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1

Developments in computing hardware and algorithms have made direct molecular dynamics simulation with the combined quantum mechanical/molecular mechanical methods affordable for small solute molecules in solution, in which much improved accuracy can be obtained via the quantum mechanical treatment of the solute molecule and even sometimes water molecules in the first solvation shell. However, unlike the conventional molecular mechanical simulations of large molecules, e.g., proteins, in solutions, special care must be taken in the technical details of the simulation, including the thermostat of the solute/solvent system, so that the conformational space of the solute molecules can be properly sampled. We show here that the common setup for classical molecular mechanical molecular dynamics simulations, such as the Berendsen or single Nose-Hoover thermostat, and/or rigid water models could lead to pathological sampling of the solutes' conformation. In the extreme example of a methanol molecule in aqueous solution, improper and sluggish setups could generate two peaks in the distribution of the O-H bond length. We discuss the factors responsible for this somewhat unexpected result and evoke a simple and ancient technical fix-up to resolve this problem. PMID:23642216

Hu, Hao; Liu, Haiyan

2013-05-30

2

Biological Applications of Hybrid Quantum Mechanics/Molecular Mechanics Calculation

Since in most cases biological macromolecular systems including solvent water molecules are remarkably large, the computational costs of performing ab initio calculations for the entire structures are prohibitive. Accordingly, QM calculations that are jointed with MM calculations are crucial to evaluate the long-range electrostatic interactions, which significantly affect the electronic structures of biological macromolecules. A UNIX-shell-based interface program connecting the quantum mechanics (QMs) and molecular mechanics (MMs) calculation engines, GAMESS and AMBER, was developed in our lab. The system was applied to a metalloenzyme, azurin, and PU.1-DNA complex; thereby, the significance of the environmental effects on the electronic structures of the site of interest was elucidated. Subsequently, hybrid QM/MM molecular dynamics (MD) simulation using the calculation system was employed for investigation of mechanisms of hydrolysis (editing reaction) in leucyl-tRNA synthetase complexed with the misaminoacylated tRNALeu, and a novel mechanism of the enzymatic reaction was revealed. Thus, our interface program can play a critical role as a powerful tool for state-of-the-art sophisticated hybrid ab initio QM/MM MD simulations of large systems, such as biological macromolecules. PMID:22536015

Kang, Jiyoung; Hagiwara, Yohsuke; Tateno, Masaru

2012-01-01

3

Biological applications of hybrid quantum mechanics/molecular mechanics calculation.

Since in most cases biological macromolecular systems including solvent water molecules are remarkably large, the computational costs of performing ab initio calculations for the entire structures are prohibitive. Accordingly, QM calculations that are jointed with MM calculations are crucial to evaluate the long-range electrostatic interactions, which significantly affect the electronic structures of biological macromolecules. A UNIX-shell-based interface program connecting the quantum mechanics (QMs) and molecular mechanics (MMs) calculation engines, GAMESS and AMBER, was developed in our lab. The system was applied to a metalloenzyme, azurin, and PU.1-DNA complex; thereby, the significance of the environmental effects on the electronic structures of the site of interest was elucidated. Subsequently, hybrid QM/MM molecular dynamics (MD) simulation using the calculation system was employed for investigation of mechanisms of hydrolysis (editing reaction) in leucyl-tRNA synthetase complexed with the misaminoacylated tRNA(Leu), and a novel mechanism of the enzymatic reaction was revealed. Thus, our interface program can play a critical role as a powerful tool for state-of-the-art sophisticated hybrid ab initio QM/MM MD simulations of large systems, such as biological macromolecules. PMID:22536015

Kang, Jiyoung; Hagiwara, Yohsuke; Tateno, Masaru

2012-01-01

4

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

5

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

6

Ab Initio Quantum Mechanical/Molecular Mechanical Studies of Histone Modifying Enzymes

NASA Astrophysics Data System (ADS)

Histone proteins that form the nucleosome core are subject to a variety of post-translational transformations. These histone modifications make up the histone code which extends the information in the genetic code and is emerging as an essential mechanism to regulate gene expression. In spite of a current flurry of significant advances in experimental studies, there has been little theoretical understanding regarding how enzymes generate or remove these modifications. Very recently, we have made excellent progresses in investigating two such important histone-modifying enzyme families: zinc-dependent histone deacetylases (HDACs) and histone lysine methyltransferases (HKMTs). Our studies on a histonedeacetylase- like protein HDLP suggested a novel catalytic mechanism. The simulations on HKMT SET7/9 have characterized the histone lysine methylation reaction and elucidated the origin of enzyme catalysis. Our computational approaches centered on the pseudobond ab initio quantum mechanical/molecular mechanical (QM/MM) method, which allows for accurate modeling of the chemistry at the reaction active site while properly including the effects of the protein environment

Zhang, Yingkai

7

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

8

NASA Astrophysics Data System (ADS)

Quantum mechanical/molecular mechanical (QM/MM) free energy calculation presents a significant challenge due to an excessive number of QM calculations. A useful approach for reducing the computational cost is that based on the mean field approximation to the QM subsystem. Here, we describe such a mean-field QM/MM theory for electronically polarizable systems by starting from the Hartree product ansatz for the total system and invoking a variational principle of free energy. The MM part is then recast to a classical polarizable model by introducing the charge response kernel. Numerical test shows that the potential of mean force (PMF) thus obtained agrees quantitatively with that obtained from a direct QM/MM calculation, indicating the utility of self-consistent mean-field approximation. Next, we apply the obtained method to prototypical reactions in several qualitatively different solvents and make a systematic comparison of polarization effects. The results show that in aqueous solution the PMF does not depend very much on the water models employed, while in nonaqueous solutions the PMF is significantly affected by explicit polarization. For example, the free energy barrier for a phosphoryl dissociation reaction in acetone and cyclohexane is found to increase by more than 10 kcal/mol when switching the solvent model from an empirical to explicitly polarizable one. The reason for this is discussed based on the parametrization of empirical nonpolarizable models.

Nakano, Hiroshi; Yamamoto, Takeshi

2012-04-01

9

The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. Using broken-symmetry unrestricted density functional theory quantum mechanical (QM) methods in concert with mixed quantum mechanics/molecular mechanics (QM/MM) methods, the hydroxylation of methane and substituted methanes by intermediate Q in methane monooxygenase hydroxylase (MMOH) has been quantitatively modeled. This protocol allows the protein environment to be included throughout the calculations and its effects (electrostatic, van der Waals, strain) upon the reaction to be accurately evaluated. With the current results, recent kinetic data for CH?X (X ) H, CH?, OH, CN, NO?) substrate hydroxylation in MMOH (Ambundo, E. A.; Friesner, R. A.; Lippard, S. J. J. Am. Chem. Soc. 2002, 124, 8770-8771) can be rationalized. Results for methane, which provide a quantitative test of the protocol, including a substantial kinetic isotope effect (KIE), are in reasonable agreement with experiment. Specific features of the interaction of each of the substrates with MMO are illuminated by the QM/MM modeling, and the resulting effects upon substrate binding are quantitatively incorporated into the calculations. The results as a whole point to the success of the QM/MM methodology and enhance our understanding of MMOH catalytic chemistry. We also identify systematic errors in the evaluation of the free energy of binding of the Michaelis complexes of the substrates, which most likely arise from inadequate sampling and/or the use of harmonic approximations to evaluate the entropy of the complex. More sophisticated sampling methods will be required to achieve greater accuracy in this aspect of the calculation.

Gherman, Benjamin F.; Lippard, Stephen J.; Friesner, Richard A.

2005-01-26

10

We studied the energetics of the closed-ring mechanism of the acid-catalysed dehydration of D-fructose to 5-hydroxymethylfurfural (HMF) by carrying out canonical ensemble free-energy calculations using bias-sampling, hybrid Quantum Mechanics/Molecular Mechanics Molecular Dynamics simulations with explicit water solvent at 363 K. The quantum mechanical calculations are performed at the PM3 theory level. We find that the reaction proceeds via intramolecular proton and hydride transfers. Solvent dynamics effects are analysed, and we show that the activation energy for the hydride transfers is due to re-organization of the polar solvent environment. We also find that in some instances intramolecular proton transfer is facilitated by mediating water, whereas in others the presence of quantum mechanical water has no effect. From a micro-kinetic point of view, we find that the rate-determining step of the reaction involves a hydride transfer prior to the third dehydration step, requiring an activation free energy of 31.8 kcal/mol, and the respective rate is found in good agreement with reported experimental values in zeolites. Thermodynamically, the reaction is exothermic by ?F=20.5kcal/mol.

Caratzoulas, S.; Vlachos, Dion G.

2011-01-01

11

Understanding the mechanism of prenyltransferases is important to the design of engineered proteins capable of synthesizing derivatives of naturally occurring therapeutic agents. CloQ is a Mg(2+)-independent aromatic prenyltransferase (APTase) that transfers a dimethylallyl group to 4-hydroxyphenylpyruvate in the biosynthetic pathway for clorobiocin. APTases consist of a common ABBA fold that defines a ?-barrel containing the reaction cavity. Positively charged basic residues line the inside of the ?-barrel of CloQ to activate the pyrophosphate leaving group to replace the function of the Mg(2+) cofactor in other APTases. Classical molecular dynamics simulations of CloQ, its E281G and F68S mutants, and the related NovQ were used to explore the binding of the 4-hydroxyphenylpyruvate (4HPP) and dimethylallyl diphosphate substrates in the reactive cavity and the role of various conserved residues. Hybrid quantum mechanics/molecular mechanics potential of mean force (PMF) calculations show that the effect of the replacement of the Mg(2+) cofactor with basic residues yields a similar activation barrier for prenylation to Mg(2+)-dependent APTases like NphB. The topology of the binding pocket for 4HPP is important for selective prenylation at the ortho position of the ring. Methylation at this position alters the conformation of the substrate for O-prenylation at the phenol group. Further, a two-dimensional PMF scan shows that a "reverse" prenylation product may be a possible target for protein engineering. PMID:25020142

Bayse, Craig A; Merz, Kenneth M

2014-08-01

12

Glycosyltransferases catalyze the formation of glycosidic bonds by assisting the transfer of a sugar residue from donors to specific acceptor molecules. Although structural and kinetic data have provided insight into mechanistic strategies employed by these enzymes, molecular modeling studies are essential for the understanding of glycosyltransferase catalyzed reactions at the atomistic level. For such modeling, combined quantum mechanics/molecular mechanics (QM/MM) methods have emerged as crucial. These methods allow the modeling of enzymatic reactions by using quantum mechanical methods for the calculation of the electronic structure of the active site models and treating the remaining enzyme environment by faster molecular mechanics methods. Herein, the application of QM/MM methods to glycosyltransferase catalyzed reactions is reviewed, and the insight from modeling of glycosyl transfer into the mechanisms and transition states structures of both inverting and retaining glycosyltransferases are discussed. PMID:25060837

