum mechanics. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on `instantaneous' projections within some externally selected measurement basis. As a result, the theory becomes essentially statistical rather than deterministic; furthermore there is an asymmetry between the observed and the observing. This is the point where consciousness may come in. Complemented by an introduction and several appendices, Henry Stapp's book consists essentially of three parts: theory, implications, and new developments. The theory part gives a very readable account of the Copenhagen interpretation, some aspects of a psychophysical theory, and, eventually, hints towards a quantum foundation of the brain--mind connection. The next part, `implications', summarizes some previous attempts to bridge the gap between the working rules of quantum mechanics and their possible consequences for our understanding of this world (Pauli, Everett, Bohm, Heisenberg). The last section, `new developments', dwells on some ideas about the conscious brain and its possible foundation on quantum mechanics. The book is an interesting and, in part, fascinating contribution to a field that continues to be a companion to `practical' quantum mechanics since its very beginning. It is doubtful whether such types of `quantum ontologies' will ever become (empirically) testable; right now one can hardly expect more than to be offered some consistent `grand picture', which the reader may find more or less acceptable or even rewarding. Many practicing quantum physicists, though, will remain unimpressed. The shift from synthetic ontology to analytic ontology is the foundation of the present work. This means that fundamental wholes are being partitioned into their ontologically subordinate components by means of `events'. The actual event, in turn, is an abrupt change in the Heisenberg state describing the quantum universe. The new state then defines the tendencies associated with the next actual event. To avoid infinite regression in terms of going from one state of tendencies to the next, consciousness is there to give these events a special `feel', to provide a status of `intrinsic actuality'. The brain of an alert human observer is similar in an important way to a quantum detection device: it can amplify small signals to large macroscopic ef

Mahler, G.

2004-07-01

289

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

290

Kink mass quantum shifts from SUSY quantum mechanics

NASA Astrophysics Data System (ADS)

In this paper a new version of the DHN (Dashen-Hasslacher-Neveu) formula, which is used to compute the one-loop order kink mass correction in (1+1)-dimensional scalar field theory models, is constructed. The new expression is written in terms of the spectral data coming from the supersymmetric partner operator of the second-order small kink fluctuation operator and allows us to compute the kink mass quantum shift in new models for which this calculation was out of reach by means of the old formula.

Izquierdo, Alberto Alonso; Guilarte, Juan Mateos; Plyushchay, Mikhail S.

2013-04-01

291

Multiple-event probability in general-relativistic quantum mechanics

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

292

'Mysticism' in quantum mechanics: the forgotten controversy

NASA Astrophysics Data System (ADS)

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 with Erwin Schrödinger's lectures published as 'Mind and Matter'. Becoming aware of the issues at stake can help us understand the historical, philosophical and cultural background from which today's physics emerged.

Marin, Juan Miguel

2009-07-01

293

Evading Quantum Mechanics: Engineering a Classical Subsystem within a Quantum Environment

NASA Astrophysics Data System (ADS)

Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement backaction often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that, by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement backaction of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, backaction evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical-force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broadband squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic-spin ensembles, and implementations of the quantum Toffoli gate.

Tsang, Mankei; Caves, Carlton M.

2012-07-01

294

Quantum mechanics with spontaneous localization and the quantum theory of measurement

Summary Quantum mechanics with spontaneous localization (QMSL) is a recently proposed stochastic modification of theN-body Schrödinger equation consistent both with microphysics and macrophysics. QMSL is applied here to the measurement problem.\\u000a It is shown that the replacement of standard quantum mechanics by QMSL has the only effect of producing an actual reduction\\u000a of the wave function.

F. Benatti; G. C. Ghirardi; A. Rimini; T. Weber

1987-01-01

295

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

296

THE QUANTUM MECHANICAL FOUNDATIONS OF PHILOSOPHY

Many of the most familiar features of our everyday environment, and some of our basic notions about it, stem from Relativistic Quantum Field Theory (RQFT). We argue in particular that the origin of common names, verbs, adjectives such as full and empty, the concepts of identity, similar- ity, Plato's Universals, natural numbers, and existence versus non-existence can be traced to

Cihan Saclõoglu

297

Quantum mechanics on profinite groups and partial order

NASA Astrophysics Data System (ADS)

Inverse limits and profinite groups are used in a quantum mechanical context. Two cases are considered: a quantum system with positions in the profinite group { {Z}}_p and momenta in the group { {Q}}_p/{ {Z}}_p, and a quantum system with positions in the profinite group {\\widehat{ {Z}}} and momenta in the group { {Q}}/{ {Z}}. The corresponding Schwatz-Bruhat spaces of wavefunctions and the Heisenberg-Weyl groups are discussed. The sets of subsystems of these systems are studied from the point of view of partial order theory. It is shown that they are directed-complete partial orders. It is also shown that they are topological spaces with T0-topologies, and this is used to define continuity of various physical quantities. The physical meaning of profinite groups, non-Archimedean metrics, partial orders and T0-topologies, in a quantum mechanical context, is discussed.

Vourdas, A.

2013-02-01

298

NASA Astrophysics Data System (ADS)

The last five years have witnessed an amazing development in the field of nano- and micromechanics. What was widely considered fantasy ten years ago is about to become an experimental reality: the quantum regime of mechanical systems is within reach of current experiments. Two factors (among many) have contributed significantly to this situation. As part of the widespread effort into nanoscience and nanofabrication, it is now possible to produce high-quality nanomechanical and micromechanical resonators, spanning length scales of millimetres to nanometres, and frequencies from kilohertz to gigahertz. Researchers coupled these mechanical elements to high-sensitivity actuation and readout systems such as single-electron transistors, quantum dots, atomic point contacts, SQUID loops, high-finesse optical or microwave-cavities etc. Some of these ultra-sensitive readout schemes are in principle capable of detection at the quantum limit and a large part of the experimental effort is at present devoted to achieving this. On the other hand, the fact that the groups working in the field come from various different physics backgrounds—the authors of this editorial are a representative sample—has been a constant source of inspiration for helpful theoretical and experimental tools that have been adapted from other fields to the mechanical realm. To name just one example: ideas from quantum optics have led to the recent demonstration (both in theory and experiment) that coupling a mechanical resonator to a high-finesse optical cavity can be fully analogous to the well-known sideband-resolved laser cooling of ions and hence is capable in principle of cooling a mechanical mode into its quantum ground state. There is no doubt that such interdisciplinarity has been a crucial element for the development of the field. It is interesting to note that a very similar sociological phenomenon occurred earlier in the quantum information community, an area which is deeply enriched by the diverse backgrounds and approaches of the researchers. As diverse as the approaches are the manifold of goals and perspectives for operating mechanical systems close to or within the quantum regime. Already now, nanomechanical sensors achieve single-molecule mass detection and magnetic resonance force detection from single-electron spins although they are operated far from quantum. Quantum-limited mechanical devices promise a new technology with hitherto unachieved performance for high-resolution sensing. This is also of high relevance for macroscopic mechanical resonators used in gravitational wave detectors. Furthermore, the increasing capability to couple mechanical modes to individual quantum systems raises the interesting question of whether mechanics can serve as a quantum bus in hybrid implementations of quantum information processing. Finally, the possibility of generating quantum superposition states that involve displacements of a massive macroscopic object (such as the center of mass of a mechanical beam) provides a completely new parameter regime for testing quantum theory over the amazing range from nanomechanical objects of several picograms up to gram-scale mirrors used in gravitational wave interferometers. We are looking forward to these fascinating developments! This Focus Issue is intended to highlight the present status of the field and to provide both introduction and motivation for students and researchers who want to get familiar with this exciting area or even want to join it. It also complements the conference activities of our community during the last year, where a series of dedicated invited sessions at several international conferences (APS March Meeting 2008, CLEO/QELS 2008, OSA Frontiers in Optics 2008, PQE 2008/2009 etc) culminated in the first Gordon Conference on 'Mechanical Systems at the Quantum Limit'. Given the fast development of the field it was not surprising to see that during the collection of the following contributions new progress was reported almost on a monthly basis and new groups entered the field. We intend to

Aspelmeyer, Markus; Schwab, Keith

2008-09-01

299

Comment on 'Nonlocality, Counterfactuals and Quantum Mechanics'

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

300

Some thoughts about consciousness: from a quantum mechanics perspective.

The article explores some of the basic findings of quantum physics and information theory and their possible usefulness in offering new vistas for understanding psychoanalysis and the patient-analyst interchange. Technical terms are explained and placed in context, and examples of applying quantum models to clinical experience are offered. Given the complexity of the findings of quantum mechanics and information theory, the article aims only to introduce some of the major concepts from these disciplines. Within this framework the article also briefly addresses the question of mind as well as the problematic of reducing the experience of consciousness to neurological brain functioning. PMID:23865992

Gargiulo, Gerald J

2013-08-01

301

ysteries, Puzzles, and Paradoxes in Quantum Mechanics. Proceedings

These proceedings represent papers presented at the Mysteries, Puzzles, and Paradoxes in Quantum Mechanics Workshop held in Italy, in August 1998. The Workshop was devoted to recent experimental and theoretical advances such as new interference, effects, the quantum eraser, non{minus}disturbing and Schroedinger{minus}cat{minus}like states, experiments, EPR correlations, teleportation, superluminal effects, quantum information and computing, locality and causality, decoherence and measurement theory. Tachyonic information transfer was also discussed. There were 45 papers presented at the conference,out of which 2 have been abstracted for the Energy,Science and Technology database.(AIP)

Rodolfo, B. [Department of Physics, University of Milan, (Italy)

1999-02-01

302

Maximum-power quantum-mechanical Carnot engine

In their work [J. Phys. AJPHAC50305-447010.1088\\/0305-4470\\/33\\/24\\/302 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through changes of both the width of the well and the quantum state in a specific manner.

Sumiyoshi Abe

2011-01-01

303

On the relation between classical and quantum statistical mechanics

Classical and quantum statistical mechanics are compared in the high temperature limit ?=1\\/kT?0. While this limit is rather trivial for spin systems, we obtain some rigorous results which suggest (and sometimes prove) different asymptotics for continuous systems, depending on the behaviour of the two-body potential for small distances: the difference between suitable classical and quantum variables vanishes as ?2 for

W. Wreszinski; G. Scharf

1987-01-01

304

Quantum Mechanics Emerges from Information Theory Applied to Causal Horizons

NASA Astrophysics Data System (ADS)

It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental roots of all physical phenomena. The connection between this theory and Verlinde's entropic gravity theory is also investigated.

Lee, Jae-Weon

2011-04-01

305

Quantum mechanics from an equivalence principle

The authors show that requiring diffeomorphic equivalence for one-dimensional stationary states implies that the reduced action S{sub 0} satisfies the quantum Hamilton-Jacobi equation with the Planck constant playing the role of a covariantizing parameter. The construction shows the existence of a fundamental initial condition which is strictly related to the Moebius symmetry of the Legendre transform and to its involutive character. The universal nature of the initial condition implies the Schroedinger equation in any dimension.

Faraggi, A.E. [Univ. of Florida, Gainesville, FL (United States). Inst. for Fundamental Theory; Matone, M. [Univ. of Padova (Italy)

1997-05-15

306

Investigations of fundamental phenomena in quantum mechanics with neutrons

NASA Astrophysics Data System (ADS)

Neutron interferometer and polarimeter are used for the experimental investigations of quantum mechanical phenomena. Interferometry exhibits clear evidence of quantum-contextuality and polarimetry demonstrates conflicts of a contextual model of quantum mechanics á la Leggett. In these experiments, entanglements are achieved between degrees of freedom in a single-particle: spin, path and energy degrees of freedom are manipulated coherently and entangled. Both experiments manifest the fact that quantum contextuality is valid for phenomena with matter waves with high precision. In addition, another experiment is described which deals with error-disturbance uncertainty relation: we have experimentally tested error-disturbance uncertainty relations, one is derived by Heisenberg and the other by Ozawa. Experimental results confirm the fact that the Heisenberg's uncertainty relation is often violated and that the new relation by Ozawa is always larger than the limit. At last, as an example of a counterfactual phenomenon of quantum mechanics, observation of so-called quantum Cheshire Cat is carried out by using neutron interferometer. Experimental results suggest that pre- and post-selected neutrons travel through one of the arms of the interferometer while their magnetic moment is located in the other arm.

Hasegawa, Yuji

2014-04-01

307

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

308

On the complexity of classical and quantum algorithms for numerical problems in quantum mechanics

NASA Astrophysics Data System (ADS)

Our understanding of complex quantum mechanical processes is limited by our inability to solve the equations that govern them except for simple cases. Numerical simulation of quantum systems appears to be our best option to understand, design and improve quantum systems. It turns out, however, that computational problems in quantum mechanics are notoriously difficult to treat numerically. The computational time that is required often scales exponentially with the size of the problem. One of the most radical approaches for treating quantum problems was proposed by Feytiman in 1982 [46]: he suggested that quantum mechanics itself showed a promising way to simulate quantum physics. This idea, the so called quantum computer, showed its potential convincingly in one important regime with the development of Shor's integer factorization algorithm which improves exponentially on the best known classical algorithm. In this thesis we explore six different computational problems from quantum mechanics, study their computational complexity and try to find ways to remedy them. In the first problem we investigate the reasons behind the improved performance of Shor's and similar algorithms. We show that the key quantum part in Shor's algorithm, the quantum phase estimation algorithm, achieves its good performance through the use of power queries and we give lower bounds for all phase estimation algorithms that use power queries that match the known upper bounds. Our research indicates that problems that allow the use of power queries will achieve similar exponential improvements over classical algorithms. We then apply our lower bound technique for power queries to the Sturm-Liouville eigenvalue problem and show matching lower bounds to the upper bounds of Papageorgiou and Wozniakowski [85]. It seems to be very difficult, though, to find nontrivial instances of the Sturm-Lionville problem for which power queries can be simulated efficiently. A quantum computer differs from a classical computer that uses randomness, because it allows "negative probabilities" that can cancel each other (destructive interference). Ideally we would like to transfer classical randomized algorithms to the quantum computer and get speed improvements. One of the simplest classical randomized algorithm is the random walk and we study the behavior of the continuous-time quantum random walk. We analyze this random walk in one dimension and give analytical formulas for its behavior that demonstrate its interference properties. Is interference or cancellation really the most important advantage that a quantum computer has over a classical computer? To answer that question we study the class StociMA of "stochastic quantum" algorithms that only use classical gates, but are given a quantum "witness", i.e. an arbitrary quantum state that can guide the algorithm in computing the correct answer, but should not be able to "fool" it. We show that there exists a complete problem for this class, which we call the stoquastic local Hamiltonian problem. In this problem we try to compute the lowest eigenvalue of a Hamiltonian with interactions that span only a fixed number of particles and all contribute negatively. With the help of this problem we prove that MA ? StocIMA ? SBP ? QMA. This shows that interference is one of the most important parts of quantum computation. The simulation of the evolution of a general quantum system in time requires a computational time that is exponential in the dimension of the system. But maybe the problem that we ask for is too general and we can simulate special systems in polynomial time. In particular it would be interesting to study quantum systems of "limited energy", i.e. for which the state at starting time consists mainly out of components with small energy. We model this in the theory of weighted reproducing kernel Hilbert spaces with two different sets of weights: product weights and finite-order weights. We will show that the information cost of computing the evolution for start

Bessen, Arvid J.

309

A deformation quantization theory for noncommutative quantum mechanics

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

310

Weyl-Wigner formulation of noncommutative quantum mechanics

We address the phase-space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativities. By resorting to a covariant generalization of the Weyl-Wigner transform and to the Darboux map, we construct an isomorphism between the operator and the phase-space representations of the extended Heisenberg algebra. This map provides a systematic approach to derive the entire structure of noncommutative quantum mechanics in phase space. We construct the extended star product and Moyal bracket and propose a general definition of noncommutative states. We study the dynamical and eigenvalue equations of the theory and prove that the entire formalism is independent of the particular choice of the Darboux map. Our approach unifies and generalizes all the previous proposals for the phase-space formulation of noncommutative quantum mechanics. For concreteness we rederive these proposals by restricting our formalism to some two-dimensional spaces.

Bastos, Catarina; Bertolami, Orfeu [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal); Dias, Nuno Costa; Prata, Joao Nuno [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Av. Campo Grande, 376, 1749-024 Lisboa (Portugal)

2008-07-15

311

Quantum-mechanical transport equation for atomic systems.

NASA Technical Reports Server (NTRS)

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

Berman, P. R.

1972-01-01

312

Lyapounov variable: Entropy and measurement in quantum mechanics

We discuss the question of the dynamical meaning of the second law of thermodynamics in the framework of quantum mechanics. Previous discussion of the problem in the framework of classical dynamics has shown that the second law can be given a dynamical meaning in terms of the existence of so-called Lyapounov variables—i.e., dynamical variables varying monotonically in time without becoming contradictory. It has been found that such variables can exist in an extended framework of classical dynamics, provided that the dynamical motion is suitably unstable. In this paper we begin to extend these results to quantum mechanics. It is found that no dynamical variable with the characteristic properties of nonequilibrium entropy can be defined in the standard formulation of quantum mechanics. However, if the Hamiltonian has certain well-defined spectral properties, such variables can be defined but only as a nonfactorizable superoperator. Necessary nonfactorizability of such entropy operators M has the consequence that they cannot preserve the class of pure states. Physically, this means that the distinguishability between pure states and corresponding mixtures must be lost in the case of a quantal system for which the algebra of observables can be extended to include a new dynamical variable representing nonequilibrium entropy. We discuss how this result leads to a solution of the quantum measurement problem. It is also found that the question of existence of entropy of superoperators M is closely linked to the problem of defining an operator of time in quantum mechanics.

Misra, B.; Prigogine, I.; Courbage, M.

1979-01-01

313

Nambu quantum mechanics on discrete 3-tori

NASA Astrophysics Data System (ADS)

We propose a quantization of linear, volume preserving, maps on the discrete and finite 3-torus \\mathbb{T}_N^3 represented by elements of the group SL(3,\\mathbb{Z}_N) . These flows can be considered as special motions of the Nambu dynamics (linear Nambu flows) in the three-dimensional toroidal phase space and are characterized by invariant vectors a of \\mathbb{T}_N^3 . We quantize all such flows, which are necessarily restricted on a planar two-dimensional phase space, embedded in the 3-torus, transverse to the vector a. The corresponding maps belong to the little group of \\bm{a} \\in SL(3,\\mathbb{Z}_N) , which is an SL(2,\\mathbb{Z}_N) subgroup. The associated linear Nambu maps are generated by a pair of linear and quadratic Hamiltonians (Clebsch-Monge potentials of the flow) and the corresponding quantum maps realize the metaplectic representation of SL(3,\\mathbb{Z}_N) on the discrete group of three-dimensional magnetic translations, i.e. the non-commutative 3-torus with a deformation parameter the Nth root of unity. Other potential applications of our construction are related to the quantization of deterministic chaos in turbulent maps as well as to quantum tomography of three-dimensional objects.

Axenides, M.; Floratos, E. G.; Nicolis, S.

2009-07-01

314

Quantum mechanisms of density wave transport.

We report on new developments in the quantum picture of correlated electron transport in charge and spin density waves. The model treats the condensate as a quantum fluid in which charge soliton domain wall pairs nucleate above a Coulomb blockade threshold field. We employ a time-correlated soliton tunneling model, analogous to the theory of time-correlated single electron tunneling, to interpret the voltage oscillations and nonlinear current-voltage characteristics above threshold. An inverse scaling relationship between threshold field and dielectric response, originally proposed by Grüner, emerges naturally from the model. Flat dielectric and other ac responses below threshold in NbSe(3) and TaS(3), as well as small density wave phase displacements, indicate that the measured threshold is often much smaller than the classical depinning field. In some materials, the existence of two distinct threshold fields suggests that both soliton nucleation and classical depinning may occur. In our model, the ratio of electrostatic charging to pinning energy helps determine whether soliton nucleation or classical depinning dominates. PMID:22711979

Miller, John H; Wijesinghe, Asanga I

2012-06-01

315

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

316

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.

317

On Quantum Statistical Mechanics of a Schwarzschild Black Hole

NASA Astrophysics Data System (ADS)

Quantum theory of geometry, developed recently in the framework of non-perturbative quantum gravity, is used in an attempt to explain thermodynamics of Schwarzschild black holes on the basis of a microscopical (quantum) description of the system. We work with the formulation of thermodynamics in which the black hole is enclosed by a spherical surface B and a macroscopic state of the system is specified by two parameters: the area of the boundary surface and a quasilocal energy contained within it. To derive thermodynamical properties of the system from its microscopics we use the standard statistical mechanical method of Gibbs. Under a certain number of assumptions on the quantum behavior of the system, we find that its microscopic (quantum) states are described by states of quantum Chern-Simons theory defined by sets of points on B with spins attached. The level of the Chern-Simons theory turns out to be proportional to the horizon area of the black hole measured in Planck units. The statistical mechanical analysis turns out to be especially simple in the case when the entire interior of B is occupied by a black hole. We find in this case that the entropy contained within B, that is, the black hole entropy, is proportional to the horizon surface area.

Krasnov, Kirill V.

1998-01-01

318

Quantum mechanical point of view to perturbative problems in classical mechanics.

National Technical Information Service (NTIS)

This paper shows that perturbative methods currently exploited in quantum mechanics can be used to treat a classical Liouville problem describing the evolution of an ensemble of non-collisional particles. The method we discuss is based on the introduction...

G. Dattoli A. Torre

1993-01-01

319

Conceptual and Mathematical Barriers to Students Learning Quantum Mechanics

NSDL National Science Digital Library

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. 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. 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.

2014-06-08

320

Quantum mechanical force field for water with explicit electronic polarization.

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

321

Quantum mechanical force field for water with explicit electronic polarization

A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 10{sup 6} self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across biological ion channels through membranes.

Han, Jaebeom; Mazack, Michael J. M.; Zhang, Peng; Truhlar, Donald G.; Gao, Jiali [Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street, SE, Minneapolis, Minnesota 55455-0431 (United States)] [Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street, SE, Minneapolis, Minnesota 55455-0431 (United States)

2013-08-07

322

Hilbert space for quantum mechanics on superspace

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

323

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

324

The quantum mechanics of perfect fluids

NASA Astrophysics Data System (ADS)

We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities, associated with the vortex degrees of freedom. On the one hand, these have formally a vanishing strong-coupling energy scale, thus suggesting that the effective theory's regime of validity is vanishingly narrow. On the other hand, we prove an analog of Coleman's theorem, whereby the semiclassical vacuum has no quantum counterpart, thus suggesting that the vortex premature strong-coupling phenomenon stems from a bad identification of the ground state and of the perturbative degrees of freedom. Finally, vortices break the usual connection between short distances and high energies, thus potentially impairing the unitarity of the effective theory.

Endlich, Solomon; Nicolis, Alberto; Rattazzi, Riccardo; Wang, Junpu

2011-04-01

325

On the Lattice Structure of Probability Spaces in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Let {C} be the set of all possible quantum states. We study the convex subsets of {C} with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.

Holik, Federico; Massri, César; Plastino, A.; Zuberman, Leandro

2013-06-01

326

PREFACE: EmQM13: Emergent Quantum Mechanics 2013

NASA Astrophysics Data System (ADS)

These proceedings comprise the invited lectures of the second international symposium on Emergent Quantum Mechanics (EmQM13), which was held at the premises of the Austrian Academy of Sciences in Vienna, Austria, 3–6 October 2013. The symposium was held at the ''Theatersaal'' of the Academy of Sciences, and was devoted to the open exploration of emergent quantum mechanics, a possible ''deeper level theory'' that interconnects three fields of knowledge: emergence, the quantum, and information. Could there appear a revised image of physical reality from recognizing new links between emergence, the quantum, and information? Could a novel synthesis pave the way towards a 21st century, ''superclassical'' physics? The symposium provided a forum for discussing (i) important obstacles which need to be overcome as well as (ii) promising developments and research opportunities on the way towards emergent quantum mechanics. Contributions were invited that presented current advances in both standard as well as unconventional approaches to quantum mechanics. The EmQM13 symposium was co–organized by Gerhard Grössing (Austrian Institute for Nonlinear Studies (AINS), Vienna), and by Jan Walleczek (Fetzer Franklin Fund, USA, and Phenoscience Laboratories, Berlin). After a very successful first conference on the same topic in 2011, the new partnership between AINS and the Fetzer Franklin Fund in producing the EmQM13 symposium was able to further expand interest in the promise of emergent quantum mechanics. The symposium consisted of two parts, an opening evening addressing the general public, and the scientific program of the conference proper. The opening evening took place at the Great Ceremonial Hall (Grosser Festsaal) of the Austrian Academy of Sciences, and it presented talks and a panel discussion on ''The Future of Quantum Mechanics'' with three distinguished speakers: Stephen Adler (Princeton), Gerard 't Hooft (Utrecht) and Masanao Ozawa (Nagoya). The articles contained in these proceedings represent the talks of the invited speakers as written immediately after the symposium. The volume starts with a contribution by organizers Jan Walleczek and Gerhard Grössing, essentially explaining why emergent quantum mechanics, and other deterministic approaches to quantum theory, must be considered viable approaches in quantum foundations today. This is followed by the exposition of Stephen Adler's talk who introduced to a general audience key questions at the current frontiers of quantum mechanics during the opening evening (with the contents of his conference talk appearing elsewhere). The conference proceedings then continues with the presentations as given in their chronological order i.e. starting with the opening talk of the scientific program by Gerard 't Hooft. While the page number was restricted for all invited speakers, the paper by Jeff Tollaksen was given more space, as his invited collaborator Yakir Aharonov was unable to deliver a separate talk, in order to represent both contributions in one paper. Note that the talks of all speakers, including the talks of those who could not be represented in this volume (M. Arndt, B. Braverman, C. Brukner, S. Colin, Y. Couder, B. Poirier, A. Steinberg, G. Weihs and H. Wiseman) are freely available on the conference website as video presentations (http://www.emqm13.org). The organizers wish to express their gratitude to Siegfried Fussy and Herbert Schwabl from AINS for the organizational support. The organizers also wish to thank Bruce Fetzer, President and CEO, John E. Fetzer Memorial Trust, and the Members of the Board of Trustees, for their strong support and for funding this symposium. We also wish to thank the Austrian Academy of Sciences for allowing the symposium to be held on their premises, and Anton Zeilinger, President of the Austrian Academy of Sciences, for his welcome address. The expertise of the Members of the Scientific Advisory Board of the EmQM13 symposium, Ana Maria Cetto (Mexico), Lajos Diósi (Budapest), Maurice de Gosson (Vienna), Edward Nelson (Princeton), The

2014-04-01

327

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

328

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

329

Holographic duals to poisson sigma models and noncommutative quantum mechanics

NASA Astrophysics Data System (ADS)

Poisson sigma models are a very rich class of two-dimensional theories that includes, in particular, all two-dimensional dilaton gravities. By using the Hamiltonian reduction method, we show that a Poisson sigma model (with a sufficiently well-behaving Poisson tensor) on a finite cylinder is equivalent to a noncommutative quantum mechanics for the boundary data.