Tvaroška, Igor

2015-02-11

13

Soluble epoxide hydrolase (sEH) is an enzyme involved in drug metabolism that catalyzes the hydrolysis of epoxides to form their corresponding diols. sEH has a broad substrate range and shows high regio- and enantioselectivity for nucleophilic ring opening by Asp333. Epoxide hydrolases therefore have potential synthetic applications. We have used combined quantum mechanics/molecular mechanics (QM/MM) umbrella sampling molecular dynamics (MD) simulations (at the AM1/CHARMM22 level) and high-level ab initio (SCS-MP2) QM/MM calculations to analyze the reactions, and determinants of selectivity, for two substrates: trans-stilbene oxide (t-SO) and trans-diphenylpropene oxide (t-DPPO). The calculated free energy barriers from the QM/MM (AM1/CHARMM22) umbrella sampling MD simulations show a lower barrier for phenyl attack in t-DPPO, compared with that for benzylic attack, in agreement with experiment. Activation barriers in agreement with experimental rate constants are obtained only with the highest level of QM theory (SCS-MP2) used. Our results show that the selectivity of the ring-opening reaction is influenced by several factors, including proximity to the nucleophile, electronic stabilization of the transition state, and hydrogen bonding to two active site tyrosine residues. The protonation state of His523 during nucleophilic attack has also been investigated, and our results show that the protonated form is most consistent with experimental findings. The work presented here illustrates how determinants of selectivity can be identified from QM/MM simulations. These insights may also provide useful information for the design of novel catalysts for use in the synthesis of enantiopure compounds. PMID:22280021

2012-01-01

14

Nature of K[sup +]/crown ether interactions. A hybrid quantum mechanical-molecular mechanical study

We present a hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics study of dimethyl ether (DME) and 18-crown-6 (18c6) interacting with K[sup +]. The QM/MM method employs the semiempirical AM1 method to describe the ethers, the MM parametrization of Dang for K[sup +], and the MM SPC/e model for H[sub 2]O. We parametrize the interaction Hamiltonian to the binding energies and optimized geometries for K[sup +]/DME using ab initio HF and MP2/6-31+G* results. The resulting QM/MM model describes the polarization response of both free DME and K[sup +]-complexed DME well. The QM/MM model gives good agreement with the experimental and ab initio structures for K[sup +]/18c6. We calculate gas-phase K[sup +]/18c6 binding energies of [minus]70.2 and [minus]72.0 kcal/mol with the QM/MM and MP2/6-31+G* (CP corrected) methods, respectively. Our simulation results for K[sup +]/18c6 in H[sub 2]O show that the most probable K[sup +]/18c6 center-of-mass displacement is 0.25 [angstrom], in marked contrast to previous molecular dynamics results of Dang and Kollman. Our result is consistent with K[sup +] having an optimal [open quotes]fit[close quotes] for the cavity of 18c6. Still, we find that K[sup +] retains significant solvent accessibility coordinating two H[sub 2]O molecules, on average, in the K[sup +]/18c6 simulation. 81 refs., 13 figs., 4 tabs.

Thompson, M.A.; Glendening, E.D.; Feller, D. (Pacific Northwest Lab., Richland, WA (United States))

1994-10-13

15

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

16

NASA Astrophysics Data System (ADS)

The vibrational absorption (IR) and vibrational circular dichroism (VCD) spectra of alanine dipeptide analog in water are directly calculated by Fourier transforming the time correlation functions of the electric and magnetic dipole moments, which are calculated using the dynamic partial charges and trajectory of the peptide generated from the quantum mechanical/molecular mechanical molecular dynamics simulations. The alanine dipeptide analog is treated at the Hartree-Fock level with 3-21G, 4-31G, 6-31G, and 6-31G? basis sets and the solvent H2O is modeled with the TIP3P water. The atomic partial charges are obtained from the Löwdin population analysis, which gives consistent IR spectral profiles irrespective of the basis sets used. The simulated VCD spectrum by a polyproline II(PII)-dominant trajectory is compatible with the previous experimental results of the polyproline peptides, where the amide I and II VCD bands are negative couplets with a weak positive peak to the high frequency region. The sampling efficiency of the PII conformer is much lower than the other ones at all basis levels used. The simulated VCD spectrum of ?-helix averaged over five trajectories has the reverse sign pattern compared to the PII spectrum and is found to be consistent with the previously observed spectral features of ?-helical polypeptides. The sign patterns of the ?-strand VCD spectrum are qualitatively similar to the experimental spectra of ?-sheet rich proteins. The VCD spectra obtained from the trajectories containing several extended conformers such as ? and PII are not clearly distinguishable from the ?-strand-dominant spectra. It is interesting that the PII and the coil VCD spectra coincide in sign pattern and relative intensity for all amide modes. This demonstrates that the negative couplet structures of the amide I and II VCD spectra do not necessarily prove the dominance of either PII or coil conformation. We anticipate that the present method can be used to directly simulate the IR and VCD spectra of structurally heterogeneous biomolecules in condensed phases.

Yang, Seongeun; Cho, Minhaeng

2009-10-01

17

This work presents a hybrid ab initio quantum mechanical/molecular mechanical simulation at the RI-MP2 level of theory investigating the hydrolysis process of arsenic(III), ultimately leading to arsenous acid (H3AsO3). A newly implemented dissociative water model has been applied to treat the interactions in the classical region, which is capable of describing non-neutral water species such as hydroxide and oxonium ions. Three stages of hydrolysis have been observed during the simulation and besides profound dynamical considerations, detailed insights into structural changes and atomic partial charge shifts are presented. In particular, the geometrical properties of H-bonds involved in each of the three proton transfer events and subsequent proton hopping reactions are discussed. A Laguerre tessellation analysis has been employed to estimate the molecular volume of H3AsO3. Estimations of pKa values of the arsenic(III)-aquo-complexes have been obtained at the G4 and CBS-Q//B3 levels of theory using a thermodynamic cycle, whereas rate constants for the final hydrolysis step have been determined via reaction path optimization and transition state theory. Newly recorded Fourier transform infrared (FT-IR) spectroscopy measurements have been compared to power spectra obtained from the simulation data, confirming its quality. The simulation findings, as well as results from computational spectroscopic calculations utilizing the PT2-VSCF methodology, proved valuable for the interpretation of the experimental FT-IR data, elucidating the particularities of the strongly observed IR Raman noncoincidence effect. PMID:25157412

Canaval, Lorenz R; Lutz, Oliver M D; Weiss, Alexander K H; Huck, Christian W; Hofer, Thomas S

2014-11-17

18

Hybrid quantum mechanics/molecular mechanics calculations using Austin Model 1 system-specific parameters were performed to study the SN2 displacement reaction of chloride from 1,2-dichloroethane (DCE) by nucleophilic attack of the carboxylate of acetate in the gas phase and by Asp-124 in the active site of haloalkane dehalogenase from Xanthobacter autotrophicus GJ10. The activation barrier for nucleophilic attack of acetate on DCE depends greatly on the reactants having a geometry resembling that in the enzyme or an optimized gas-phase structure. It was found in the gas-phase calculations that the activation barrier is 9 kcal/mol lower when dihedral constraints are used to restrict the carboxylate nucleophile geometry to that in the enzyme relative to the geometries for the reactants without dihedral constraints. The calculated quantum mechanics/molecular mechanics activation barriers for the enzymatic reaction are 16.2 and 19.4 kcal/mol when the geometry of the reactants is in a near attack conformer from molecular dynamics and in a conformer similar to the crystal structure (DCE is gauche), respectively. This haloalkane dehalogenase lowers the activation barrier for dehalogenation of DCE by 2–4 kcal/mol relative to the single point energies of the enzyme's quantum mechanics atoms in the gas phase. SN2 displacements of this sort in water are infinitely slower than in the gas phase. The modest lowering of the activation barrier by the enzyme relative to the reaction in the gas phase is consistent with mutation experiments. PMID:10963662

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

2000-01-01

19

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, E-mail: hli4@unl.edu [Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 (United States)] [Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 (United States)

2014-05-07

20

We re-visited the results of quantum mechanics--molecular mechanics (QM/MM) approaches aiming to construct the reaction energy profile for the acylation stage of acetylcholine hydrolysis by acetylcholinesterase. The main emphasis of this study was on the energy of the first tetrahedral intermediate (TI) relative to the level of the enzyme-substrate (ES) complex for which contradictory data from different works had been reported. A new series of stationary points on the potential energy surface was calculated by using electronically embedding QM/MM schemes when starting from the crystal structure mimicking features of the reaction intermediate (PDB ID: 2VJA). A thoughtful analysis allows us to conclude that the energy of TI should be lower than that of ES, and a proper treatment of contributions from the oxyanion hole residues accounts for their relative positions. PMID:22982775

Nemukhin, Alexander V; Grigorenko, Bella L; Morozov, Dmitry I; Kochetov, Mikhail S; Lushchekina, Sofya V; Varfolomeev, Sergei D

2013-03-25

21

Link molecule method for quantum mechanical/molecular mechanical hybrid simulations

We present a new coupling method for hybrid simulations in which the system is partitioned into covalently linked quantum mechanical (QM) and molecular mechanical (MM) regions. Our method, called the 'link molecule method (LMM),' is substantially different from the link atom methods in that LMM is free from the delicate issue of how to remove the additional degrees of freedom with respect to the position of the virtual atoms linking the QM and the MM regions. The force acting on the atom at the regional boundary is obtained in a simple form based on the total energy conservation. The accuracy of LMM is demonstrated in detail using a system of silicon partitioned into the QM and the MM region at the (1 0 0) boundary plane. This condition has been difficult to simulate by conventional methods employing the link atoms because of the strong repulsion between the nearby link atoms.

Nakamura, Yoshimichi [Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Megro, Tokyo 153-8505 (Japan) and Computational Materials Science Center, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan)]. E-mail: NAKAMURA.Yoshimichi@nims.go.jp; Takahashi, Norihiko [Computational Materials Science Center, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan); Okamoto, Masakuni [Mechanical Engineering Research Laboratory, Hitachi Ltd., 832-2 Horiguchi, Hitachinaka, Ibaraki 312-0034 (Japan); Uda, Tsuyoshi [Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Megro, Tokyo 153-8505 (Japan); AdvanceSoft Corporation, 4-6-1 Komaba, Megro, Tokyo 153-8904 (Japan); Ohno, Takahisa [Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Megro, Tokyo 153-8505 (Japan) and Computational Materials Science Center, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan)]. E-mail: OHNO.Takahisa@nims.go.jp

2007-08-10

22

In combined quantum mechanical/molecular mechanical (QM/MM) free energy calculations, it is often advantageous to have a frozen geometry for the quantum mechanical (QM) region. For such multiple-environment single-system (MESS) cases, two schemes are proposed here for estimating the polarization energy: the first scheme, termed MESS-E, involves a Roothaan step extrapolation of the self-consistent field (SCF) energy; whereas the other scheme, termed MESS-H, employs a Newton-Raphson correction using an approximate inverse electronic Hessian of the QM region (which is constructed only once). Both schemes are extremely efficient, because the expensive Fock updates and SCF iterations in standard QM/MM calculations are completely avoided at each configuration. They produce reasonably accurate QM/MM polarization energies: MESS-E can predict the polarization energy within 0.25 kcal/mol in terms of the mean signed error for two of our test cases, solvated methanol and solvated ?-alanine, using the M06-2X or ?B97X-D functionals; MESS-H can reproduce the polarization energy within 0.2 kcal/mol for these two cases and for the oxyluciferin-luciferase complex, if the approximate inverse electronic Hessians are constructed with sufficient accuracy. PMID:25321186