Vassilevich, D. V.

2013-05-01

330

New Approach to N-Body Relativistic Quantum Mechanics

In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this approach provides the exact Newtonian dynamics for many-body, and the nonrelativistic approximation gives the complete Schrödinger equation for many-body.

Ying-Qiu Gu

2007-01-01

331

The two-body quantum mechanical problem on spheres

The quantum mechanical two-body problem with a central interaction on the sphere Sn is considered. Using recent results in representation theory, an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.

Alexey V. Shchepetilov

2006-01-01

332

Completeness of the Coulomb Wave Functions in Quantum Mechanics

ERIC Educational Resources Information Center

Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

Mukunda, N.

1978-01-01

333

Nonlinear nonlocal Schrödinger equation in the context of quantum mechanics

NASA Astrophysics Data System (ADS)

The nonlinear nonlocal equation describing the evolution of a fluctuating scalar field is studied. This nonlinear system naturally produces stable static configurations as a result of its relaxation to the dissipative attractors. It is found that the structures (and their spectra) observed in the frame of the model coincide with the eigenfunctions (and eigenvalues, respectively) of the linear quantum mechanical Schrödinger equation.

Filippov, A. E.

1996-02-01

334

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

335

a q-DEFORMATION of the Parasupersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

A q-deformation of the parasupersymmetric quantum mechanics of one boson and one parafermion of an arbitrary order p is constructed. The deformed commutators in the algebra generate braid-type relations which lift the degeneracy originally present in the undeformed case. The connection between the deformed algebra and a class of self-similar potentials is discussed.

Chakrabarti, R.; Jagannathan, R.

336

Hidden algebra method (quasi-exact-solvability in quantum mechanics)

A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.

Turbiner, Alexander [Institute for Theoretical and Experimental Physics, Moscow 117259 (Russian Federation); Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F. (Mexico)

1996-02-20

337

Quantum Mechanics of the Einstein-Hopf Model.

ERIC Educational Resources Information Center

The Einstein-Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantum mechanics. Both the wave and particle aspects of the Einstein fluctuation formula are interpreted in terms of the fundamental absorption and emission processes. (Author/SK)

Milonni, P. W.

1981-01-01

338

Quantum mechanics and faster-than-light communication: Methodological considerations

Summary A detailed quantum-mechanical analysis of a recent proposal of faster-than-light communication through wave packet reduction\\u000a is performed. The discussion allows us to focus some methodological problems about critical investigations on physical theories.

G. C. Ghirardi; T. Weber

1983-01-01

339

Quantum-mechanical theory of optomechanical Brillouin cooling

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

340

Cell motility and thermodynamic fluctuations tailoring quantum mechanics for biology

Cell motility underlying muscle contraction is an instance of thermodynamics tailoring quantum mechanics for biology. Thermodynamics is intrinsically multi-agential in admitting energy consumers in the form of energy-deficient thermodynamic fluctuations. The onset of sliding movement of an actin filament on myosin molecules in the presence of ATP molecules to be hydrolyzed demonstrates that thermodynamic fluctuations transform their nature so as

Koichiro Matsuno

2001-01-01

341

Relativistic-Particle Quantum Mechanics (Applications and Approximations) II.

National Technical Information Service (NTIS)

In this lecture I hope to show that relativistic-particle quantum mechanics with direct interactions is a useful tool for building models applicable to hadron systems at intermediate energies. To do this I will first describe a class of models designed to...

F. Coester

1981-01-01

342

Physics on the boundary between classical and quantum mechanics

NASA Astrophysics Data System (ADS)

Nature's laws in the domain where relativistic effects, gravitational effects and quantum effects are all comparatively strong are far from understood. This domain is called the Planck scale. Conceivably, a theory can be constructed where the quantum nature of phenomena at such scales can be attributed to something fundamentally simpler. However, arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there can't be physical laws that require "conspiracy". It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In the lecture we will show several such counterexamples. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. This theory is often portrayed as to underly the quantum field theory of the subatomic particles, including the "Standard Model". So now the question is asked: how can this model feature "conspiracy", and how bad is that? Is there conspiracy in the vacuum fluctuations?

't Hooft, Gerard

2014-04-01

343

Quantum-mechanical coherence in cell microtubules: a realistic possibility?

We discuss the possibility of quantum-mechanical coherence in Cell MicroTubules (MT), based on recent developments in quantum physics. We focus on potential mechanisms for 'energy-loss-free' transport along the microtubules, which could be considered as realizations of Frohlich's ideas on the role of solitons for superconductivity and/or biological matter. In particular, by representing the MT arrangements as cavities, we review a novel scenario, suggested in collaboration with D.V. Nanopoulos, concerning the formation of macroscopic (or mesoscopic) quantum-coherent states, as a result of the (quantum-electromagnetic) interactions of the MT dimers with the surrounding molecules of the ordered water in the interior of the MT cylinders. We suggest specific experiments to test the above-conjectured quantum nature of the microtubular arrangements inside the cell. These experiments are similar in nature to those in atomic physics, used in the detection of the Rabi-Vacuum coupling between coherent cavity modes and atoms. Our conjecture is that a similar Rabi-Vacuum-splitting phenomenon occurs in the absorption (or emission) spectra of the MT dimers, which would constitute a manifestation of the dimer coupling with the coherent modes in the ordered-water environment (dipole quanta), which emerge due to the phenomenon of 'super-radiance'. PMID:10379540

Mavromatos, N E

1999-05-01

344

An extended phase-space SUSY quantum mechanics

NASA Astrophysics Data System (ADS)

In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N = 2) realization of extended supersymmetry algebra and discuss the vacuum energy and topology of super-potentials. Shape invariance of exactly solvable extended SUSY potentials allows us to obtain analytic expressions for the entire energy spectrum of an extended Hamiltonian with, for example, Scarf potential without ever referring to an underlying differential equation.

Ter-Kazarian, G.

2009-02-01

345

Adiabatic approximation in PT-symmetric quantum mechanics

NASA Astrophysics Data System (ADS)

In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics, which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.

Guo, ZhiHua; Cao, HuaiXin; Lu, Ling

2014-05-01

346

Duality and the Equivalence Principle of Quantum Mechanics

Following a suggestion by Vafa, we present a quantum-mechanical model for\\u000aS-duality symmetries observed in the quantum theories of fields, strings and\\u000abranes. Our formalism may be understood as the topological limit of Berezin's\\u000ametric quantisation of the upper half-plane H, in that the metric dependence\\u000ahas been removed. Being metric-free, our prescription makes no use of global\\u000aquantum numbers.

Jose M. ISIDRO; G. Galilei

2000-01-01

347

Noncommutative unification of general relativity and quantum mechanics

We present a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry is developed in terms of a noncommutative algebra A which is defined on a transformation groupoid {gamma} given by the action of a noncompact group G on the total space E of a principal fiber bundle over space-time M. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model 'collapses' to the usual quantum mechanics.

Heller, Michael; Pysiak, Leszek; Sasin, Wieslaw [Vatican Observatory, Vatican City, V-00120 Vatican City, Rome (Italy); Department of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw (Poland)

2005-12-15

348

Quantum mechanics and faster-than-light communication Methodological considerations

NASA Astrophysics Data System (ADS)

A critical analysis is made of proposals for faster-than-light communications schemes based on quantum mechanics concepts. The point of view taken is that no reduction in one physical system can have an instantaneous effect on another, isolated system. It is shown that the philosophical contradictions exposed by the Einstein-Podolsky Rosen can be directly transferred to an interpretation of physical events. Attention is directed toward the possibility of a photon, propagating in one direction with either circular or plane polarization, entering a nonselective laser tube. The photon originally emerged from a quantum decay process which yielded two photons traveling in opposite directions. The photon in the laser gain tube precipitates a beam which is polarized as the initiating photon. A first observer can then determine the polarization observed by a second observer (with the laser) before the signal arrives. It is concluded that the FLASH argument of Herbert (1982) therefore assumes a violation of quantum mechanical laws in order to use quantum mechanics to prove that faster-than-light communication is possible.

Ghirardi, G. C.; Weber, T.

1983-11-01

349

A perspective on quantum mechanics calculations in ADMET predictions.

Understanding the molecular basis of drug action has been an important objective for pharmaceutical scientists. With the increasing speed of computers and the implementation of quantum chemistry methodologies, pharmacodynamic and pharmacokinetic problems have become more computationally tractable. Historically the former has been the focus of drug design, but within the last two decades efforts to understand the latter have increased. It takes about fifteen years and over $1 billion dollars for a drug to go from laboratory hit, through lead optimization, to final approval by the U.S. Food and Drug Administration. While the costs have increased substantially, the overall clinical success rate for a compound to emerge from clinical trials is approximately 10%. Most of the attrition rate can be traced to ADMET (absorption, distribution, metabolism, excretion, and toxicity) problems, which is a powerful impetus to study these issues at an earlier stage in drug discovery. Quantum mechanics offers pharmaceutical scientists the opportunity to investigate pharmacokinetic problems at the molecular level prior to laboratory preparation and testing. This review will provide a perspective on the use of quantum mechanics or a combination of quantum mechanics coupled with other classical methods in the pharmacokinetic phase of drug discovery. A brief overview of the essential features of theory will be discussed, and a few carefully selected examples will be given to highlight the computational methods. PMID:23675934

Bowen, J Phillip; Güner, Osman F

2013-01-01

350

Quantum gauge models without (classical) Higgs mechanism

NASA Astrophysics Data System (ADS)

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRST formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is understood without recourse to a Higgs(-Englert-Brout-Guralnik-Hagen-Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.

Dütsch, Michael; Gracia-Bondía, José M.; Scheck, Florian; Várilly, Joseph C.

2010-10-01

351

A broken symmetry ontology: Quantum mechanics as a broken symmetry

The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance.

Buschmann, J.E.

1988-01-01

352

Entropy production and equilibration in Yang-Mills quantum mechanics

NASA Astrophysics Data System (ADS)

The Husimi distribution provides for a coarse-grained representation of the phase-space distribution of a quantum system, which may be used to track the growth of entropy of the system. We present a general and systematic method of solving the Husimi equation of motion for an isolated quantum system, and we construct a coarse-grained Hamiltonian whose expectation value is exactly conserved. As an application, we numerically solve the Husimi equation of motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and calculate the time evolution of the coarse-grained entropy of a highly excited state. We show that the coarse-grained entropy saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system.

Tsai, Hung-Ming; Müller, Berndt

2012-01-01

353

Entropy production and equilibration in Yang-Mills quantum mechanics.

The Husimi distribution provides for a coarse-grained representation of the phase-space distribution of a quantum system, which may be used to track the growth of entropy of the system. We present a general and systematic method of solving the Husimi equation of motion for an isolated quantum system, and we construct a coarse-grained Hamiltonian whose expectation value is exactly conserved. As an application, we numerically solve the Husimi equation of motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and calculate the time evolution of the coarse-grained entropy of a highly excited state. We show that the coarse-grained entropy saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system. PMID:22400515

Tsai, Hung-Ming; Müller, Berndt

2012-01-01

354

Nonrelativistic quantum mechanics with consideration of influence of fundamental environment

NASA Astrophysics Data System (ADS)

Spontaneous transitions between bound states of an atomic system, the "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations ( fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger type and is defined on the extended space ?3?? n , where ?3 and ? n are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.

Gevorkyan, A. S.

2013-08-01

355

Emergence of a New Quantum Mechanics by Multivalued Logic

NASA Astrophysics Data System (ADS)

Quantum Mechanics associated with new logic like Multivalued Logic and Fuzzy Logic has progressed in different ways and their applications can be found in many fields of sciences and technologies. All the concepts attached to this theory are far from the classical view. Classical mechanics can be viewed as crisp limit of a Fuzzy quantum mechanics. This leads to the following interpretation: It is the consequence of an assumption that a quantum particle "reside" in different place or in every path of the continuum of paths which collapse into a single "unique" trajectory of an observed classical motion The reality is "Fuzzy" and nonlocal not only in space but also in time. In this sense, idealised pointlike particles of classical mechanics corresponding to the ultimate sharpness of the fuzziness density emerge in a process of interaction between different parts of fuzzy wholeness. This process is viewed as a continuous process of defuzzification. It transforms a fuzzy reality into a crisp one. It is clear that the emerging crisp reality as a final step of measurements carries less of information that the underlying fuzzy reality. This means that there is an irreversible loss of information usually called "collapse of the wave function". It is not so much a "collapse" as a realization of one of the many possibilities existing within a fuzzy reality. Any measurements rearrange the fuzzy reality leading to different detection outcomes.

de Gerlicz, Claude Gaudeau; Antoine, Mathias; Bobola, Philippe; Flawisky, Nicolas; Hebras, Xavier; Mundedi, Musa

2013-09-01

356

Third emission mechanism in solid-state nanocavity quantum electrodynamics.

Photonic crystal (PC) nanocavities have been receiving a great deal of attention recently because of their ability to strongly confine photons in a tiny space with a high quality factor. According to cavity quantum electrodynamics (cavity QED), such confined photons can achieve efficient interactions with excitons in semiconductors, leading to the Purcell effect in the weak coupling regime and vacuum Rabi splitting (VRS) in the strong coupling regime. These features are promising for applications such as quantum information processing, highly efficient single photon sources and ultra-low threshold lasers. In this context, the coupled system of a semiconductor quantum dot (QD) and a PC nanocavity has been intensively investigated in recent years.Although experimental reports have demonstrated such fundamental features, two anomalous phenomena have also been observed. First, photon emission from the cavity occurs even when it is significantly detuned from the QD. Second, spectral triplets are formed by additional bare-cavity lines between the VRS lines. These features cannot be explained by standard cavity QED theories and have prompted controversy regarding their physical mechanisms. In this review we describe the recent experimental and theoretical progress made in the investigation of these phenomena. Similar mechanisms will also occur in many other coupled quantum systems, and thus the findings are applicable to a wide range of fields. PMID:22885777

Yamaguchi, Makoto; Asano, Takashi; Noda, Susumu

2012-09-01

357

Measurement and quasi-states in quantum mechanics

Part of the task of quantum logic is to account for the collapse of the state vector during measurement. A difficulty in this is that it is not obvious how to describe measurement quantum mechanically as the interaction of two or more systems; interacting quantum-mechanical systems do not possess states, so their states cannot collapse. This dissertation shows that component systems of a composite system possess families of state-like vectors. These are the quasi-projections of the state vector of the composite system, each associated with a family of commutable observables. Often these quasi-projections cluster so closely around a quasi-state that they are practically indistinguishable from it. A description of measurement based on quasi-projections reveals the apparent collapse of the state vector during measurement to be illusory. The continuous evolution of the state of the composite system give rise to abrupt changes in the quasi-projections which make it appear that the state has changed. The quasi-projections cease to cluster near one quasi-state, are momentarily scattered, and then cluster again near another quasi-state. The concept of quasi-projection is also used to generalize the quantum logic of Birkhoff and von Neumann in such a fashion that a proposition can always be assigned a truth value.

Harper, C.D.

1987-01-01

358

Delirium Quantum Or, where I will take quantum mechanics if it will let me

NASA Astrophysics Data System (ADS)

Once again, I take advantage of the wonderfully liberal and tolerant mood Andrei Khrennikov sets at his yearly conferences by submitting a nonstandard paper for the proceedings. This pseudo-paper consists of excerpts drawn from two of my samizdats [Quantum States: What the Hell Are They? and Darwinism All the Way Down (and Probabilism All the Way Back Up)] that I think best summarize what I am aiming for on the broadest scale with my quantum foundations program. Section 1 tries to draw a picture of a physical world whose essence is ``Darwinism all the way down.'' Section 2 outlines how quantum theory should be viewed in light of that, i.e., as being an expression of probabilism (in Bruno de Finetti or Richard Jeffrey's sense) all the way back up. Section 3 describes how the idea of ``identical'' quantum measurement outcomes, though sounding atomistic in character, nonetheless meshes well with a William Jamesian style ``radical pluralism.'' Sections 4 and 5 further detail how quantum theory should not be viewed so much as a ``theory of the world,'' but rather as a theory of decision-making for agents immersed within a quantum world-that is, a world in continual creation. Finally, Sections 6 and 7 attempt to sketch once again the very positive sense in which quantum theory is incomplete, but still just as complete is it can be. In total, I hope these heady speculations convey some of the excitement and potential I see for the malleable world quantum mechanics hints of.

Fuchs, Christopher A.

2007-02-01

359

A quantum mechanical polarizable force field for biomolecular interactions

We introduce a quantum mechanical polarizable force field (QMPFF) fitted solely to QM data at the MP2/aTZ(-hp) level. Atomic charge density is modeled by point-charge nuclei and floating exponentially shaped electron clouds. The functional form of interaction energy parallels quantum mechanics by including electrostatic, exchange, induction, and dispersion terms. Separate fitting of each term to the counterpart calculated from high-quality QM data ensures high transferability of QMPFF parameters to different molecular environments, as well as accurate fit to a broad range of experimental data in both gas and liquid phases. QMPFF, which is much more efficient than ab initio QM, is optimized for the accurate simulation of biomolecular systems and the design of drugs.

Donchev, A. G.; Ozrin, V. D.; Subbotin, M. V.; Tarasov, O. V.; Tarasov, V. I.

2005-01-01

360

A quantum mechanical polarizable force field for biomolecular interactions.

We introduce a quantum mechanical polarizable force field (QMPFF) fitted solely to QM data at the MP2/aTZ(-hp) level. Atomic charge density is modeled by point-charge nuclei and floating exponentially shaped electron clouds. The functional form of interaction energy parallels quantum mechanics by including electrostatic, exchange, induction, and dispersion terms. Separate fitting of each term to the counterpart calculated from high-quality QM data ensures high transferability of QMPFF parameters to different molecular environments, as well as accurate fit to a broad range of experimental data in both gas and liquid phases. QMPFF, which is much more efficient than ab initio QM, is optimized for the accurate simulation of biomolecular systems and the design of drugs. PMID:15911753

Donchev, A G; Ozrin, V D; Subbotin, M V; Tarasov, O V; Tarasov, V I

2005-05-31

361

The equivalence principle of quantum mechanics: Uniqueness theorem

Recently the authors showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p = {partial_derivative}{sub q}S{sub 0} and exploits a basic GL(2,C)-symmetry which underlies the canonical formalism. In particular, they looked for the special transformations leading to the free system with vanishing energy. Furthermore, they saw that while on the one hand the equivalence principle cannot be consistently implemented in classical mechanics, on the other it naturally led to the quantum analogue of the Hamilton-Jacobi equation, thus implying the Schroedinger equation. In this letter they show that actually the principle uniquely leads to this solution. The authors also express the canonical and Schroedinger equations by means of the brackets recently introduced in the framework of N = 2 SYM. These brackets are the analogue of the Poisson brackets with the canonical variables taken as dependent.

Faraggi, A.E. [Univ. of Florida, Gainesville, FL (United States). Inst. for Fundamental Theory; Matone, M. [Univ. of Padova (Italy)

1997-10-28

362

Developing and evaluating animations for teaching quantum mechanics concepts

NASA Astrophysics Data System (ADS)

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 including animated step-by-step explanations of key points. The animations are freely available, with additional resources available to instructors. We have investigated their educational effectiveness both in terms of student attitude and performance. Questionnaires showed that students are on the whole very positive about the animations and make substantial use of them. A diagnostic survey administered to level 2 and 3 students showed that level 2 students significantly outperformed level 3 students on topics which they had investigated using the animations.

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

2010-11-01

363

F-theory Yukawa couplings and supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

The localized fermions on the intersection curve ? of D7-branes, are connected to a N=2 supersymmetric quantum mechanics algebra. Due to this algebra the fields obey a global U(1) symmetry. This symmetry restricts the proton decay operators and the neutrino mass terms. Particularly, we find that several proton decay operators are forbidden and the Majorana mass term is the only one allowed in the theory. A special SUSY QM algebra is studied at the end of the paper. In addition we study the impact of a non-trivial holomorphic metric perturbation on the localized solutions along each matter curve. Moreover, we study the connection of the localized solutions to an N=2 supersymmetric quantum mechanics algebra when background fluxes are turned on.

Oikonomou, V. K.

2012-03-01

364

Novel symmetries in N=2 supersymmetric quantum mechanical models

NASA Astrophysics Data System (ADS)

We demonstrate the existence of a novel set of discrete symmetries in the context of the N=2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X-Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N=2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory.

Malik, R. P.; Khare, Avinash

2013-07-01

365

Quantum mechanical properties of graphene nano-flakes and quantum dots.

In recent years considerable attention has been given to methods for modifying and controlling the electronic and quantum mechanical properties of graphene quantum dots. However, as these types of properties are indirect consequences of the wavefunction of the material, a more efficient way of determining properties may be to engineer the wavefunction directly. One way of doing this may be via deliberate structural modifications, such as producing graphene nanostructures with specific sizes and shapes. In this paper we use quantum mechanical simulations to determine whether the wavefunction, quantified via the distribution of the highest occupied molecular orbital, has a direct and reliable relationship to the physical structure, and whether structural modifications can be useful for wavefunction engineering. We find that the wavefunction of small molecular graphene structures can be different from those of larger nanoscale counterparts, and the distribution of the highest occupied molecular orbital is strongly affected by the geometric shape (but only weakly by edge and corner terminations). This indicates that both size and shape may be more useful parameters in determining quantum mechanical and electronic properties, which should then be reasonably robust against variations in the chemical passivation or functionalisation around the circumference. PMID:22903345

Shi, Hongqing; Barnard, Amanda S; Snook, Ian K

2012-11-01

366

Relationship between quantum mechanics with and without monopoles

We show that the inclusion of the monopole field in the three- and\\u000afive-dimensional spherically symmetric quantum mechanical systems, supplied by\\u000athe addition of the special centrifugal term, does not yield any change in the\\u000aradial wavefunction and in the functional dependence of the energy spectra on\\u000aquantum numbers. The only change in the spectrum is the lift of the

Levon Mardoyan; Armen Nersessian; Armen Yeranyan

2006-01-01

367

Maximum-power quantum-mechanical Carnot engine

In their work [J. Phys. A: Math. Gen. 33, 4427 (2000)], Bender, Brody, and\\u000aMeister have shown by employing a two-state model of a particle confined in the\\u000aone-dimensional infinite potential well that it is possible to construct a\\u000aquantum-mechanical analog of the Carnot engine through the changes of both the\\u000awidth of the well and the quantum state in

Sumiyoshi Abe

2010-01-01

368

Meshless local Petrov-Galerkin (MLPG) methods in quantum mechanics

Purpose – The purpose of this paper is to solve both eigenvalue and boundary value problems coming from the field of quantum mechanics through the application of meshless methods, particularly the one known as meshless local Petrov-Galerkin (MLPG). Design\\/methodology\\/approach – Regarding eigenvalue problems, the authors show how to apply MLPG to the time-independent Schrödinger equation stated in three dimensions. Through

Williams L. Nicomedes; Renato C. Mesquita; Fernando J. S. Moreira

2011-01-01

369

Degree of polarization and quantum-mechanical purity

NASA Astrophysics Data System (ADS)

The purity parameter is used in quantum mechanics to discriminate pure states from mixed states. We employ this concept to define a degree of polarization for general, three-dimensional, classical random electric fields. Our approach leads to a result that is identical with a recent definition obtained by a decomposition of the polarization matrix in terms of the Gell-Mann matrices. We also give an expression for this degree of polarization based on the constituent two-dimensional subsystems.

Moya-Cessa, H.; Moya-Cessa, J. R.; Landgrave, J. E. A.; Martinez-Niconoff, G.; Perz Leija, A.; Friberg, A. T.

2008-04-01

370

When is a hidden variable theory compatible with quantum mechanics?

This paper is devoted to a study of some of the basic conditions which have to be satisfied by a hidden variable theory in\\u000a order that it can reproduce the quantum mechanical probabilities. Of course one such condition, which emerges from the important\\u000a theorem of Bell, is that a hidden variable theory has to be non-local. It is shown that

M D Srinivas

1982-01-01

371

Supersymmetric quantum mechanics on non-commutative space

We construct a supersymmetric quantum mechanics in terms of two real supercharges on non-commutative space in arbitrary dimensions. We obtain the exact eigenspectra of the two- and three-dimensional non-commutative superoscillators. We further show that a reduction in the phase space occurs for a critical surface in the space of parameters. At this critical surface, the energy spectrum of the bosonic

Pijush K. Ghosh

2005-01-01

372

Lyapounov Variable: Entropy and Measurement in Quantum Mechanics

We discuss the question of the dynamical meaning of the second law of thermodynamics in the framework of quantum mechanics. Previous discussion of the problem in the framework of classical dynamics has shown that the second law can be given a dynamical meaning in terms of the existence of so-called Lyapounov variables-i.e., dynamical variables varying monotonically in time without becoming

B. Misra; I. Prigogine; M. Courbage

1979-01-01

373

Hidden algebra method (quasi-exact-solvability in quantum mechanics)

A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland {ital N}-body problems ass ociated with an existence of the hidden algebra {ital sl}{sub {ital N}} is discussed extensively. {copyright} {ital 1996 American Institute of Physics.}

Turbiner, A. [Institute for Theoretical and Experimental Physics, Moscow 117259 (Russia)]|[Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F. (Mexico)

1996-02-01

374

Quantum mechanics versus local realism for neutral kaon pairs

We formulate the theory of K0K0 pairs by including variables which determine when the two kaons will undergo a simultaneous jump of strangeness. This approach is a direct consequence of the EPR reality criterion when locality is also taken into account. The probabilities of observing K0K0 and KSK0 pairs at different proper times are shown to disagree with quantum mechanical

Paolo Privitera; Franco Selleri

1992-01-01

375

Quantum Mechanics in Chemistry (by Jack Simons and Jeff Nichols)

NASA Astrophysics Data System (ADS)

Topics in Physical Chemistry Series. Oxford University Press: New York, 1997. xxiii + 612 pp. Illustrations. ISBN 0-19-508200-1. $75.00. One of the problems faced by graduate-level quantum mechanics courses in chemistry is that there is often little time for studying chemical problems. Students must learn so much matrix algebra and notation that a first-semester course seems more like a math or physics course than chemistry. Another problem is the focus of most graduate texts. Excellent texts, such as those by Sakurai, and older treatments, such as Messiah and Cohen-Tannoudji, offer a comprehensive amount of mathematical rigor to go along with chemistry problems, but it seems the intended audience is hard-core theoretical or physical chemistry students. Requirements that are more general, such as reaction-path dynamics, structure and term symbols, and symmetry in quantum mechanical problems, are often left behind. Schatz and Ratner's Book Quantum Mechanics in Chemistry (Prentice Hall) is one book that fills this gap (at least for second-semester students); Simons and Nichols' new book is another, but it is a book that requires revision before it can be seriously considered.