Sodt, Alexander J; Mei, Ye; König, Gerhard; Tao, Peng; Steele, Ryan P; Brooks, Bernard R; Shao, Yihan

2015-03-01

23

NASA Astrophysics Data System (ADS)

Multidimensional infrared (IR) spectroscopy has emerged as a viable tool to study molecular structure and dynamics in condensed phases, and the third-order vibrational response function is the central quantity underlying various nonlinear IR spectroscopic techniques, such as pump-probe, photon echo and two-dimensional (2D) IR spectroscopy. In this paper, a new computational method is presented that calculates this nonlinear response function in the classical limit from a series of classical molecular dynamics (MD) simulations, employing a quantum mechanical/molecular mechanical (QM/MM) force field. The method relies on the stability matrix formalism where the dipole-dipole quantum mechanical commutators appearing in the exact quantum response function are replaced by the corresponding Poisson brackets. We present the formulation and computational algorithm of the method for both the classical and the QM/MM force fields and apply it to the 2D IR spectroscopy of carbon monoxide (CO) and N-methylacetamide (NMA), each solvated in a water cluster. The conventional classical force field with harmonic bond potentials is shown to be incapable of producing a reliable 2D IR signal because intramolecular vibrational anharmonicity, essential to the production of the nonlinear signal, is absent in such a model. The QM/MM force field, on the other hand, produces distinct 2D spectra for the NMA and CO systems with clear vertical splitting and cross peaks, reflecting the vibrational anharmonicities and the vibrational couplings between the underlying vibrational modes, respectively. In the NMA spectrum, the coupling between the amide I and II modes is also well reproduced. While attaining the converged spectrum is found to be challenging with this method, with an adequate amount of computing it can be straightforwardly applied to new systems containing multiple chromophores with little modeling effort, and therefore it would be useful in understanding the multimode 2D IR spectrum of complex molecular systems.

Jeon, Jonggu; Cho, Minhaeng

2010-06-01

24

NASA Astrophysics Data System (ADS)

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

Biswas, P. K.; Gogonea, Valentin

2008-10-01

25

NASA Astrophysics Data System (ADS)

Cysteine protease enzymes are important for human physiology and catalyze key protein degradation pathways. These enzymes react via a nucleophilic reaction mechanism that involves a cysteine residue and the proton of a proximal histidine. Particularly efficient inhibitors of these enzymes are nitrile-based, however, the details of the catalytic reaction mechanism currently are poorly understood. To gain further insight into the inhibition of these molecules, we have performed a combined density functional theory and quantum mechanics/molecular mechanics study on the reaction of a nitrile-based inhibitor with the enzyme active site amino acids. We show here that small perturbations to the inhibitor structure can have dramatic effects on the catalysis and inhibition processes. Thus, we investigated a range of inhibitor templates and show that specific structural changes reduce the inhibitory efficiency by several orders of magnitude. Moreover, as the reaction takes place on a polar surface, we find strong differences between the DFT and QM/MM calculated energetics. In particular, the DFT model led to dramatic distortions from the starting structure and the convergence to a structure that would not fit the enzyme active site. In the subsequent QM/MM study we investigated the use of mechanical versus electronic embedding on the kinetics, thermodynamics and geometries along the reaction mechanism. We find minor effects on the kinetics of the reaction but large geometric and thermodynamics differences as a result of inclusion of electronic embedding corrections. The work here highlights the importance of model choice in the investigation of this biochemical reaction mechanism.

De Visser, Sam; Quesne, Matthew; Ward, Richard

2013-12-01

26

The hepatitis delta virus (HDV) ribozyme catalyzes a self-cleavage reaction using a combination of nucleobase and metal ion catalysis. Both divalent and monovalent ions can catalyze this reaction, although the rate is slower with monovalent ions alone. Herein, we use quantum mechanical/molecular mechanical (QM/MM) free energy simulations to investigate the mechanism of this ribozyme and to elucidate the roles of the catalytic metal ion. With Mg2+ at the catalytic site, the self-cleavage mechanism is observed to be concerted with a phosphorane-like transition state and a free energy barrier of ?13 kcal/mol, consistent with free energy barrier values extrapolated from experimental studies. With Na+ at the catalytic site, the mechanism is observed to be sequential, passing through a phosphorane intermediate, with free energy barriers of 2–4 kcal/mol for both steps; moreover, proton transfer from the exocyclic amine of protonated C75 to the nonbridging oxygen of the scissile phosphate occurs to stabilize the phosphorane intermediate in the sequential mechanism. To explain the slower rate observed experimentally with monovalent ions, we hypothesize that the activation of the O2? nucleophile by deprotonation and orientation is less favorable with Na+ ions than with Mg2+ ions. To explore this hypothesis, we experimentally measure the pKa of O2? by kinetic and NMR methods and find it to be lower in the presence of divalent ions rather than only monovalent ions. The combined theoretical and experimental results indicate that the catalytic Mg2+ ion may play three key roles: assisting in the activation of the O2? nucleophile, acidifying the general acid C75, and stabilizing the nonbridging oxygen to prevent proton transfer to it. PMID:24383543

2015-01-01

27

Ab Initio Quantum Mechanical\\/Molecular Mechanical Studies of Histone Modifying Enzymes

Histone proteins that form the nucleosome core are subject to a variety of post-translational transformations. These histone\\u000a modifications make up the histone code which extends the information in the genetic code and is emerging as an essential mechanism\\u000a to regulate gene expression. In spite of a current flurry of significant advances in experimental studies, there has been\\u000a little theoretical understanding

Yingkai Zhang

2009-01-01

28

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

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

2008-01-01

29

We use the conversion of protonated glycerol to acrolein for a case study of the mechanism of acid-catalyzed dehydration of polyols in aqueous environments. We employ hybrid Quamtum Mechanics/Molecular Mechanics Molecular Dynamics (QM/MM MD) simulations with biased sampling and perform free energy calculations for the elementary steps of the reaction. We investigate the effects of solvent dynamics and in particular the role of quantum mechanical water in the dehydration mechanism. We present results supporting a mechanism that proceeds via water-mediated proton transfers and thus through an enol intermediate. We find that the first dehydration may take place by two, low-energy pathways requiring, respectively, 20.9 and 18.8 kcal/mol of activation free energy. The second dehydration requires 19.9 kcal/mol of activation free energy while for the overall reaction we compute a free energy change of ?8 kcal/mol.

Caratzoulas, Stavros [Catalysis Center for Energy Innovation, Univ. of Delaware, Newark, DE (United States); Courtney, Timothy [Univ. of Delaware, Newark, DE (United States); Vlachos, Dionisios G. [Catalysis Center for Energy Innovation, Univ. of Delaware, Newark, DE (United States)

2011-08-18

30

Over the past several years, rapid advances in computational hardware, quantum chemical methods, and mixed quantum mechanics/molecular mechanics (QM/MM) techniques have made it possible to model accurately the interaction of ligands with metal-containing proteins at an atomic level of detail. In this paper, we describe the application of our computational methodology, based on density functional (DFT) quantum chemical methods, to two diiron-containing proteins that interact with dioxygen: methane monooxygenase (MMO) and hemerythrin (Hr). Although the active sites are structurally related, the biological function differs substantially. MMO is an enzyme found in methanotrophic bacteria and hydroxylates aliphatic C-H bonds, whereas Hr is a carrier protein for dioxygen used by a number of marine invertebrates. Quantitative descriptions of the structures and energetics of key intermediates and transition states involved in the reaction with dioxygen are provided, allowing their mechanisms to be compared and contrasted in detail. An in-depth understanding of how the chemical identity of the first ligand coordination shell, structural features, electrostatic and van der Waals interactions of more distant shells control ligand binding and reactive chemistry is provided, affording a systematic analysis of how iron-containing proteins process dioxygen. Extensive contact with experiment is made in both systems, and a remarkable degree of accuracy and robustness of the calculations is obtained from both a qualitative and quantitative perspective.

Friesner, Richard A.(Columbia University) [Columbia University; Baik, Mu-Hyun (Columbia University) [Columbia University; Gherman, Benjamin F.(Columbia University) [Columbia University; Guallar, Victor (Washington University) [Washington University; Wirstam, Maria E.(1836) [1836; Murphy, Robert B.(Schrodinger Inc) [Schrodinger Inc; Lippard, Stephen J.(Massachusetts Institute of Technology) [Massachusetts Institute of Technology

2003-03-01

31

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

Zheng, Min; Xu, Dingguo

2013-09-01

32

The Role of Magnesium for Geometry and Charge in GTP Hydrolysis, Revealed by Quantum Mechanics, People's Republic of China ABSTRACT The coordination of the magnesium ion in proteins by triphosphates conversion. For example, in Ras the magnesium ion contributes to the catalysis of GTP hydrolysis

Gerwert, Klaus

33

The caffeine biosynthetic pathway is of considerable importance for the beverage and pharmaceutical industries which produces two blockbuster products: theobromine and caffeine. The major biochemistry in caffeine biosynthesis starts from the initial substrate of xanthosine and ends with the final product caffeine, with theobromine serving as an intermediate. The key enzyme, S-adenosyl-l-methionine (SAM) dependent 3,7-dimethyl-xanthine methyltransferase (DXMT), catalyzes two important methyl transfer steps in caffeine biosynthesis: (1) methylation of N3 of 7-methylxanthine (7mX) to form theobromine (Tb); (2) methylation of N1 of theobromine to form caffeine (Cf). Although DXMT has been structurally characterized recently, our understanding of the detailed catalytic mechanism and role of key catalytic residues is still lacking. In this work, the quantum mechanical/molecular mechanical (QM/MM) MD and free energy simulations are performed to elucidate the catalytic mechanism of the enzyme-catalyzed reactions and to explain experimental observations concerning the activity of this enzyme. The roles of certain active-site residues are studied, and the results of computer simulation seem to suggest that a histidine residue (His160) at the active site of DXMT may act as a general base/acid catalyst during the methyl transfer process. PMID:24479684

Yue, Yufei; Guo, Hong

2014-02-24

34

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

35

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. PMID:24339041

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

2014-01-01

36

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. PMID:23202934

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

2012-01-01

37

Irreversible epidermal growth factor receptor (EGFR) inhibitors can circumvent resistance to first-generation ATP-competitive inhibitors in the treatment of nonsmall-cell lung cancer. They covalently bind a noncatalytic cysteine (Cys797) at the surface of EGFR active site by an acrylamide warhead. Herein, we used a hybrid quantum mechanics/molecular mechanics (QM/MM) potential in combination with umbrella sampling in the path-collective variable space to investigate the mechanism of alkylation of Cys797 by the prototypical covalent inhibitor N-(4-anilinoquinazolin-6-yl) acrylamide. Calculations show that Cys797 reacts with the acrylamide group of the inhibitor through a direct addition mechanism, with Asp800 acting as a general base/general acid in distinct steps of the reaction. The obtained reaction free energy is negative (?A = -12 kcal/mol) consistent with the spontaneous and irreversible alkylation of Cys797 by N-(4-anilinoquinazolin-6-yl) acrylamide. Our calculations identify desolvation of Cys797 thiolate anion as a key step of the alkylation process, indicating that changes in the intrinsic reactivity of the acrylamide would have only a minor impact on the inhibitor potency. PMID:25658136