McCallum, C. Michael

1998-12-01

376

Quantum Mechanical Probabilities on a General Spacetime-Surface

NASA Astrophysics Data System (ADS)

A theoretical aspect of quantum mechanical probabilities is studied. In nonrelativistic quantum mechanics (NRQM) for a particle, Schrödinger's wave function assigns probabilities to possible places where the particle is found on a surface (hypersurface in Newtonian spacetime) of constant time. We may then ask if quantum mechanical probabilities can be defined for an exhaustive set of exclusive outcomes of observations made on a surface on which Newtonian time is not constant. Such a question may be said to belong to the study of the role of time in NRQM in a broad sense. Specifically we investigate the theoretical possibility of a probabilistic description of (I) where and how many times the particle intersects the surface, and of (II) where and how many times the particle is found on the surface. For each case we formulate two conditions for the success of a probabilistic description. They are the classifiability condition and the no-interference condition, both of which are conditions on the propagator of the particle. For each case it is proved that the former condition does not hold and that consequently a probabilistic description is theoretically impossible either for (I) or for (II).

Yamada, N.; Takagi, S.

1991-05-01

377

Novel symmetries in N=2 supersymmetric quantum mechanical models

We demonstrate the existence of a novel set of discrete symmetries in the context of the N=2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X–Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N=2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory. -- Highlights: •Discrete symmetries of two completely different kinds of N=2 supersymmetric quantum mechanical models have been discussed. •The discrete symmetries provide physical realizations of Hodge duality. •The continuous symmetries provide the physical realizations of de Rham cohomological operators. •Our work sheds a new light on the meaning of the above abstract operators.

Malik, R.P., E-mail: malik@bhu.ac.in [Physics Department, BHU-Varanasi-221 005 (India); DST-CIMS, Faculty of Science, BHU-Varanasi-221 005 (India); Khare, Avinash, E-mail: khare@iiserpune.ac.in [Indian Institute of Science for Education and Research, Pune-411 021 (India)] [Indian Institute of Science for Education and Research, Pune-411 021 (India)

2013-07-15

378

A discussion about the quantum mechanical effects on noise properties of ballistic (phase-coherent) nanoscale devices is presented. It is shown that quantum noise can be understood in terms of quantum trajectories. This interpretation provides a simple and intuitive explanation of the origin of quantum noise that can be very salutary for nanoelectronic engineers. In particular, an injection model is presented

Xavier Oriols

2003-01-01

379

Np Incorporation into Uranyl Alteration Phases: A Quantum Mechanical Approach

Neptunium is a major contributor to the long-term radioactivity in a geologic repository for spent nuclear fuel (SNF) due to its long half-life (2.1 million years). The mobility of Np may be decreased by its incorporation into the U{sup 6+} phases that form during the corrosion of SNF. The ionic radii of Np{sup 5+} (0.089 nm) and U{sup 6+} (0.087 nm) are similar, as is their chemistry. Experimental studies have shown that Np can be incorporated into uranyl phases up to concentrations on the order of 100 ppm. The low concentration of Np in the uranyl phases complicates experimental detection and presents a significant challenge for determining the incorporation mechanism. Therefore, we have used quantum mechanical calculations to investigate incorporation mechanisms and evaluate the energetics of Np substituting for U. CASTEP, a density functional theory based code that uses plane waves to model the behavior of the valence electrons and pseudo-potentials to model the behavior of the core and inner valence electrons, was used to calculate optimal H positions, relaxed geometry, and the energy of different uranyl phases. The incorporation energy for Np into uranyl alteration phases was calculated for studtite, [(UO{sub 2})O{sub 2}(H{sub 2}O){sub 2}](H{sub 2}O){sub 2}, and boltwoodite, HK(UO{sub 2})(SiO{sub 4}) 1.5(H{sub 2}O). Studtite is the rare case of a stable, naturally-occurring peroxide mineral, in this case a uranyl hydroxyl peroxide that forms in the presence of H{sub 2}O{sub 2} from the radiolysis of H{sub 2}O. For studtite, two incorporation mechanisms were evaluated: (1) charge-balanced substitution of Np{sup 5+} and H{sup +} for one U{sup 6+}, and (2) direct substitution of Np{sup 6+} for U{sup 6+}. For boltwoodite, the H atomic positions prior to Np incorporation were determined, as well as the Np incorporation mechanisms and the corresponding substitution energies. The preferential incorporation of Np into different structure types of U{sup 6+} minerals was also investigated. Quantum mechanical substitution energies have to be derived at Np concentrations higher than the ones found in experiments or expected in a repository in order to avoid the calculation of unit cells that are too large to be handled quantum mechanically. However, the quantum mechanical results are crucial for subsequent empirical force-field and Monte-Carlo simulations to determine the thermodynamically stable limit of Np incorporation into these uranyl phases. (authors)

Shuller, Lindsay [Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, 48109 (United States); Ewing, Rodney C. [Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, 48109 (United States)]|[Department of Geological Sciences, University of Michigan, Ann Arbor, MI, 48109 (United States); Becker, Udo [Department of Geological Sciences, University of Michigan, Ann Arbor, MI, 48109 (United States)

2007-07-01

380

NASA Astrophysics Data System (ADS)

A theoretical attempt is made to find a nontrivial example of a set of non-interfering (decohering) alternatives which are not restrictecd to an instant of time and for which quantum mechanical probabilities can be defined. Confining ourselves to nonrelativistic quantum mechanics for a particle, we find an example of such a set. The set consists of two alternatives which formally correspond to two outcomes of a `Yes-No' experiment. `Yes' is the occurrence that a particle is found on a given domain on a simple hypersurface in Newtonian spacetime, and `No' is the complement to `Yes'. in this example, absence of interference between the two alternatives is a consequence of a special choice of the symmetry of an initial amplitude. It turns out that the probabilities are 1 for `No' and 0 for `Yes'.

Yamada, N.; Takagi, S.

1991-09-01

381

The measurement problem in quantum mechanics: A phenomenological investigation

NASA Astrophysics Data System (ADS)

This dissertation is a phenomenological investigation of the measurement problem in quantum mechanics. The primary subject matter for description and analysis is scientific instruments and their use in experiments which elicit the measurement problem. A methodological critique is mounted against the ontological commitments taken for granted in the canonical interpretations of quantum theory and the scientific activity of measurement as the necessary interface between theoretical interest and perceptual results. I argue that an aesthetic dimension of reality functions as aproto-scientific establishment of sense-making that constantly operates to set integratively all other cognitively neat determinations, including scientifically rendered objects that are intrinsically non-visualizable. The way in which data "key in" to the original and originative register of the sensible in observation is clarified by examining prostheses, measuring apparatuses and instruments that are sense-conveying and -integrative with the human sensorium. Experiments, technology and instrumentation are examined in order to understand how knowing and that which is known is bonded by praxis-aisthesis. Quantum measurement is a praxic-dynamie activity and homologically structured and structur ing functional engagement in terms of instantiation, quantifiability, and spatiotemporal differentiation. The distinctions between a beauty-aesthetic and praxis-aisthesis are delineated. It is argued that a beauty-aesthetic is a construal of the economic dimension of scientific objects and work, and is not the primary manner in which the aesthetic dimension is disclosed. The economic dimension of abstractions reduces to an austere aesthetic of calculative economy. Nature itself, however, is not stingy; it is intrinsically capacious, extravagant, full of surprise, nuance, ambiguity and allusiveness. The capaciousness of Nature and the way in which we are integratively set within Nature in a materiality-phenomenality correlation discloses Nature's constituent potential, a condition more primitive than causal interplay. Finally, the relation between a physical mechanism or process and its functional mathematical representation is clarified. No physical mechanism or process accounts for the empirical effects of measurement outcomes in some quantum mechanical experiments. Within the milieu of ordinary perceptual experience, complete with its horizonal structure of spatiality and temporality, something uncaused is encountered which resists full determination in terms of mathematical representation. Keywords: Quantum Mechanics, Measurement Problem, Phenomenology, Prosthesis, Aesthetic

Hunter, Joel Brooks

382

The Density Matrix Deformation in Quantum and Statistical Mechanics of the Early Universe

NASA Astrophysics Data System (ADS)

In this paper a new approach to investigation of Quantum and Statistical Mechanics of the Early Universe (Planck scale) - density matrix deformation - is proposed. Quantum Mechanics of the Early Universe is chosen as Quantum Mechanics with Fundamental Length. Here Quantum Mechanics with Fundamental Length is obtained as a deformation of well-known Quantum Mechanics. The proposed approach allows to describe dynamics. It is demonstrated that Statistical Mechanics of the Early Universe is a deformation of the conventional Statistical Mechanics. The statistical-mechanics deformation is constructed by analogy to the earlier quantum mechanical results. Some implications of the obtained results are discussed. In particular, the problem of singularity, possible improvement of the definition of statistical entropy and the problem of information loss in black holes are considered. It is noted that the obtained results enable the derivation of the Bekenstein-Hawking's formula for the black hole entropy in a semiclassical approximation in a simple and natural way.

Shalyt-Margolin, Alexander E.; Strazhev, Vassilii I.

383

The modern tools of quantum mechanics. A tutorial on quantum states, measurements, and operations

NASA Astrophysics Data System (ADS)

We address the basic postulates of quantum mechanics and point out that they are formulated for a closed isolated system. Since we are mostly dealing with systems that interact or have interacted with the rest of the universe one may wonder whether a suitable modification is needed, or in order. This is indeed the case and this tutorial is devoted to review the modern tools of quantum mechanics, which are suitable to describe states, measurements, and operations of realistic, not isolated, systems. We underline the central role of the Born rule and and illustrate how the notion of density operator naturally emerges, together with the concept of purification of a mixed state. In reexamining the postulates of standard quantum measurement theory, we investigate how they may be formally generalized, going beyond the description in terms of selfadjoint operators and projective measurements, and how this leads to the introduction of generalized measurements, probability operator-valued measures (POVMs) and detection operators. We then state and prove the Naimark theorem, which elucidates the connections between generalized and standard measurements and illustrates how a generalized measurement may be physically implemented. The "impossibility" of a joint measurement of two non commuting observables is revisited and its canonical implementation as a generalized measurement is described in some details. The notion of generalized measurement is also used to point out the heuristic nature of the so-called Heisenberg principle. Finally, we address the basic properties, usually captured by the request of unitarity, that a map transforming quantum states into quantum states should satisfy to be physically admissible, and introduce the notion of complete positivity (CP). We then state and prove the Stinespring/Kraus-Choi-Sudarshan dilation theorem and elucidate the connections between the CP-maps description of quantum operations, together with their operator-sum representation, and the customary unitary description of quantum evolution. We also address transposition as an example of positive map which is not completely positive, and provide some examples of generalized measurements and quantum operations.

Paris, M. G. A.

2012-04-01

384

Elementary Quantum Mechanics in a Space-Time Lattice

NASA Astrophysics Data System (ADS)

Studies of quantum fields and gravity suggest the existence of a minimal length, such as Planck length. It is natural to ask how the existence of a minimal length may modify the results in elementary quantum mechanics (QM) problems familiar to us. In this paper we address a simple problem from elementary non-relativistic quantum mechanics, called "particle in a box", where the usual continuum (1+1)-space-time is supplanted by a space-time lattice. Our lattice consists of a grid of ? 0× ? 0 rectangles, where ? 0, the lattice parameter, is a fundamental length (say Planck length) and, we take ? 0 to be equal to ? 0/ c. The corresponding Schroedinger equation becomes a difference equation, the solution of which yields the q-eigenfunctions and q-eigenvalues of the energy operator as a function of ? 0. The q-eigenfunctions form an orthonormal set and both q-eigenfunctions and q-eigenvalues reduce to continuum solutions as ? 0?0. The corrections to eigenvalues because of the assumed lattice is shown to be O(?02). We then compute the uncertainties in position and momentum, ? x, ? p for the box problem and study the consequent modification of Heisenberg uncertainty relation due to the assumption of space-time lattice, in contrast to modifications suggested by other investigations.