Capoferri, Luigi; Lodola, Alessio; Rivara, Silvia; Mor, Marco

2015-03-23

38

Using ethanol-water solutions as illustration, we demonstrate the capability of the hybrid quantum mechanics/molecular mechanics (QM/MM) paradigm to simulate core photoelectron spectroscopy: the binding energies and the chemical shifts. An integrated approach with QM/MM binding energy calculations coupled to preceding molecular dynamics sampling is adopted to generate binding energies averaged over the solute-solvent configurations available at a particular temperature and pressure and thus allowing for a statistical assessment with confidence levels for the final binding energies. The results are analyzed in terms of the contributions in the molecular mechanics model-electrostatic, polarization, and van der Waals-with atom or bond granulation of the corresponding MM charge and polarizability force-fields. The role of extramolecular charge transfer screening of the core-hole and explicit hydrogen bonding is studied by extending the QM core to cover the first solvation shell. The results are compared to those obtained from pure electrostatic and polarizable continuum models. Particularly, the dependence of the carbon 1s binding energies with respect to the ethanol concentration is studied. Our results indicate that QM/MM can be used as an all-encompassing model to study photoelectron binding energies and chemical shifts in solvent environments. PMID:25340948

Löytynoja, T; Niskanen, J; Jänkälä, K; Vahtras, O; Rinkevicius, Z; Ågren, H

2014-11-20

39

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

40

We address the challenges of treating polarization and covalent interactions in docking by developing a hybrid quantum mechanical/molecular mechanical (QM/MM) scoring function based on the semiempirical self-consistent charge density functional tight-binding (SCC-DFTB) method and the CHARMM force field. To benchmark this scoring function within the EADock DSS docking algorithm, we created a publicly available dataset of high-quality X-ray structures of zinc metalloproteins ( http://www.molecular-modelling.ch/resources.php ). For zinc-bound ligands (226 complexes), the QM/MM scoring yielded a substantially improved success rate compared to the classical scoring function (77.0% vs 61.5%), while, for allosteric ligands (55 complexes), the success rate remained constant (49.1%). The QM/MM scoring significantly improved the detection of correct zinc-binding geometries and improved the docking success rate by more than 20% for several important drug targets. The performance of both the classical and the QM/MM scoring functions compare favorably to the performance of AutoDock4, AutoDock4Zn, and AutoDock Vina. PMID:25296988

Chaskar, Prasad; Zoete, Vincent; Röhrig, Ute F

2014-11-24

41

The applicability of combined quantum mechanics/molecular mechanics (QM/MM) methods for the calculation of absolute binding free energies of conserved water molecules in protein/ligand complexes is demonstrated. Here, we apply QM/MM Monte Carlo simulations to investigate binding of water molecules to influenza neuraminidase. We investigate five different complexes, including those with the drugs oseltamivir and peramivir. We investigate water molecules in two different environments, one more hydrophobic and one hydrophilic. We calculate the free-energy change for perturbation of a QM to MM representation of the bound water molecule. The calculations are performed at the BLYP/aVDZ (QM) and TIP4P (MM) levels of theory, which we have previously demonstrated to be consistent with one another for QM/MM modeling. The results show that the QM to MM perturbation is significant in both environments (greater than 1 kcal mol(-1)) and larger in the more hydrophilic site. Comparison with the same perturbation in bulk water shows that this makes a contribution to binding. The results quantify how electronic polarization differences in different environments affect binding affinity and also demonstrate that extensive, converged QM/MM free-energy simulations, with good levels of QM theory, are now practical for protein/ligand complexes. PMID:25340313

Woods, Christopher J; Shaw, Katherine E; Mulholland, Adrian J

2015-01-22

42

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

43

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

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

2012-11-01

44

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

45

NASA Astrophysics Data System (ADS)

A comparison of the hydration characteristics of di- and trivalent europium ions in aqueous solution is presented. The established quantum mechanical charge-field molecular dynamics (QMCF-MD) approach yielded two 30 ps simulations. Significant differences among the two species were found in the Eu-O radial distribution functions, both in good agreement with experiments. The first shell coordination numbers of 8.1 and 8.9 were observed for Eu(II) and Eu(III), respectively. The mean residence time of first shell ligands differ by more than one order of magnitude, the divalent ion's hydration shell being more flexible, which is underlined by a weak ion-water bond strength.

Canaval, Lorenz R.; Rode, Bernd M.

2015-01-01

46

Kynurenine aminotransferase (KAT) is a key enzyme of the kynurenine pathway along the route of tryptophan catabolism. It catalyzes the irreversible transamination reaction of L-kynurenine (L-Kyn) to kynurenic acid (KYNA), an important neuroactive metabolite that plays a role in protecting neurons from excitatory neurotransmission. Although four isoforms (KAT-I to -IV) of this enzyme have been hitherto identified, KAT-II is the enzymatic isoform that mainly accounts for the synthesis of cerebral KYNA. In this study, the transamination mechanism of L-Kyn catalyzed by KAT-II is theoretically determined by performing combined quantum mechanical and molecular mechanical (QM/MM) simulations. The results are instrumental to explore the catalytic properties of the enzyme and to provide theoretical details on the mechanism of the intramolecular condensation of the ketoacid intermediate, leading to the final product KYNA. Ultimately, they will also be of value in the future design of new KAT-II selective inhibitors. PMID:19715778

Bellocchi, Daniele; Macchiarulo, Antonio; Carotti, Andrea; Pellicciari, Roberto

2009-12-01

47

DNA polymerases play a crucial role in the cell cycle due to their involvement in genome replication and repair. Understanding the reaction mechanism by which these polymerases carry out their function can provide insights into these processes. Recently, the crystal structures of human DNA polymerase ? (Pol?) have been reported both for pre- and post-catalytic complexes [García-Díaz et al., DNA

G. Andrés Cisneros; Lalith Perera; Miguel García-Díaz; Katarzyna Bebenek; Thomas A. Kunkel; Lee G. Pedersen

2008-01-01

48

We present an alternative approach to determine "density-dependent property"-derived charges for molecules in the condensed phase. In the case of a solution, it is essential to take into consideration the electron polarization of molecules in the active site of this system. The solute and solvent molecules in this site have to be described by a quantum mechanical technique and the others are allowed to be treated by a molecular mechanical method (QM/MM scheme). For calculations based on this scheme, using the forces and interaction energy as density-dependent property our charges from interaction energy and forces (CHIEF) approach can provide the atom-centered charges on the solute atoms. These charges reproduce well the electrostatic potentials around the solvent molecules and present properly the picture of the electron density of the QM subsystem in the solution system. Thus, the CHIEF charges can be considered as the atomic charges under the conditions of the QM/MM simulation, and then enable one to analyze electrostatic interactions between atoms in the QM and MM regions. This approach would give a view of the QM nuclei and electrons different from the conventional methods. PMID:21815177

Yamada, Kenta; Koyano, Yoshiyuki; Okamoto, Takuya; Asada, Toshio; Koga, Nobuaki; Nagaoka, Masataka

2011-11-15

49

Heterogeneous reactions catalyzed by transition-metal-containing nanoparticles represent a crucial type of reaction in chemical industry. Because of the existing gap in understanding heterogeneous catalysis between a cluster of a few atoms and a bulk model of periodic slabs, reactions catalyzed by transition-metal-containing nanoparticles are still not well understood. Herein, we provide a multiscale modeling approach to study the benzene hydrogenation reactions on molybdenum carbide nanoparticles (MCNPs) in the process of in situ heavy oil upgrading. By coupling the quantum mechanical (QM) density functional tight-binding (DFTB) method with a molecular mechanical (MM) force field, a QM/MM model was built to describe the reactants, the nanoparticles and the surroundings. Umbrella sampling (US) was used to calculate the free energy profiles of the benzene hydrogenation reactions in a model aromatic solvent in the in situ heavy oil upgrading conditions. By comparing with the traditional method in computational heterogeneous catalysis, the results reveal new features of the metallic MCNPs. Rather than being rigid, they are very flexible under working condition due to the entropic contributions of the MCNPs and the solvent, which greatly affect the free energy profiles of these nanoscale heterogeneous reactions. PMID:25774905

Liu, Xingchen; Salahub, Dennis R

2015-04-01

50

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

51

NASA Astrophysics Data System (ADS)

A novel molecular dynamics methodology recently proposed by our group [Rega et al., Chem. Phys. Lett. 422, 367 (2006)], which is based on an integrated hybrid potential rooted in high level quantum mechanical methods using localized basis functions and nonperiodic boundary conditions, has been applied to study acrolein in aqueous solution. The solute structural rearrangement and its hydrogen-bonding pattern due to the interactions with water have been analyzed in some detail. Moreover, the solvent effects on the UV n ??? vertical transition and on the NMR C13 and O17 shielding constants of acrolein have been investigated theoretically by performing a posteriori quantum mechanical calculations on a statistically significant number of snapshots extracted from both gas-phase and aqueous solution simulations. Results show that such effective computational strategy can be successfully used to improve our understanding, at atomic level, of important spectroscopic observables.

Brancato, Giuseppe; Rega, Nadia; Barone, Vincenzo

2006-10-01

52

NASA Astrophysics Data System (ADS)

The isoalloxazine ring (flavin ring) is a part of the coenzyme flavin adenine dinucleotide and acts as an active site in the oxidation of a substrate. We have computed the free energy change ??red associated with one-electron reduction of the flavin ring immersed in water by utilizing the quantum mechanical/molecular mechanical method combined with the theory of energy representation (QM/MM-ER method) recently developed. As a novel treatment in implementing the QM/MM-ER method, we have identified the excess charge to be attached on the flavin ring as a solute while the remaining molecules, i.e., flavin ring and surrounding water molecules, are treated as solvent species. Then, the reduction free energy can be decomposed into the contribution ??red(QM) due to the oxidant described quantum chemically and the free energy ??red(MM) due to the water molecules represented by a classical model. By the sum of these contributions, the total reduction free energy ??red has been given as -80.1 kcal/mol. To examine the accuracy and efficiency of this approach, we have also conducted the ??red calculation using the conventional scheme that ??red is constructed from the solvation free energies of the flavin rings at the oxidized and reduced states. The conventional scheme has been implemented with the QM/MM-ER method and the calculated ??red has been estimated as -81.0 kcal/mol, showing excellent agreement with the value given by the new approach. The present approach is efficient, in particular, to compute free energy change for the reaction occurring in a protein since it enables ones to circumvent the numerical problem brought about by subtracting the huge solvation free energies of the proteins in two states before and after the reduction.

Takahashi, Hideaki; Ohno, Hajime; Kishi, Ryohei; Nakano, Masayoshi; Matubayasi, Nobuyuki

2008-11-01

53

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction; 2. Mathematical preliminaries; 3. The rules of quantum mechanics; 4. The connection between the fundamental rules and wave mechanics; 5. Further illustrations of the rules of quantum mechanics; 6. Further developments in one-dimensional wave mechanics; 7. The theory of angular momentum; 8. Wave mechanics in three dimensions: hydrogenic atoms; 9. Time-independent approximations for bound state problems; 10. Applications of static perturbation theory; 11. Identical particles; 12. Atomic structure; 13. Molecules; 14. The stability of matter; 15. Photons; 16. Interaction of non-relativistic charged particles and radiation; 17. Further topics in perturbation theory; 18. Scattering; 19. Special relativity and quantum mechanics: the Klein–Gordon equation; 20. The Dirac equation; 21. Interaction of a relativistic spin 1/2 particle with an external electromagnetic field; 22. The Dirac field; 23. Interaction between relativistic electrons, positrons, and photons; 24. The quantum mechanics of weak interactions; 25. The quantum measurement problem; Appendix A: useful inequalities for quantum mechanics; Appendix B: Bell's inequality; Appendix C: spin of the photon: vector spherical waves; Works cited; Bibliography; Index.

Commins, Eugene D.

2014-10-01

54

NASA Astrophysics Data System (ADS)

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

Mandl, F.

1992-07-01

55

Bohmian mechanics contradicts quantum mechanics

Bohmian mechanics contradicts quantum mechanics Arnold Neumaier Institut fur Mathematik, Universit and quantum mechanics predict values of opposite sign for certain time correlations. The discrepancy can no loophole for claiming that Bohmian mechanics reproduces all predictions of quantum mechanics exactly

Neumaier, Arnold

56

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

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

2013-01-01

57

Introduction: quantum resonances Classical and quantum mechanics

: quantum resonances Classical and quantum mechanics Microlocal analysis Resonances associated;..... . .... . .... . ..... . .... . .... . .... . ..... . .... . .... . .... . ..... . .... . .... . .... . ..... . .... . ..... . .... . .... . Introduction: quantum resonances Classical and quantum mechanics Microlocal analysis Resonances associated with homoclinic orbits Outline Introduction: quantum resonances Classical and quantum mechanics Microlocal

Ramond, Thierry

58

Quantum Mechanics Measurements, Mutually

Quantum Mechanics Measurements, Mutually Unbiased Bases and Finite Geometry Or why six is the first) #12;Quantum Mechanics for Dummies Finite dimensional quantum states are represented by trace one,1 -icS1,1[ ] #12;Quantum systems evolve and are measured. The evolution of a quantum system using

Gruner, Daniel S.

59

NASA Astrophysics Data System (ADS)

A development of quantum theory that was initiated in the 1920s by Werner Heisenberg (1901-76) and Erwin Schrödinger (1887-1961). The theory drew on a proposal made in 1925 Prince Louis de Broglie (1892-1987), that particles have wavelike properties (the wave-particle duality) and that an electron, for example, could in some respects be regarded as a wave with a wavelength that depended on its mo...

Murdin, P.

2000-11-01

60

A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Lévy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Lévy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and

Nikolai Laskin

2000-01-01

61

Quantum Mechanics + Open Systems

Quantum Mechanics + Open Systems = Thermodynamics ? Jochen Gemmer TÂ¨ubingen, 09.02.2006 #12., World Scientific) #12;Fundamental Law or Emergent Description? Quantum Mechanics i t = (- 2 2m + V or Emergent Description? Quantum Mechanics i t = (- 2 2m + V ) "Heisenberg Cut" Classical Mechanics: m d2

Steinhoff, Heinz-JÃ¼rgen

62

Dissipative and quantum mechanics

Three existing interpretations of quantum mechanics, given by Heisenberg, Bohm and Madelung, are examined to describe dissipative quantum systems as well. It is found that the Madelung quantum hydrodynamics is the only correct approach. A new stochastic reinterpretation of the quantum mechanics is proposed, which represents the microscopic face of the Madelung hydrodynamics. The main idea is that the vacuum

Roumen Tsekov

2009-01-01

63

Astrophysics Geometry QuantumMechanics Stochasticanalysis DifferentialEquations A N N U A L R E P O report 2010 6 Geometry 6 Stochastic analysis 8 Differential Equations 9 Astrophysics 11 Quantum Mechanics

Johansen, Tom Henning

64

Quantum Mechanics Based Multiscale Modeling of Materials

NASA Astrophysics Data System (ADS)

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

Lu, Gang

2013-03-01

65

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

66

Introduction to Quantum Mechanics

The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.

Eduardo J. S. Villaseñor

2008-04-23

67

Geometrization of Quantum Mechanics

We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.

J. F. Carinena; J. Clemente-Gallardo; G. Marmo

2007-03-23

68

Introduction to Quantum Mechanics

NSDL National Science Digital Library

The microscopic world is full of phenomena very different from what we see in everyday life. Some of those phenomena can only be explained using quantum mechanics. This activity introduces basic quantum mechanics concepts about electrons that are essential to understanding modern and future technology, especially nanotechnology. Start by exploring probability distribution, then discover the behavior of electrons with a series of simulations.

2012-07-19

69

Geometrization of quantum mechanics

Quantum mechanics is cast into a classical Hamiltonian form in terms of a symplectic structure, not on the Hilbert space of state-vectors but on the more physically relevant infinite-dimensional manifold of instantaneous pure states. This geometrical structure can accommodate generalizations of quantum mechanics, including the nonlinear relativistic models recently proposed. It is shown that any such generalization satisfying a few

T. W. B. Kibble

1979-01-01

70

Covariant quantum mechanics and quantum symmetries

Covariant quantum mechanics and quantum symmetries Josef JanyÅ¸ska 1 , Marco Modugno 2 , Dirk Saller: quantum mechanics, classical mechanics, general relativity, infinitesimal symmetries. 2000 MSC: 81P99, 81Q Introduction 2 2 Covariant quantum mechanics 5 2.1 Classical background

JanyÂ?ka, Josef

71

An introduction to quantum probability, quantum mechanics, and quantum computation

An introduction to quantum probability, quantum mechanics, and quantum computation Greg Kuperberg". Recently quantum computation has entered as a new reason for both mathematicians and computer scientists deterministic algorithms for some computational problems, quantum algorithms can be moderately faster

Thomases, Becca

72

Quantum Statistical Mechanics and Quantum Computation

Quantum Statistical Mechanics and Quantum Computation 22-23 March 2012 Room 111, Jadwin Hall, focused meeting to explore the intersection between quantum statistical mechanics and quantum computation of statistical mechanical methods allows useful statements to be made about the average complexity of various

73

Quantum Mechanics Without Observers

The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process theory and utilizing methods from combinatorial games, interpolation theory and complex systems theory results in a novel realist version of quantum mechanics incorporating quasi-local, nondeterministic hidden variables that are compatible with the no-hidden variable theorems and relativistic invariance, and reproduce the standard results of quantum mechanics to a high degree of accuracy without invoking observers.

W. H. Sulis

2013-03-03

74

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 [California Institute of Technology, Pasadena, California 91125 (United States)] [California Institute of Technology, Pasadena, California 91125 (United States)

2013-06-15

75

Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a probability calculus. Its providing a general framework for prediction accounts for its distinctive traits, which one should be careful not to mistake for reflections of any strange ontology. The suggestion is also made that quantum theory unwittingly emerged, in Schroedinger's formulation, as a 'lossy' by-product of a quantum-mechanical variant of the Hamilton-Jacobi equation. As it turns out, the effectiveness of quantum theory qua predictive algorithm makes up for the computational impracticability of that master equation.

Jean-Michel Delhotel

2014-10-27

76

Contextual Deterministic Quantum Mechanics

We present a simple proof of quantum contextuality for a spinless particle with a one dimensional configuration space. We then discuss how the maximally realistic deterministic quantum mechanics recently constructed by this author and V. Singh can be applied to different contexts.

S. M. Roy

1999-08-18

77

Quantum mechanics is one of the most successful theoretical structures in all of science. Developed between 1925-26 to explain the optical spectrum of atoms, the theory over the succeeding 80 years has been extended, first to quantum field theories, gauge field theories, and now even string theory. It is used every day by thousands of physicists to calculate physical phenomena

W G Unruh

2006-01-01

78

Beyond conventional quantum mechanics

NASA Astrophysics Data System (ADS)

The author reviews some recent attempts to overcome the conceptual difficulties encountered by trying to interpret quantum mechanics as giving a complete, objective and unified description of natural phenomena.

Ghirardi, C.

1991-10-01

79

Quantum Mechanics From the Cradle?

ERIC Educational Resources Information Center

States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)

Martin, John L.

1974-01-01

80

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

81

Nonlocality beyond quantum mechanics

NASA Astrophysics Data System (ADS)

Nonlocality is the most characteristic feature of quantum mechanics, but recent research seems to suggest the possible existence of nonlocal correlations stronger than those predicted by theory. This raises the question of whether nature is in fact more nonlocal than expected from quantum theory or, alternatively, whether there could be an as yet undiscovered principle limiting the strength of nonlocal correlations. Here, I review some of the recent directions in the intensive theoretical effort to answer this question.

Popescu, Sandu

2014-04-01

82

Probability in Quantum Mechanics

The concept of probability played an important role in the very beginning of ? quantum theory, when Max Planck (1858–1947)\\u000a postulated the discrete emission and absorption of radiation in a ? black body radiation. The quantum statistical mechanics\\u000a developed by Planck and his successors has extraordinary consequences treated elsewhere in this Compendium. Here, however,\\u000a the emphasis will be upon the

Abner Shimony

83

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.

Zollman, Dean

84

We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position or in the momentum representation. As a way to support this complementation, starting from the action that describes conformal gravity in the world-line formalism, we show that there are duality transformations that relate the dynamics in the presence of position dependent vector and tensor fields to the dynamics in the presence of momentum dependent vector and tensor fields.

W. Chagas-Filho

2009-05-11

85

Quantum Mechanics in Phase Space

The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.

Ali Mohammad Nassimi

2008-06-11

86

27 September 2002 Abstract Over the past several years, rapid advances in computational hardware accurate quantum chemical and mixed quantum mechanics/molecular mechanics calculations Richard A. Friesner, quantum chemical methods, and mixed quantum mechanics/molecular mechanics (QM/MM) techniques have made

Baik, Mu-Hyun

87

We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics.

Argyris Nicolaidis

2012-11-09

88

Quantum Mechanics and Gravitation

In summer 1999 an experiment at ILL, Grenoble was conducted. So-called ultra-cold neutrons (UCN) were trapped in the vertical direction between the Fermi-potential of a smooth mirror below and the gravitational potential of the earth above [Ne00, Ru00]. If quantum mechanics turns out to be a sufficiently correct description of the phenomena in the regime of classical, weak gravitation, one should observe the forming of quantized bound states in the vertical direction above a mirror. Already in a simplified view, the data of the experiment provides strong evidence for the existence of such gravitationally bound quantized states. A successful quantum-mechanical description would then provide a convincing argument, that the socalled first quantization can be used for gravitation as an interaction potential, as this is widely expected. Furthermore, looking at the characteristic length scales of about 10 mikron of such bound states formed by UCN, one sees, that a complete quantum mechanical description of this experiment additionally would enable one to check for possible modifications of Newtonian gravitation on distance scales being one order of magnitude below currently available tests [Ad00]. The work presented here deals mainly with the development of a quantum mechanical description of the experiment.