Bhatia, Manjit; Swamy, P. Narayana

2011-06-01

385

Objectivity in Perspective: Relationism in the Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Pekka Lahti is a prominent exponent of the renaissance of foundational studies in quantum mechanics that has taken place during the last few decades. Among other things, he and coworkers have drawn renewed attention to, and have analyzed with fresh mathematical rigor, the threat of inconsistency at the basis of quantum theory: ordinary measurement interactions, described within the mathematical formalism by Schrödinger-type equations of motion, seem to be unable to lead to the occurrence of definite measurement outcomes, whereas the same formalism is interpreted in terms of probabilities of precisely such definite outcomes. Of course, it is essential here to be explicit about how definite measurement results (or definite properties in general) should be represented in the formalism. To this end Lahti et al. have introduced their objectification requirement that says that a system can be taken to possess a definite property if it is certain (in the sense of probability 1) that this property will be found upon measurement. As they have gone on to demonstrate, this requirement entails that in general definite outcomes cannot arise in unitary measuring processes. In this paper we investigate whether it is possible to escape from this deadlock. As we shall argue, there is a way out in which the objectification requirement is fully maintained. The key idea is to adapt the notion of objectivity itself, by introducing relational or perspectival properties. It seems that such a “relational perspective” offers prospects of overcoming some of the long-standing problems in the interpretation of quantum mechanics.

Dieks, Dennis

2009-07-01

386

Draft paper Understanding Student Diculties in First Year Quantum Mechanics Courses

From February through May 2005, two courses on quantum me- chanics have been closely observed to identify problems students may have when learning quantum mechanics. These observations were done in the first phase of a PhD project on the teaching and learn- ing of introductory quantum mechanics. The observations show that students seem to have diculties with the Copenhagen interpretation

Lodewijk Koopman

387

The mathematical apparatus of quantum mechanics as applied to investigation into biological systems

NASA Astrophysics Data System (ADS)

Diffusion-Schrödinger quantum mechanics unusual as to its physics has been constructed by introducing a diffusion analog of the Planck constant and generalizing the diffusion equation. The mechanics can be widely used in quantum biology, biological electronics, synthetic biology, quantum geometrodynamics, and in other fields of science and technology.

Lasukov, V. V.; Lasukova, T. V.

2013-08-01

388

Creative Confusion. Quantum Theory on the Way to Wave Mechanics

NASA Astrophysics Data System (ADS)

When wave mechanics was formulated by de Broglie and Schrödinger in the mid-twenties, there was practically no empirical evidence for wave-like behavior of matter. What then were the motivations for pursuing an idea that was rather at odds with the discontinuity that quantum theory seemed to demand? Paradoxically, they can be found in the attempts to understand the quantum nature of light, for which just at that time empirical evidence could not be ignored anymore. In my talk, I will argue that ``wave-particle duality'' was initially nothing more than a confusion of competing theoretical explanations. It was in statistical mechanics where this idea first took on a more concrete form of a symmetry of two different theoretical explanations. And it was statistical mechanics that allowed this model of dual explanations to be transferred to the theory of matter. This transfer culminated in Schrödinger's paper of December 1925 ``On Einstein's Gas Theory,'' which explicitly uses the symmetry of explanations to motivate a wave theory of matter. It is here that Schrödinger's equivalent to Heisenberg's ``Umdeutung'' (reinterpretation) of mechanical quantities is to be found, not in his more famous 1926 papers on atomic theory.

Lehner, Christoph

2008-04-01

389

Representations for a spins-first approach to quantum mechanics

NSDL National Science Digital Library

In the Paradigms in Physics Curriculum at Oregon State University, we take a spins-first approach to quantum mechanics using a java simulation of successive Stern-Gerlach experiments to explore the postulates. The experimental schematic is a diagrammatic representation that we use throughout our discussion of quantum measurements. With a spins-first approach, it is natural to start with Dirac bra-ket language for states, observables, and projection operators. We also use explicit matrix representations of operators and ask students to translate between the Dirac and matrix languages. The projection of the state onto a basis is represented with a histogram. When we subsequently introduce wave functions, the wave function attains a natural interpretation as the continuous limit of these discrete histograms or a projection of a Dirac ket onto position or momentum eigenstates. We are able to test the students' facility with moving between these representations in later modules.

Manogue, Corinne A.; Gire, Elizabeth; Mcintyre, David; Tate, Janet

2012-05-15

390

Maximum-power quantum-mechanical Carnot engine.

In their work [J. Phys. A 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through changes of both the width of the well and the quantum state in a specific manner. Here, a discussion is developed about realizing the maximum power of such an engine, where the width of the well moves at low but finite speed. The efficiency of the engine at the maximum power output is found to be universal independently of any of the parameters contained in the model. PMID:21599125

Abe, Sumiyoshi

2011-04-01

391

Anomalous paths in quantum mechanical path-integrals

NASA Astrophysics Data System (ADS)

We investigate modifications of the discrete-time lattice action, for a quantum mechanical particle in one spatial dimension, that vanish in the naïve continuum limit but which, nevertheless, induce non-trivial effects due to quantum fluctuations. These effects are seen to modify the geometry of the paths contributing to the path-integral describing the time evolution of the particle, which we investigate through numerical simulations. In particular, we demonstrate the existence of a modified lattice action resulting in paths with any fractal dimension, df, between one and two. We argue that df=2 is a critical value, and we exhibit a type of lattice modification where the fluctuations in the position of the particle becomes independent of the time step, in which case the paths are interpreted as superdiffusive Lévy flights. We also consider the jaggedness of the paths, and show that this gives an independent classification of lattice theories.

Grimsmo, Arne L.; Klauder, John R.; Skagerstam, Bo-Sture K.

2013-11-01

392

Representations for a spins-first approach to quantum mechanics

NASA Astrophysics Data System (ADS)

In the Paradigms in Physics Curriculum at Oregon State University, we take a spins-first approach to quantum mechanics using a java simulation of successive Stern-Gerlach experiments to explore the postulates. The experimental schematic is a diagrammatic representation that we use throughout our discussion of quantum measurements. With a spins-first approach, it is natural to start with Dirac bra-ket language for states, observables, and projection operators. We also use explicit matrix representations of operators and ask students to translate between the Dirac and matrix languages. The projection of the state onto a basis is represented with a histogram. When we subsequently introduce wave functions, the wave function attains a natural interpretation as the continuous limit of these discrete histograms or a projection of a Dirac ket onto position or momentum eigenstates. We are able to test the students' facility with moving between these representations in later modules.

Manogue, Corinne; Gire, Elizabeth; McIntyre, David; Tate, Janet

2012-02-01

393

Classical and quantum-mechanical plane switching in CO2

NASA Astrophysics Data System (ADS)

Classical plane switching takes place in systems with a pronounced 1:2 resonance, where the degree of freedom with the lowest frequency is doubly degenerate. Under appropriate conditions, one observes a periodic and abrupt precession of the plane in which the doubly degenerate motion takes place. In this article, we show that quantum plane switching exists in CO2. Based on our analytical solutions of classical Hamilton's equations of motion, we describe the dependence on vibrational angular momentum and energy of the frequency of switches and the plane switching angle. Using these results, we find optimal initial wave-packet conditions for CO2 and show, through quantum-mechanical propagation, that such a wave packet indeed displays plane switching at energies around 10 000 cm-1 above the ground state on time scales of about 100 fs.

Sanrey, Michaël; Joyeux, Marc; Sadovskii, Dmitrii A.

2006-02-01

394

Communication: Quantum Zeno-based control mechanism for molecular fragmentation

NASA Astrophysics Data System (ADS)

A quantum control mechanism is proposed for molecular fragmentation processes within a scenario grounded on the quantum Zeno effect. In particular, we focus on the van der Waals Ne-Br2 complex, which displays two competing dissociation channels via vibrational and electronic predissociation. Accordingly, realistic three-dimensional wave packet simulations are carried out by using ab initio interaction potentials recently obtained to reproduce available experimental data. Two numerical models to simulate the repeated measurements are reported and analyzed. It is found that the otherwise fast vibrational predissociation is slowed down in favor of the slow electronic (double fragmentation) predissociation, which is enhanced by several orders of magnitude. Based on these theoretical predictions, some hints to experimentalists to confirm their validity are also proposed.

Sanz-Sanz, C.; Sanz, A. S.; González-Lezana, T.; Roncero, O.; Miret-Artés, S.

2012-03-01

395

Probing scattering mechanisms with symmetric quantum cascade lasers.

A characteristic feature of quantum cascade lasers is their unipolar carrier transport. We exploit this feature and realize nominally symmetric active regions for terahertz quantum cascade lasers, which should yield equal performance with either bias polarity. However, symmetric devices exhibit a strongly bias polarity dependent performance due to growth direction asymmetries, making them an ideal tool to study the related scattering mechanisms. In the case of an InGaAs/GaAsSb heterostructure, the pronounced interface asymmetry leads to a significantly better performance with negative bias polarity and can even lead to unidirectionally working devices, although the nominal band structure is symmetric. The results are a direct experimental proof that interface roughness scattering has a major impact on transport/lasing performance. PMID:23546105

Deutsch, Christoph; Detz, Hermann; Zederbauer, Tobias; Andrews, Aaron M; Klang, Pavel; Kubis, Tillmann; Klimeck, Gerhard; Schuster, Manfred E; Schrenk, Werner; Strasser, Gottfried; Unterrainer, Karl

2013-03-25

396

Black hole thermodynamics from near-horizon conformal quantum mechanics

The thermodynamics of black holes is shown to be directly induced by their near-horizon conformal invariance. This behavior is exhibited using a scalar field as a probe of the black hole gravitational background, for a general class of metrics in D spacetime dimensions (with D{>=}4). The ensuing analysis is based on conformal quantum mechanics, within a hierarchical near-horizon expansion. In particular, the leading conformal behavior provides the correct quantum statistical properties for the Bekenstein-Hawking entropy, with the near-horizon physics governing the thermodynamics from the outset. Most importantly: (i) this treatment reveals the emergence of holographic properties; (ii) the conformal coupling parameter is shown to be related to the Hawking temperature; and (iii) Schwarzschild-like coordinates, despite their 'coordinate singularity', can be used self-consistently to describe the thermodynamics of black holes.

Camblong, Horacio E. [Department of Physics, University of San Francisco, San Francisco, California 94117-1080 (United States); Ordonez, Carlos R. [Department of Physics, University of Houston, Houston, Texas 77204-5506 (United States); World Laboratory Center for Pan-American Collaboration in Science and Technology, University of Houston Center, Houston, Texas 77204-5506 (United States)

2005-05-15

397

Definition and Evolution of States in Relativistic Classical and Quantum Mechanics.

National Technical Information Service (NTIS)

Some of the problems associated with the construction of a manifestly covariant relativistic quantum theory are discussed. A resolution of the problem is given in terms of the off mass shell classical and quantum mechanics of Stueckelberg, Horwitz and Pir...

L. P. Horwitz

1991-01-01

398

Metric space formulation of quantum mechanical conservation laws

NASA Astrophysics Data System (ADS)

We show that conservation laws in quantum mechanics naturally lead to metric spaces for the set of related physical quantities. All such metric spaces have an "onion-shell" geometry. We demonstrate the power of this approach by considering many-body systems immersed in a magnetic field, with a finite ground state current. In the associated metric spaces we find regions of allowed and forbidden distances, a "band structure" in metric space directly arising from the conservation of the z component of the angular momentum.

Sharp, P. M.; D'Amico, I.

2014-03-01

399

Multiplication of distributions and Dirac formalism of quantum mechanics

We define multiplication and convolution of distributions and ultradistributions by introducing the notions of evaluation of distributions and integration of ultradistributions. An application is made to an interpretation of the Dirac formalism of quantum mechanics. The role of the Hilbert space of states is played by what is termed a Hermitian orthonormal system, and operators are replaced by the generalized matrices. We describe a simple example of one dimensional free particle and construct explicitly a representation of the Weyl algebra as the generalized matrices.

Kim, Namhoon [Department of Mathematics Education, Hongik University, 72-1 Sangsu-dong, Mapo-gu, Seoul 121-791 (Korea, Republic of)

2010-02-15

400

Minimum length from quantum mechanics and classical general relativity.

We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length lP. This suggests a Planck-size minimum ball of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order lP. Our results imply a device independent limit on possible position measurements. PMID:15600988

Calmet, Xavier; Graesser, Michael; Hsu, Stephen D H

2004-11-19

401

A finite Zitterbewegung model for relativistic quantum mechanics

Starting from steps of length h/mc and time intervals h/mc{sup 2}, which imply a quasi-local Zitterbewegung with velocity steps {plus minus}c, we employ discrimination between bit-strings of finite length to construct a necessary 3+1 dimensional event-space for relativistic quantum mechanics. By using the combinatorial hierarchy to label the strings, we provide a successful start on constructing the coupling constants and mass ratios implied by the scheme. Agreement with experiments is surprisingly accurate. 22 refs., 1 fig.

Noyes, H.P.