A. Westphal

2003-04-08

89

Physicalism versus quantum mechanics

In the context of theories of the connection between mind and brain, physicalism is the demand that all is basically purely physical. But the concept of "physical" embodied in this demand is characterized essentially by the properties of the physical that hold in classical physical theories. Certain of these properties contradict the character of the physical in quantum mechanics, which provides a better, more comprehensive, and more fundamental account of phenomena. It is argued that the difficulties that have plaged physicalists for half a century, and that continue to do so, dissolve when the classical idea of the physical is replaced by its quantum successor. The argument is concretized in a way that makes it accessible to non-physicists by exploiting the recent evidence connecting our conscious experiences to macroscopic measurable synchronous oscillations occurring in well-separated parts of the brain. A specific new model of the mind-brain connection that is fundamentally quantum mechanical but that ties conscious experiences to these macroscopic synchronous oscillations is used to illustrate the essential disparities between the classical and quantum notions of the physical, and in particular to demonstrate the failure in the quantum world of the principle of the causal closure of the physical, a failure that goes beyond what is entailed by the randomness in the outcomes of observations, and that accommodates the efficacy in the brain of conscious intent.

Henry P. Stapp

2008-03-11

90

On Randomness in Quantum Mechanics

The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.

Alberto C. de la Torre

2007-07-19

91

Quantum Mechanical Models of Solids

NSDL National Science Digital Library

This web site contains the class notes for a course on Quantum Mechanical Models of Solids. Topics cover basic quantum mechanics, crystallography, exchange-correlation, metals, and semiconductors. The site also includes a list of useful books and references.

Heggie, Malcom

92

TRANSIENT QUANTUM MECHANICAL PROCESSES

Our principal objective has centered on the development of sophisticated computational techniques to solve the time-dependent Schroedinger equation that governs the evolution of quantum mechanical systems. We have perfected two complementary methods, discrete variable representation and real space product formula, that show great promise in solving these complicated temporal problems. We have applied these methods to the interaction of laser light with molecules with the intent of not only investigating the basic mechanisms but also devising schemes for actually controlling the outcome of microscopic processes. Lasers now exist that produce pulses of such short duration as to probe a molecular process many times within its characteristic period--allowing the actual observation of an evolving quantum mechanical system. We have studied the potassium dimer as an example and found agreement with experimental changes in the intermediate state populations as a function of laser frequency--a simple control prescription. We have also employed elaborate quantum chemistry programs to improve the accuracy of basic input such as bound-bound and bound-free coupling moments. These techniques have far-ranging applicability; for example, to trapped quantum systems at very low temperatures such as Bose-Einstein condensates.

L. COLLINS; J. KRESS; R. WALKER

1999-07-01

93

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

94

Probabilistic Interpretation of Quantum Mechanics

The probabilistic interpretation of quantum mechanics is based on Born's 1926 papers and von Neumann's formal account of quantum\\u000a mechanics in ? Hilbert space. According to Max Born (1882–1970), the quantum mechanical ? wave function ? does not have any\\u000a direct physical meaning, whereas its square ???2 is a probability [1] ? Born rule, probability in quantum mechanics. According to

Brigitte Falkenburg; Peter Mittelstaedt

95

Nonlinear friction in quantum mechanics

The effect of nonlinear friction forces in quantum mechanics is studied via dissipative Madelung hydrodynamics. A new thermo-quantum diffusion equation is derived, which is solved for the particular case of quantum Brownian motion with a cubic friction. It is extended also by a chemical reaction term to describe quantum reaction-diffusion systems with nonlinear friction as well.

Roumen Tsekov

2013-03-10

96

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

97

Gaussian effective potential: Quantum mechanics

NASA Astrophysics Data System (ADS)

We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantum mechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.

Stevenson, P. M.

1984-10-01

98

Advanced Concepts in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction: the need for a quantum theory; 2. Experimental foundations of quantum theory; 3. Waves and particles; 4. Schrödinger picture, Heisenberg picture and probabilistic aspects; 5. Integrating the equations of motion; 6. Elementary applications: 1-dimensional problems; 7. Elementary applications: multidimensional problems; 8. Coherent states and related formalism; 9. Introduction to spin; 10. Symmetries in quantum mechanics; 11. Approximation methods; 12. Modern pictures of quantum mechanics; 13. Formulations of quantum mechanics and their physical implications; 14. Exam problems; Glossary of geometric concepts; References; Index.

Esposito, Giampiero; Marmo, Giuseppe; Miele, Gennaro; Sudarshan, George

2014-11-01

99

Principles of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Preface; Introduction: 1. Observation and interpretation; 2. Difficulties of the classical theories; 3. The purpose of quantum theory; Part I. Elementary Theory of Observation (Principle of Complementarity): 4. Refraction in inhomogeneous media (force fields); 5. Scattering of charged rays; 6. Refraction and reflection at a plane; 7. Absolute values of momentum and wave length; 8. Double ray of matter diffracting light waves; 9. Double ray of matter diffracting photons; 10. Microscopic observation of ? (x) and ? (p); 11. Complementarity; 12. Mathematical relation between ? (x) and ? (p) for free particles; 13. General relation between ? (q) and ? (p); 14. Crystals; 15. Transition density and transition probability; 16. Resultant values of physical functions; matrix elements; 17. Pulsating density; 18. General relation between ? (t) and ? (?); 19. Transition density; matrix elements; Part II. The Principle of Uncertainty: 20. Optical observation of density in matter packets; 21. Distribution of momenta in matter packets; 22. Mathematical relation between ? and ?; 23. Causality; 24. Uncertainty; 25. Uncertainty due to optical observation; 26. Dissipation of matter packets; rays in Wilson Chamber; 27. Density maximum in time; 28. Uncertainty of energy and time; 29. Compton effect; 30. Bothe-Geiger and Compton-Simon experiments; 31. Doppler effect; Raman effect; 32. Elementary bundles of rays; 33. Jeans' number of degrees of freedom; 34. Uncertainty of electromagnetic field components; Part III. The Principle of Interference and Schrödinger's equation: 35. Physical functions; 36. Interference of probabilities for p and q; 37. General interference of probabilities; 38. Differential equations for ?p (q) and Xq (p); 39. Differential equation for ?? (q); 40. The general probability amplitude ??' (Q); 41. Point transformations; 42. General theorem of interference; 43. Conjugate variables; 44. Schrödinger's equation for conservative systems; 45. Schrödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.

Landé, Alfred

2013-10-01

100

NASA Astrophysics Data System (ADS)

I do not agree with mind-body dualism. Today the consensus view is that thought and mind is a combination of processes like memory, generalization, comparison, deduction, organization, induction, classification, feature detection, analogy, etc. performed by computational machinery. (R. Jones, Trans. of the Kansas Acad. Sci., vol. 109, # 3/4, 2006 and www.robert-w-jones.com, philosopher, theory of thought) But I believe that quantum mechanics is a more plausible dualist theory of reality. The quantum mechanical wave function is nonphysical, it exists in a 3N space (for an N body system) not in (x,y,z,t) 4-space, and does not possess physical properties. But real physical things like energy (which do exist in our 4-space world) influence the wave function and the wave function, in its turn, influences real physical things, like where a particle can be found in 4-space. The coupling between the spirit-like wave function and things found in the real (4-space) world (like energy) is via mathematical equations like the Schrodinger equation and Born normalization.

Jones, Robert

2011-03-01

101

Quantum mechanics probes superspace

We study quantum mechanics in one space dimension in the stochastic formalism. We show that the partition function of the theory is, in fact, equivalent to that of a model, whose action is explicitly invariant (up to surface terms) under supersymmetry transformations--but whose invariance under the stochastic identities is not obvious, due to an apparent mismatch between fermions and bosons. The resolution of the riddle is that one "fermion" is a gauge artifact and, upon fixing the local, fermionic symmetry, called $\\kappa-$symmetry, we recover the stochastic partition function. The "fermions" do not propagate in the bulk, since their kinetic term is a total derivative. Their contribution to the action is through an ultra--local bilinear term, that may be exactly integrated out, as long as the superpotential has a unique minimum and we obtain a local action for the scalar. When the superpotential does not have a unique minimum, we use a Hubbard-Stratonovich transformation of the kinetic term to obtain an action in terms of the Fourier transform of the velocity, a kind of duality transformation. The classical particle thus moves in a medium of dipoles, that parametrize the quantum fluctuations and the classical trajectory $\\phi(\\tau)$, becomes a chiral superfield, $(\\phi(\\tau),\\psi_\\alpha(\\tau),F(\\tau))$, when quantum effects are taken into account. The observable superpartner of the scalar, however, is the fermion bilinear and thus, while supersymmetry may be realized, the observable partner excitations are not degenerate in mass. We compute the stochastic identities of the auxiliary field, using a lattice regularization of the equivalent "bosonic" action, for the case of a superpotential with a single minimum. We show that the lattice action can be expressed as an ultra--local functional of the auxiliary field, up to terms that vanish with the lattice spacing.

S. Nicolis

2014-05-05

102

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

103

The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can be represented in a Hilbert space, that a self-adjoint operator is associated to any observable, that the result of a measure must be the eigen value of the operator and appear with the usual probability. Furthermore an equivalent of the Wigner's theorem holds, which leads to the Schr\\"{o}dinger equation. These results are based on well known mathematics, and do not involve any specific hypothesis in Physics. They validate and explain the methods currently used, which are made simpler and safer, and open new developments. In the second edition of this paper important developments have been added about interacting systems and the transitions of phases.

Jean-Paul Metailié; Jean Claude Dutailly

2014-08-20

104

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

105

Invariance in adelic quantum mechanics

Adelic quantum mechanics is form invariant under an interchange of real and p-adic number fields as well as rings of p-adic integers. We also show that in adelic quantum mechanics Feynman's path integrals for quadratic actions with rational coefficients are invariant under changes of their entries within nonzero rational numbers.

Branko Dragovich

2006-12-07

106

QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES

The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory.

G. GEIGER; ET AL

2000-11-01

107

Conceptual problems in quantum mechanics

This review is devoted to a discussion of the interpretation of quantum mechanics. The heuristic role and limitations of the principle of observability and of operationalism are discussed. It is shown that the probabilistic approach to quantum mechanics is essential as a way of reconciling the conflicting concepts of particle and wave. The reason why the reduction of the wave

V. P. Demutskii; R. V. Polovin

1993-01-01

108

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

109

Decoherence in quantum mechanics and quantum cosmology

NASA Technical Reports Server (NTRS)

A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.

Hartle, James B.

1992-01-01

110

Scattering Relativity in Quantum Mechanics

Transforming from one reference frame to another yields an equivalent physical description. If quantum fields are transformed one way and quantum states transformed a different way then the physics changes. We show how to use the resulting changed physical description to obtain the equations of motion of charged, massive particles in electromagnetic and gravitational fields. The derivation is based entirely on special relativity and quantum mechanics.