1990-02-19

402

Twisting all the way: From classical mechanics to quantum fields

We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its deformed Poisson bracket and hence time evolution and symmetries. The twisting is then extended to classical fields, and then to the main interest of this work: quantum fields. This leads to a geometric formulation of quantization on noncommutative space-time, i.e., we establish a noncommutative correspondence principle from *-Poisson brackets to * commutators. In particular commutation relations among creation and annihilation operators are deduced.

Aschieri, Paolo [Centro Studi e Ricerche 'Enrico Fermi' Compendio Viminale, 00184 Rome (Italy); Dipartimento di Scienze e Tecnologie Avanzate, Universita del Piemonte Orientale, and INFN, Sezione di Torino Via Bellini 25/G 15100 Alessandria (Italy); Lizzi, Fedele; Vitale, Patrizia [Dipartimento di Scienze Fisiche, Universita di Napoli Federico II and INFN, Sezione di Napoli Monte S. Angelo, Via Cintia, 80126 Naples (Italy)

2008-01-15

403

Simple models in supersymmetric quantum mechanics on a graph

NASA Astrophysics Data System (ADS)

We study some types of dimensionally-deconstructed models for supersymmetric (Euclidean) quantum mechanics, or zero-dimensional field theory. In these models, we assign bosonic and fermionic variables to vertices and the edges of a graph. We investigate a discrete version of the Gaussian model and the Wess-Zumino-type model on a graph. The topological index as a multiple integral is discussed on these models. In addition, we propose simple examples of supersymmetric extensions of the Lee-Wick model and the Galileon model. A model with two supersymmetries is also provided and generalization to ‘local’ supersymmtric models is examined.

Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi

2013-09-01

404

On fractional partial differential equations related to quantum mechanics

NASA Astrophysics Data System (ADS)

In this paper, we investigate the solutions of generalized fractional partial differential equations involving the Caputo time-fractional derivative and the Liouville space-fractional derivatives. The solutions of these equations are obtained by employing the joint Laplace and Fourier transforms. Several special cases as solutions of one-dimensional non-homogeneous fractional equations occurring in quantum mechanics are presented in the concluding section. The results given earlier by Debnath (2003 Fract. Calc. Appl. Anal. 6 119-55), Saxena et al (2010 Appl. Math. Comput. 216 1412-7) and Pagnini and Mainardi (2010 J. Comput. Appl. Math. 233 1590-5) follow as special cases of our findings.

Purohit, S. D.; Kalla, S. L.

2011-01-01

405

DNA Sequencing via Quantum Mechanics and Machine Learning

Rapid sequencing of individual human genome is prerequisite to genomic\\u000amedicine, where diseases will be prevented by preemptive cures.\\u000aQuantum-mechanical tunneling through single-stranded DNA in a solid-state\\u000ananopore has been proposed for rapid DNA sequencing, but unfortunately the\\u000atunneling current alone cannot distinguish the four nucleotides due to large\\u000afluctuations in molecular conformation and solvent. Here, we propose a\\u000amachine-learning

Henry Yuen; Fuyuki Shimojo; Kevin J. Zhang; Ken-ichi Nomura; Rajiv K. Kalia; Aiichiro Nakano; Priya Vashishta

2010-01-01

406

Teaching Quantum Mechanics through Project-based Learning

NASA Astrophysics Data System (ADS)

Project/Problem-based learning (PBL) is an active area of research within the physics education research (PER) community, however, work done to date has focused on introductory courses. This talk will explore research on upper division quantum mechanics, a junior/senior level course at Creighton, which was taught using PBL pedagogy with no in-class lectures. The talk will explore: 1. student learning in light of the new pedagogy and embedded meta-cognitive self-monitoring and reflective exercises and 2. the effect of the PBL curriculum on student attitudes students’ epistemologies.

Duda, Gintaras

2013-04-01

407

NASA Astrophysics Data System (ADS)

The Polish-German project QUEST aims at studying relativistic quantum spin correlations of the Einstein-Rosen-Podolsky-Bohm type, through measurement of the correlation function and the corresponding probabilities for relativistic electron pairs. The results will be compared to theoretical predictions obtained by us within the framework of relativistic quantum mechanics, based on assumptions regarding the form of the relativistic spin operator. Agreement or divergence will be interpreted in the context of non-uniqueness of the relativistic spin operator in quantum mechanics as well as dependence of the correlation function on the choice of observables representing the spin. Pairs of correlated electrons will originate from the Mo/ller scattering of polarized 15 MeV electrons provided by the superconducting Darmstadt electron linear accelerator S-DALINAC, TU Darmstadt, incident on a Be target. Spin projections will be determined using the Mott polarimetry technique. Measurements (starting 2013) are planned for longitudinal and transverse beam polarizations and different orientations of the beam polarization vector w.r.t. the Mo/ller scattering plane. This is the first project to study relativistic spin correlations for particles with mass.

Bodek, K.; Caban, P.; Ciborowski, J.; Enders, J.; Köhler, A.; Kozela, A.; Rembieli?ski, J.; Rozpedzik, D.; W?odarczyk, M.; Zejma, J.

2013-11-01

408

Noncommutative quantum mechanics: Uniqueness of the functional description

The generalized Weyl transform of index {alpha} is used to implement the time-slice definition of the phase space path integral yielding the Feynman kernel in the case of noncommutative quantum mechanics. As expected, this representation for the Feynman kernel is not unique but labeled by the real parameter {alpha}. We succeed in proving that the {alpha}-dependent contributions disappear at the limit where the time slice goes to zero. This proof of consistency turns out to be intricate because the Hamiltonian involves products of noncommuting operators originating from the noncommutativity. The antisymmetry of the matrix parametrizing the noncommutativity plays a key role in the cancellation mechanism of the {alpha}-dependent terms.

Bemfica, F. S.; Girotti, H. O. [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970-Porto Alegre, RS (Brazil)

2008-12-15

409

Metaphysical Underdetermination and Logical Determination: the Case of Quantum Mechanics

NASA Astrophysics Data System (ADS)

The `underdetermination of metaphysics by the physics' is the thesis that our best scientific theories do not uniquely determine their ontologies. Non-relativistic quantum mechanics is famously thought to exemplify this kind of underdetermination: it may be seen as compatible with both an ontology of individual objects and with an ontology of non-individual objects. A possible way out of the dilema thus created consists in adopting some version of Ontic Structural Realism (OSR), a view according to which the metaphysically relevant aspect of the theory is its structure, not the nature of the objects dealt with. According to OSR, particular objects may be dispensed with (eliminated or re-conceptualized) in favor of the structure of the theory. In this paper we shall argue that the underdetermination of metaphysics by the physics is a consequence of a too strict naturalism in ontology. As a result, when a mitigated ontological naturalism is taken into account, underdetermination does not appear to have such dark consequences for object-oriented ontologies in quantum mechanics.

Arenhart, Jonas R. B.

2014-03-01

410

The Quantum and Fluid Mechanics of Global Warming

NASA Astrophysics Data System (ADS)

Quantum physics and fluid mechanics are the foundation of any understanding of the Earth's climate. In this talk I invoke three well-known aspects of quantum mechanics to explore what will happen as the concentrations of greenhouse gases such as carbon dioxide continue to increase. Fluid dynamical models of the Earth's atmosphere, demonstrated here in live simulations, yield further insight into past, present, and future climates. Statistics of geophysical flows can, however, be ascertained directly without recourse to numerical simulation, using concepts borrowed from nonequilibrium statistical mechanicsootnotetextJ. B. Marston, E. Conover, and Tapio Schneider, ``Statistics of an Unstable Barotropic Jet from a Cumulant Expansion,'' arXiv:0705.0011, J. Atmos. Sci. (in press).. I discuss several other ways that theoretical physics may be able to contribute to a deeper understanding of climate changeootnotetextJ. Carlson, J. Harte, G. Falkovich, J. B. Marston, and R. Pierrehumbert, ``Physics of Climate Change'' 2008 Program of the Kavli Institute for Theoretical Physics..

Marston, Brad

2008-03-01

411

Coulomb problem in non-commutative quantum mechanics

NASA Astrophysics Data System (ADS)

The aim of this paper is to find out how it would be possible for space non-commutativity (NC) to alter the quantum mechanics (QM) solution of the Coulomb problem. The NC parameter ? is to be regarded as a measure of the non-commutativity - setting ? = 0 which means a return to the standard quantum mechanics. As the very first step a rotationally invariant NC space R?3, an analog of the Coulomb problem configuration space (R3 with the origin excluded) is introduced. R?3 is generated by NC coordinates realized as operators acting in an auxiliary (Fock) space . The properly weighted Hilbert-Schmidt operators in form ?, a NC analog of the Hilbert space of the wave functions. We will refer to them as ``wave functions'' also in the NC case. The definition of a NC analog of the hamiltonian as a hermitian operator in ? is one of the key parts of this paper. The resulting problem is exactly solvable. The full solution is provided, including formulas for the bound states for E < 0 and low-energy scattering for E > 0 (both containing NC corrections analytic in ?) and also formulas for high-energy scattering and unexpected bound states at ultra-high energy (both containing NC corrections singular in ?). All the NC contributions to the known QM solutions either vanish or disappear in the limit ? --> 0.

Gáliková, Veronika; Prešnajder, Peter

2013-05-01

412

An opto-magneto-mechanical quantum interface between distant superconducting qubits

A quantum internet, where widely separated quantum devices are coherently connected, is a fundamental vision for local and global quantum information networks and processing. Superconducting quantum devices can now perform sophisticated quantum engineering locally on chip and a detailed method to achieve coherent optical quantum interconnection between distant superconducting devices is a vital, but highly challenging, goal. We describe a concrete opto-magneto-mechanical system that can interconvert microwave-to-optical quantum information with high fidelity. In one such node we utilise the magnetic fields generated by the supercurrent of a flux qubit to coherently modulate a mechanical oscillator that is part of a high-Q optical cavity to achieve high fidelity microwave-to-optical quantum information exchange. We analyze the transfer between two spatially distant nodes connected by an optical fibre and using currently accessible parameters we predict that the fidelity of transfer could be as high as ~80%, even with significant loss.

Xia, Keyu; Vanner, Michael R.; Twamley, Jason

2014-01-01

413

An opto-magneto-mechanical quantum interface between distant superconducting qubits.

A quantum internet, where widely separated quantum devices are coherently connected, is a fundamental vision for local and global quantum information networks and processing. Superconducting quantum devices can now perform sophisticated quantum engineering locally on chip and a detailed method to achieve coherent optical quantum interconnection between distant superconducting devices is a vital, but highly challenging, goal. We describe a concrete opto-magneto-mechanical system that can interconvert microwave-to-optical quantum information with high fidelity. In one such node we utilise the magnetic fields generated by the supercurrent of a flux qubit to coherently modulate a mechanical oscillator that is part of a high-Q optical cavity to achieve high fidelity microwave-to-optical quantum information exchange. We analyze the transfer between two spatially distant nodes connected by an optical fibre and using currently accessible parameters we predict that the fidelity of transfer could be as high as ~80%, even with significant loss. PMID:24994063

Xia, Keyu; Vanner, Michael R; Twamley, Jason

2014-01-01

414

A new hybrid QM/DIM approach aimed at describing equilibrium structures and spectroscopic properties of medium size mixed molecular clusters is developed. This methodology is applied to vibrational spectra of hydrogen chloride and hydrogen fluoride clusters with up to four monomer molecules embedded in argon shells Arn(H(Cl/F))m (n = 1-62, m = 1-4). The hydrogen halide complexes (QM part) are treated at the MP2/aug-cc-pVTZ level, while the interaction between HX molecules and Ar atoms (MM part) is described in terms of the semiempirical DIM methodology, based on the proper mixing between neutral and ionic states of the system [Grigorenko et al., J. Chem. Phys. 104, 5510 (1996)]. A detailed analysis of the resulting topology of the QM/DIM potential energy (hyper-)surface in the triatomic subsystem Ar-HX reveals more pronounced nonadditive atomic induction and dispersion contributions to the total interaction energy in the case of the Ar-HCl system. An extension of the original analytical DIM-based potential in the frame of the present model as well as the current limitations of the method are discussed. A modified algorithm for the gradient geometry optimization, along with partly analytical force constant matrix evaluation, is developed to treat large cages of argon atoms around molecular clusters. Calculated frequency redshifts of HX stretching vibrations in the mixed clusters relative to the isolated hydrogen-bonded complexes are in good agreement with experimental findings. PMID:15268536

Bochenkova, A V; Suhm, M A; Granovsky, A A; Nemukhin, A V

2004-02-22

415

Quantum mechanics and free will: counter-arguments

NASA Astrophysics Data System (ADS)

Since quantum mechanics (QM) was formulated, many voices have claimed this to be the basis of free will in the human beings. Basically, they argue that free will is possible because there is an ontological indeterminism in the natural laws, and that the mind is responsible for the wave function collapse of matter, which leads to a choice among the different possibilities for the body. However, I defend the opposite thesis, that free will cannot be defended in terms of QM. First, because indeterminism does not imply free will, it is merely a necessary condition but not enough to defend it. Second, because all considerations about an autonomous mind sending orders to the body is against our scientific knowledge about human beings; in particular, neither neurological nor evolutionary theory can admit dualism. The quantum theory of measurement can be interpreted without the intervention of human minds, but other fields of science cannot contemplate the mentalist scenario, so it is concluded that QM has nothing to say about the mind or free will, and its scientific explanation is more related to biology than to physics. A fatalistic or materialist view, which denies the possibility of a free will, makes much more sense in scientific terms.