Richard Shurtleff

2011-08-09

111

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

2014-12-01

112

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

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

2013-08-28

113

in a Penicillin Binding Protein (PBP) versus in a Class C -Lactamase Benjamin F. Gherman, Shalom D. Goldberg in penicillin-binding proteins (PBPs) and -lactamases has remained an unsolved puzzle whose solution is of great has emerged as a major health care problem.1-8 -Lactam antibiotics (e.g., penicillins

Gherman, Benjamin F.

114

From Quantum Mechanics to Thermodynamics?

From Quantum Mechanics to Thermodynamics? Dresden, 22.11.2004 Jochen Gemmer UniversitÂ¨at OsnabrÂ¨uck #12;Table of Contents Â· Motivation and perspective Â· Brief review of historical approaches to thermodynamical behavior Â· Quantum approach to thermodynamical behavior Â· The route to equilibrium Â· Summary

Steinhoff, Heinz-JÃ¼rgen

115

Quantum mechanics from classical statistics

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.

Wetterich, C. [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)], E-mail: c.wetterich@thphys.uni-heidelberg.de

2010-04-15

116

Free will and quantum mechanics

A simple example is provided showing that violation of free will allows to reproduce the quantum mechanical predictions, and that the Clauser-Horne parameter can take the maximum value 4 for a proper choice.

Antonio Di Lorenzo

2011-05-05

117

Missing experiments in quantum mechanics

We discuss the two-slit experiment and the Aharonov-Bohm (AB) experiment in the magnetic field. In such a case the electron moving in the magnetic field produces so called synchrotron radiation. In other words the photons are emitted from the points of the electron trajectory and it means that the trajectory of electron is visible in the synchrotron radiation spectrum. The axiomatic system of quantum mechanics does not enable to define the trajectory of the elementary particle. The two-slit experiment and AB experiment in a magnetic field was never performed and it means that they are the missing experiments of quantum mechanics. The extension of the discussion to the cosmical rays moving in the magnetic field of the Saturn magnetosphere and its rings is mentioned. It is related to the probe CASSINI. The solution of the problem in the framework of the hydrodynamical model of quantum mechanics and the nonlinear quantum mechanics is also mentioned.

Miroslav Pardy

2008-01-16

118

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

119

Towards Adelic Noncommutative Quantum Mechanics

A motivation of using noncommutative and nonarchimedean geometry on very short distances is given. Besides some mathematical\\u000a preliminaries, we give a short introduction in adelic quantum mechanics. We also recall to basic ideas and tools embedded\\u000a in q-deformed and noncommutative quantum mechanics. A rather fundamental approach, called deformation quantization, is noted.\\u000a A few relations between noncommutativity and nonarchimedean spaces as

Goran S. Djordjevic; Ljubiša Neši?

120

Quantum Mechanics in Insulators

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

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

2009-08-20

121

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

122

What quantum computers may tell us about quantum mechanics

17 What quantum computers may tell us about quantum mechanics Christopher R. Monroe University of Michigan, Ann Arbor Quantum mechanics occupies a unique position in the history of science. It has sur successes of quantum mechanics, its foundations are often questioned, owing to the glaring difficulties

Monroe, Christopher

123

NSDL National Science Digital Library

This web site, authored by Enrique Galvez and Charles Holbrow of Colgate University, outlines a project to develop undergraduate physics labs that investigate quantum interference and entanglement with photons. The labs are designed for simplicity and low cost. A description of the lab set up, background information, and an article on the project are provided.

Galvez, Enrique

124

Quantum Mechanics (QM) Measurement Package

NSDL National Science Digital Library

This set of tutorial worksheets, based on the OSP Quantum Mechanics Simulations, help students explore the effects of position, momentum, and energy measurements on quantum state wavepackets. The probabilistic change in the wavefunction upon measurements and the time propagation of the states are illustrated. Similar worksheets are available for measurements of single and superpositions of energy eigenstates. The worksheets can be run online or downloaded as a pdf (attached).

Belloni, Mario

125

Large scale quantum mechanical enzymology

for Physics were awarded to the predominant developers of the theory of quantum mechanics (QM). These laureates were Max Planck, Niels Bohr, Louis de Broglie, Werner Heisenberg, Erwin Schro¨dinger and Paul Dirac, in chronological order. In addition, Albert... Einstein’s significant contributions cannot go unmentioned. These theoretical insights laid the foundations for the quantum chemical approach that won Walter Kohn and John Pople the prize for Chemistry in 1998. Considering earlier works, Johannes Diderik...

Lever, Greg

2014-10-07

126

QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT

QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT Abstract. The quantum measurement problem has led, and in a no-collapse formulation of quantum mechanics, a strong variety of dualism provides a way to account with Eugene Wigner's understanding of the standard collapse formulation of quantum mechanics. Two years prior

Stanford, Kyle

127

A Criterion for Holism in Quantum Mechanics

A Criterion for Holism in Quantum Mechanics # M.P Seevinck # # Utrecht University, The Netherlands, June 2003. # 1 #12; # Motivation # . The question whether or not quantum mechanics (QM) gives rise. Orthodox Quantum Mechanics . Criterion for Holism in the Quantum Formalism . Orthodox QM is Holistic

Seevinck, Michiel

128

A Criterion for Holism in Quantum Mechanics

A Criterion for Holism in Quantum Mechanics M.P Seevinck Utrecht University, The Netherlands, June 2003. 1 #12; Motivation Â· The question whether or not quantum mechanics (QM) gives rise to some. Orthodox Quantum Mechanics Â· Criterion for Holism in the Quantum Formalism Â· Orthodox QM is Holistic

Seevinck, Michiel

129

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

130

Quantum mechanics from invariance laws

Quantum mechanics is an extremely successful theory of nature and yet it has resisted all attempts to date to have an intuitive axiomatization. In contrast, special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we show an axiomatization approach to quantum mechanics which is very similar with how special theory of relativity can be derived. The core idea is that of composing two systems and the fact that the composed system should have an invariant description in terms of dynamics. This leads to a Lie-Jordan algebraic formulation of quantum mechanics which can be converted into the usual Hilbert space formalism by the standard GNS construction. The starting assumptions are minimal: the existence of time and that of a configuration space which supports a tensor product as a way to compose two physical systems into a larger one.

Florin Moldoveanu

2014-08-24

131

THE OBJECTIVE INDEFINITENESS INTERPRETATION OF QUANTUM MECHANICS: Partition logic, logical information theory, and quantum mechanics David Ellerman University of California at Riverside www ago that quantum mechanics was not compatible with Boolean logic, then the natural thing to do would

WÃ¼thrich, Christian

132

The quantum field theory interpretation of quantum mechanics

It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.

Alberto C. de la Torre

2015-03-02

133

Remarks on osmosis, quantum mechanics, and gravity

Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.

Carroll, Robert

2011-01-01

134

Remarks on osmosis, quantum mechanics, and gravity

Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.

Robert Carroll

2011-04-03

135

Quantum Mechanical Methods for Enzyme Kinetics

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

Jiali Gao; Donald G. Truhlar

2002-01-01

136

Negative Observations in Quantum Mechanics

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

Douglas M. Snyder

1999-01-01

137

Renormalization group in quantum mechanics

The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright {copyright} 1996 Academic Press, Inc.

Polony, J. [Laboratory of Theoretical Physics, Louis Pasteur University, 3 rue de l`Universite, 67084 Strasbourg Cedex (France)] [Laboratory of Theoretical Physics, Louis Pasteur University, 3 rue de l`Universite, 67084 Strasbourg Cedex (France); [Department of Atomic Physics, Lorand Eoelvos University, Puskin u 5-7, 1088 Budapest (Hungary)

1996-12-01

138

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

139

QUICK QUANTUM MECHANICS ---Introduction ---

of Classical Mechanics After Newton found his equations of motion, physicists knew they would have to wait are completely equivalent to Newton's laws. 2 A generalized coordinate can be, e.g., a Cartesian coordinate the behaviour of all of the generalized coordinates, q(t), subject to initial boundary conditions. Since Newton

Jackson, Andrew D.

140

Ab initio quantum mechanical charge field molecular dynamics (QMCF-MD) were successfully applied to Cu(II) embedded in water to elucidate structure and to understand dynamics of ligand exchange mechanism. From the simulation studies, it was found that using an extended large quantum mechanical region including two shells of hydration is required for a better description of the dynamics of exchanging water molecules. The structural features characterized by radial distribution function, angular distribution function and other analytical parameters were consistent with experimental data. The major outcome of this study was the dynamics of exchange mechanism and reactions in the first hydration shell that could not be studied so far. The dynamical data such as mean residence time of the first shell water molecules and other relevant data from the simulations are close to the results determined experimentally. Another major characteristic of hydrated Cu(II) is the Jahn-Teller distortion which was also successfully reproduced, leading to the final conclusion that the dominating aqua complex is a 6-coordinated species. The ab initio QMCF-MD formalism proved again its capabilities of unraveling even ambiguous properties of hydrated species that are far difficult to explore by any conventional quantum mechanics/molecular mechanics (QM/MM) approach or experiment.

Moin, Syed Tarique; Hofer, Thomas S.; Weiss, Alexander K. H.; Rode, Bernd M. [Theoretical Chemistry Division, Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innrain 80-82, A-6020 Innsbruck (Austria)

2013-07-07

141

Star Products for Relativistic Quantum Mechanics

The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.

P. Henselder

2007-05-24

142

Quantum Ballistic Evolution in Quantum Mechanics: Application to Quantum Computers

Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators $T$ is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e. motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also proved that, given a step operator T for an arbitrary deterministic quantum Turing machine, it is decidable if T is stable and orthogonality preserving, and if quantum ballistic evolution is possible. The proof fails if T is a step operator for a nondeterministic machine. It is an open question if such a decision procedure exists for nondeterministic machines. This problem does not occur in classical mechanics.

Paul Benioff

1996-05-15

143

The Transactional Interpretation of Quantum Mechanics and Quantum Nonlocality

Quantum nonlocality is discussed as an aspect of the quantum formalism that is seriously in need of interpretation. The Transactional Interpretation of quantum mechanics, which describes quantum processes as transactional "handshakes" between retarded $\\psi$ waves and advanced $\\psi*$ waves, is discussed. Examples of the use of the Transactional Interpretation in resolving quantum paradoxes and in understanding the counter-intuitive aspects of the formalism, particularly quantum nonlocality, are provided.

John G. Cramer

2015-02-28

144

A Criterion for Holism in Quantum Mechanics

A Criterion for Holism in Quantum Mechanics M.P Seevinck E-mail: M.P.Seevinck@phys.uu.nl Utrecht University, The Netherlands, August 2003. 1 #12; Motivation Â· The question whether or not quantum mechanics is it that makes quantum mechanics a holistic theory (if so), and other physical theories not (if so). Â· I propose

Seevinck, Michiel

145

Entanglement and Disentanglement in Relativistic Quantum Mechanics

Entanglement and Disentanglement in Relativistic Quantum Mechanics Jeffrey A. Barrett August 16, 2014 Abstract A satisfactory formulation of relativistic quantum mechanics re- quires that one be able in relativistic quantum mechanics must ultimately depend on the details of one's strategy for addressing

Stanford, Kyle

146

Quantum Mechanics: Structures, Axioms and Paradoxes

Quantum Mechanics: Structures, Axioms and Paradoxes Diederik Aerts Center Leo Apostel, Brussels present an analysis of quantum mechanics and its problems and para- doxes taking into account the results a genuine incomplete- ness of standard quantum mechanics, however not an incompleteness that means

Aerts, Diederik

147

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Review of Quantum Mechanics In general, particles

148

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra) New Particles anti-particles (combining special relativity and quantum mechanics pions (mediator

149

Quantum Mechanics and Representation Theory Columbia University

Quantum Mechanics and Representation Theory Peter Woit Columbia University Texas Tech, November 21 2013 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 1 / 30, 1967 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 2 / 30

Woit, Peter

150

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions, 2009 #12;Quantum Mechanics: Measurement and Uncertainty Thursday, May 7, 2009 #12;Puzzle: The Stern

151

Visualizing quantum mechanics in phase space

We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner function formalism resembles the mathematical language of classical mechanics of non-interacting particles. Thus, it allows a more direct comparison between classical and quantum dynamical features.