López-Corredoira, Martín

416

Q-spaces and the Foundations of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics.

Domenech, Graciela; Holik, Federico; Krause, Décio

2008-11-01

417

Transforming Upper-Division Quantum Mechanics: Learning Goals and Assessment

NSDL National Science Digital Library

In order to help students overcome documented difficulties learning quantum mechanics (QM) concepts, we have transformed our upper-division QM I course using principles of learning theory and active engagement. Key components of this process include establishing learning goals and developing a valid, reliable conceptual assessment tool to measure the extent to which students achieve these learning goals. The course learning goals were developed with broad faculty input, and serve as the basis for the design of the course assessment tool. The development of the assessment tool has included significant faculty input and feedback, twenty-one student interviews, a review of PER literature, and administration of the survey to two semesters of QM I students as well as to a cohort of graduate students. Here, we discuss this ongoing development process and present initial findings from our QM class for the past two semesters.

Goldhaber, Steve; Pollock, Steven J.; Dubson, Michael; Beale, Paul; Perkins, Katherine K.

2010-01-19

418

Quantum mechanics prescriptions for compound-semiconductor transistor technologies

NASA Astrophysics Data System (ADS)

We employ an accurate one-dimensional, self-consistent quantum-mechanical-Poisson solver to derive parameters that enable the Poisson solver to accurately compute charge- or capacitance-voltage curves for use in two-dimensional solvers. We consider metal-oxide-semiconductor field effect transistors (MOSFETs), where we adjust gate work functions and oxide thicknesses and SiGe MOSFETs with spacer layers where we adjust gate work functions and the carrier densities in the spacer layers. For GaAs pHEMTs, InP lattice-matched high electron mobility transistors (HEMTs), SiGe HEMTs, double-heterojunction pHEMTs, AlGaN/GaN HEMTs and delta-doped MESFETs we adjust the Schottky barrier heights to shift pinchoff voltages.

Anholt, R.

2001-07-01

419

Spectral geometry of power-law potentials in quantum mechanics

NASA Astrophysics Data System (ADS)

It is supposed that a single particle moves in openR3 in an attractive central power-law potential V(q)(r)=sgn(q)rq, q>-2, and obeys nonrelativistic quantum mechanics. This paper is concerned with the question: How do the discrete eigenvalues Enl(q) of the Hamiltonian H=-?+V(q) depend on the power parameter q\\? Pure power-law potentials have the elementary property that, for p

Hall, Richard L.

1989-06-01

420

Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

NASA Astrophysics Data System (ADS)

We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.

Al-Hashimi, M. H.; Salman, M.; Shalaby, A.; Wiese, U.-J.

2013-10-01

421

Quantum mechanical model for J/? suppression in the LHC era

NASA Astrophysics Data System (ADS)

We discuss the interplay of screening, absorption and regeneration effects, on the quantum mechanical evolution of quarkonia states, within a time-dependent harmonic oscillator (THO) model with complex oscillator strength. We compare the results with data for RAA/RAA(CNM) from CERN and RHIC experiments. In the absence of a measurement of cold nuclear matter (CNM) effects at LHC we estimate their role and interpret the recent data from the ALICE experiment. We also discuss the temperature dependence of the real and imaginary parts of the oscillator frequency which stand for screening and absorption/regeneration, respectively. We point out that a structure in the J/? suppression pattern for In-In collisions at SPS is possibly related to the recently found X(3872) state in the charmonium spectrum. Theoretical support for this hypothesis comes from the cluster expansion of the plasma Hamiltonian for heavy quarkonia in a strongly correlated medium.

Peña, C.; Blaschke, D.

2014-07-01

422

Geometric phase in PT-symmetric quantum mechanics

Unitary evolution in PT-symmetric quantum mechanics (QM) with a time-dependent metric is found to yield an interesting class of adiabatic processes. As an explicit example, a Berry-like phase associated with a PT-symmetric two-level system is derived and is interpreted as the flux of a fictitious monopole with a tunable charge plus a singular string component with nontrivial phase contributions. To gain more insight, the Hermitian analog of our non-Hermitian problem is also analyzed, which results in an intriguing class of geometric-phase problems in conventional QM as well, where the Hamiltonian includes a perturbative term that is proportional to the rate of change in adiabatic parameters.

Gong Jiangbin [Department of Physics, National University of Singapore, Singapore 117542 (Singapore); Centre for Computational Science and Engineering, National University of Singapore (NUS), Singapore 117542 (Singapore); NUS Graduate School for Integrative Sciences and Engineering, Singapore 117597 (Singapore); Wang Qinghai [Department of Physics, National University of Singapore, Singapore 117542 (Singapore)

2010-07-15

423

Dirac Operator on Complex Manifolds and Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

We explore a simple N = 2 supersymmetric quantum mechanics (SQM) model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model realizes the twisted Dolbeault complex. The sum Q+\\bar Q can be interpreted as the Dirac operator: the standard Dirac operator if the manifold is Kähler and the Dirac operator involving certain particular extra torsions for a generic complex manifold. Focusing on the Kähler case, we give new simple physical proofs of the two mathematical facts: (i) the equivalence of the twisted Dirac and twisted Dolbeault complexes and (ii) the Atiyah-Singer theorem.

Ivanov, E. A.; Smilga, A. V.

2012-10-01

424

A semiclassical correction for quantum mechanical energy levels

We propose a semiclassical method for correcting molecular energy levels obtained from a quantum mechanical variational calculation. A variational calculation gives the energy level (i.e., eigenvalue) as the expectation value of the molecular Hamiltonian <{phi}|H|{phi}>, where |{phi}> is the trial wave function. The true (i.e., exact) eigenvalue E can thus be expressed as this variational result plus a correction, i.e., E=<{phi}|H|{phi}>+{Delta}E, the correction being due to the lack of exactness of the trial wave function. A formally exact expression for {Delta}E is usually given (via Loewdin partitioning methodology) in terms of the Greens function of the Hamiltonian projected onto the orthogonal complement of |{phi}>. Formal treatment of this expression (using Brillouin-Wigner perturbation theory to infinite order) leads to an expression for {Delta}E that involves matrix elements of the Greens function for the unprojected, i.e., full molecular Hamiltonian, which can then be approximated semiclassically. (Specifically, the Greens function is expressed as the Fourier transform of the quantum mechanical time evolution operator, e{sup -}iHt/({h_bar}/2{pi}), which in turn is approximated by using an initial value representation of semiclassical theory.) Calculations for several test problems (a one dimensional quartic potential, and vibrational energy levels of H{sub 2}O and H{sub 2}CO) clearly support our proposition that the error in the total eigenvalue E arises solely due to the semiclassical error in approximating {Delta}E, which is usually a small fraction of the total energy E itself.

Kaledin, Alexey L. [Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322 (United States); McCurdy, C. William [Department of Applied Science and Department of Chemistry, University of California, Davis, California 95616, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Miller, William H. [Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, California (United States) and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)

2010-08-07

425

PREFACE: DICE 2006—Quantum Mechanics between Decoherence and Determinism

NASA Astrophysics Data System (ADS)

These proceedings are based on the Invited Lectures and Contributed Papers of the Third International Workshop on Decoherence, Information, Complexity and Entropy—DICE 2006, which was held at Castello di Piombino (Tuscany), 11 15 September 2006. They are meant to document the stimulating exchange of ideas at this interdisciplinary workshop and to share it with the wider scientific community. It successfully continued what was begun with DICE 20021 and followed by DICE 20042 uniting more than seventy participants from more than a dozen different countries worldwide. It has been a great honour and inspiration for all of us to have Professor G. 't Hooft (Nobel Prize for Physics 1999) from the Spinoza Institute and University of Utrecht with us, who presented the lecture `A mathematical theory for deterministic quantum mechanics' (included in this volume). Discussions under the wider theme `Quantum Mechanics between decoherence and determinism: new aspects from particle physics to cosmology' took place in the very pleasant and productive atmosphere at the Castello di Piombino, with a fluctuation of stormy weather only on the evening of the conference dinner. The program of the workshop was grouped according to the following topics: complex systems, classical and quantum aspects Lorentz symmetry, neutrinos and the Universe reduction, decoherence and entanglement quantum, gravity and spacetime -- emergent reality? quantum gravity/cosmology The traditional Public Opening Lecture was presented this time by E. Del Giudice (Milano), who captivated the audience with `Old and new views on the structure of matter and the special case of living matter' on the evening of the arrival day. The workshop has been organized by S. Boccaletti (Firenze), L. Diósi (Budapest), H.-T. Elze (Pisa, chair), L. Fronzoni (Pisa), J. Halliwell (London), and G. Vitiello (Salerno), with great help from our conference secretaries M. Pesce-Rollins (Siena) and L. Baldini (Pisa). Several institutions and sponsors generously supported the workshop and their representatives and, in particular, the citizens of Piombino are deeply thanked for the hospitality: G. Anselmi (Sindaco del Comune di Piombino), O. Dell'Omodarme (Assessore alle Culture), A. Tempestini (Assessore alla Pubblica Istruzione), E. Murzi (Assessore al Turismo), A. Falchi (Dirigente dei Servizi Educativi e Culturali), M. Gianfranchi (Responsabile del Servizio Promozione Culturale), T. Ghini (Ufficio Beni Culturali), and L. Grilli, C. Boggero and P. Venturi (Ufficio Cultura), M. Pierulivo (Segreteria del Sindaco), L. Pasquinucci (URP e Comunicazione). Thanks go to Idearte (Cooperativa di Servizi Culturali) and especially to L. Pesce (Vitrium Galleria, Populonia). Funds made available by Universitá di Pisa (Centro Interdisciplinare per lo Studio dei Sistemi Complessi -- CISSC and Domus Galilaeana) and Universitá di Salerno (Dipartimento di Fisica and INFN) are gratefully acknowledged. The research papers presented at the workshop, often incorporating further developments since then, have been edited by L. Diósi, H.-T. Elze and G. Vitiello. They are collected here, essentially following the program of the workshop, however, divided into Invited Lectures and Contributed Papers, respectively. In the name of all participants, we would like to thank G. Douglas (IOP Publishing, Bristol) for his friendly advice and immediate help during the editing process. Lajos Diósi, Hans-Thomas Elze and Giuseppe Vitiello Budapest, Pisa, Salerno, March 2007 1Decoherence and Entropy in Complex Systems ed H-T Elze Lecture Notes in Physics 633 (Berlin: Springer, 2004) 2Proceedings of the Second International Workshop on Decoherence, Information, Complexity and Entropy DICE 2004 ed H-T Elze Braz. J. Phys. 35, 2A and 2B (2005) pp 205 529 freely accessible at: www.sbfisica.org.br/bjp

Diósi, Lajos; Elze, Hans-Thomas; Vitiello, Giuseppe

2007-06-01

426

Suppression of the quantum-mechanical collapse by repulsive interactions in a quantum gas

The quantum-mechanical collapse (alias fall onto the center of particles attracted by potential -r{sup -2}) is a well-known issue in quantum theory. It is closely related to the quantum anomaly, i.e., breaking of the scaling invariance of the respective Hamiltonian by quantization. We demonstrate that the mean-field repulsive nonlinearity prevents the collapse and thus puts forward a solution to the quantum-anomaly problem that differs from that previously developed in the framework of the linear quantum-field theory. This solution may be realized in the 3D or 2D gas of dipolar bosons attracted by a central charge and in the 2D gas of magnetic dipoles attracted by a current filament. In the 3D setting, the dipole-dipole interactions are also taken into regard, in the mean-field approximation, resulting in a redefinition of the scattering length which accounts for the contact repulsion between the bosons. In lieu of the collapse, the cubic nonlinearity creates a 3D ground state (GS), which does not exist in the respective linear Schroedinger equation. The addition of the harmonic trap gives rise to a tristability, in the case when the Schroedinger equation still does not lead to the collapse. In the 2D setting, the cubic nonlinearity is not strong enough to prevent the collapse; however, the quintic term does it, creating the GS, as well as its counterparts carrying the angular momentum (vorticity). Counterintuitively, such self-trapped 2D modes exist even in the case of a weakly repulsive potential r{sup -2}. The 2D vortical modes avoid the phase singularity at the pivot (r=0) by having the amplitude diverging at r{yields}0 instead of the usual situation with the amplitude of the vortical mode vanishing at r{yields}0 (the norm of the mode converges despite of the singularity of the amplitude at r{yields}0). In the presence of the harmonic trap, the 2D quintic model with a weakly repulsive central potential r{sup -2} gives rise to three confined modes, the middle one being unstable, spontaneously developing into a breather. In both the 3D and 2D cases, the GS wave functions are found in a numerical form and in the form of an analytical approximation, which is asymptotically exact in the limit of the large norm.

Sakaguchi, Hidetsugu [Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580 (Japan); Malomed, Boris A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

2011-01-15

427

Ab initio quantum chemistry: Methodology and applications

This Perspective provides an overview of state-of-the-art ab initio quantum chemical methodology and appli