Heiko Bauke; Noya Ruth Itzhak

2011-01-11

152

Nonlinear Boundaries in Quantum Mechanics

Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a linear boundary condition, but not both. Further analysis shows that non-linear boundaries for the ring restore gauge invariance but lead unexpectedly to eigenfunctions with a continuous eigenvalue spectrum, a discreet subset of which forms a Hilbert space with energy bands. This Hilbert space maintains the principle of superposition of eigenfunctions despite the nonlinearity. The momentum operator remains Hermitian. If physical reality requires gauge invariance, it would appear that quantum mechanics should incorporate these nonlinear boundary conditions.

Arthur Davidson

2011-08-01

153

Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology

We investigate the origin of the arrow of time in quantum mechanics in the\\u000acontext of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured\\u000asubsystems incorporates a fundamental arrow of time. Extending discussions of\\u000aAharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a\\u000ageneralized quantum mechanics for cosmology that utilizes both an initial and a\\u000afinal density matrix to

Murray Gell-Mann; James B. Hartle

1993-01-01

154

Statistical Mechanics and Quantum Cosmology

Statistical mechanical concepts and processes such as decoherence, correlation, and dissipation can prove to be of basic importance to understanding some fundamental issues of quantum cosmology and theoretical physics such as the choice of initial states, quantum to classical transition and the emergence of time. Here we summarize our effort in 1) constructing a unified theoretical framework using techniques in interacting quantum field theory such as influence functional and coarse-grained effective action to discuss the interplay of noise, fluctuation, dissipation and decoherence; and 2) illustrating how these concepts when applied to quantum cosmology can alter the conventional views on some basic issues. Two questions we address are 1) the validity of minisuperspace truncation, which is usually assumed without proof in most discussions, and 2) the relevance of specific initial conditions, which is the prevailing view of the past decade. We also mention how some current ideas in chaotic dynamics, dissipative collective dynamics and complexity can alter our view of the quantum nature of the universe.

B. L. Hu

1995-11-29

155

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

156

Effective equations for the quantum pendulum from momentous quantum mechanics

In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)

2012-08-24

157

Hermeneutics, underdetermination and quantum mechanics

NASA Astrophysics Data System (ADS)

There exists an essential underdetermination in the interpretation of the formalism of quantum mechanics and this extends even to the question of whether or not physical phenomena at the most fundamental level are irreducibly and ineliminably indeterministic or absolutely deterministic. This is true in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics. This lends support to Martin Eger's analysis of a role for hermeneutics in science education.

Cushing, James T.

1995-04-01

158

Supersymmetric Quantum Mechanics with Reflections

A novel realization of supersymmetric quantum mechanics is obtained by using as supercharges, differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wave functions of extended Scarf I potentials with different parameters are presented.

Post, S; Zhedanov, A

2011-01-01

159

Supersymmetric Quantum Mechanics with Reflections

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

S. Post; L. Vinet; A. Zhedanov

2011-08-09

160

Game Theory in Categorical Quantum Mechanics

Categorical quantum mechanics, which examines quantum theory via dagger-compact closed categories, gives satisfying high-level explanations to the quantum information procedures such as Bell-type entanglement or complementary observables (\\cite{AC}, \\cite{Co}, \\cite{Co2}). Inspired by the fact that Quantum Game Theory can be seen as branch of quantum information, we express Quantum Game Theory procedures using the topological semantics provided by Categorical Quantum Mechanics. We also investigate Bayesian Games with correlation from this novel point of view while considering the connection between Bayesian game theory and Bell non-locality investigated recently by Brunner and Linden \\cite{BL}.

Ali Nabi Duman

2014-05-17

161

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification color, which is the "charge" of the strong force, mediated by gluons (which also carry color) quantum

162

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Particle Interaction Summary quantum

163

Quantum mechanical effects from deformation theory

We consider deformations of quantum mechanical operators by using the novel construction tool of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a role. Furthermore, a quantum plane can be defined by using the deformation techniques. This in turn gives an experimentally verifiable effect.

Much, A. [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)

2014-02-15

164

SENSIBLE QUANTUM MECHANICS: ARE ONLY PERCEPTIONS

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

Don N. Page

165

Quantum mechanics as a sociology of matter

Analogies between quantum mechanics and sociology lead to the hypothesis that quantum objects are complex products of evolution. Like biological objects they are able to receive, to work on, and to spread semantic information. In general meaning we can name it "consciousness". The important ability of consciousness is ability to predict future. Key words: Evolution, consciousness, information, quantum mechanics, EPR, decoherence.

Raoul Nakhmanson

2003-08-01

166

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

167

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

168

Orthodox Quantum Mechanics Free from Paradoxes

A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The classical paradoxes of quantum mechanics are analyzed and their origin is found to be the fictitious properties that are usually attributed to quantum-mechanical states. The hypothesis that any mixed state can always be considered as an incoherent superposition of pure states is found to contradict quantum mechanics. A solution of EPR paradox is proposed. It is shown that entanglement of quantum states is compatible with realism and locality of events, but implies non-local encoding of information.

Rodrigo Medina

2005-08-02

169

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

170

Quantum mechanics: Myths and facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.

Nikolic, H

2006-01-01

171

Quantum mechanics: Myths and facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.

H. Nikolic

2007-04-16

172

Conjugates, Filters and Quantum Mechanics

The Jordan structure of finite-dimensional quantum theory is derived, in a conspicuously easy way, from a few simple postulates concerning abstract probabilistic models (each defined by a set of basic measurements and a convex set of states). A key assumption is that each system $A$ can be paired with an isomorphic conjugate system, $\\bar{A}$, by means of a non-signaling bipartite state $\\eta_A$ perfectly and uniformly correlating each basic measurement on $A$ with its counterpart on $\\bar{A}$. In the case of a quantum-mechanical system associated with a complex Hilbert space ${\\mathbf H}$, the conjugate system is that associated with the conjugate Hilbert space $\\bar{\\mathbf H}$, and $\\eta_A$ corresponds to the standard maximally entangled EPR state on ${\\mathbf H} \\otimes \\bar{\\mathbf H}$.

Alexander Wilce

2014-11-18

173

Treating Time Travel Quantum Mechanically

The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their non-linearity and time travel paradoxes. In particular, the "equivalent circuit model"---which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory---is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of new theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features---such as time travel paradoxes, the ability to distinguish non-orthogonal states with certainty, and the ability to clone or delete arbitrary pure states---that are present with D-CTCs and P-CTCs. The problems with non-linear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.

John-Mark A. Allen

2014-10-10

174

Treating time travel quantum mechanically

NASA Astrophysics Data System (ADS)

The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilizing the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their nonlinearity and time-travel paradoxes. In particular, the "equivalent circuit model"—which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory—is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of alternate theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features—such as time-travel paradoxes, the ability to distinguish nonorthogonal states with certainty, and the ability to clone or delete arbitrary pure states—that are present with D-CTCs and P-CTCs. The problems with nonlinear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.

Allen, John-Mark A.

2014-10-01

175

Errors and paradoxes in quantum mechanics

Errors and paradoxes in quantum mechanics, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear

D. Rohrlich

2007-08-28

176

A quantum mechanical model of "dark matter"

The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.

V. V. Belokurov; E. T. Shavgulidze

2014-03-28

177

Correspondence Truth and Quantum Mechanics

The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either 'true' or 'false', describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of 'no go' theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton 'uniqueness theorem' is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state...

Karakostas, Vassilios

2015-01-01

178

Multiverse interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

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

Bousso, Raphael; Susskind, Leonard

2012-02-01

179

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

180

Transfer of Learning in Quantum Mechanics

NASA Astrophysics Data System (ADS)

We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting individual interviews. Quantum mechanics is abstract and its paradigm is very different from the classical one. A good grasp of the principles of quantum mechanics requires creating and organizing a knowledge structure consistent with the quantum postulates. Previously learned concepts such as the principle of superposition and probability can be useful in quantum mechanics if students are given opportunity to build associations between new and prior knowledge. We also discuss the need for better alignment between quantum mechanics and modern physics courses taken previously because semi-classical models can impede internalization of the quantum paradigm in more advanced courses.

Singh, Chandralekha

2005-09-01

181

A concise introduction to quantum probability, quantum mechanics, and quantum computation

A concise introduction to quantum probability, quantum mechanics, and quantum computation Greg called "non-commutative probability". Recently quantum computation has entered as a new reason for both mathematicians and computer scientists to learn the precepts of quantum mechan- ics. Just as randomized

Thomases, Becca

182

Notes on Quantum Mechanics and Consciousness

There have lately been a variety of attempts to connect, or even explain, if not in fact, reduce human consciousness to quantum mechanical processes. Such attempts tend to draw a sharp and fundamental distinction between the role of consciousness in classical mechanics, and on the other hand, in quantum mechanics, with an insistence on the assumed exceptional character of the

Elemer E Rosinger

2005-01-01

183

Quantum mechanics without state vectors

NASA Astrophysics Data System (ADS)

Because the state vectors of isolated systems can be changed in entangled states by processes in other isolated systems, keeping only the density matrix fixed, it is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying only on density matrices. The density matrix is defined here by the formula giving the mean values of physical quantities, which implies the same properties as the usual definition in terms of state vectors and their probabilities. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semigroup. Here, new transformation properties are studied for general symmetry transformations forming groups, not just semigroups. Arguments that such symmetries should act on the density matrix as in ordinary quantum mechanics are presented, but all of these arguments are found to be inconclusive.

Weinberg, Steven

2014-10-01

184

Quantum Mechanics Without State Vectors

It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical state, even in entangled states nothing that is done in one isolated system can instantaneously effect the physical state of a distant isolated system. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semi-group. Here new transformation properties are studied for general symmetry transformations forming groups, rather than semi-groups. Arguments are given that such symmetries should act on the density matrix as in ordinary quantum mechanics, but loopholes are found for all of these arguments.

Steven Weinberg

2014-05-14

185

Bananaworld: Quantum Mechanics for Primates

This is intended to be a serious paper, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, since a theory of information is essentially a theory of probabilistic correlations. To make this clear, it suffices to consider measurements of two binary-valued observables, x with outcomes a = 0 or 1, performed by Alice in a region A, and y with outcomes b = 0 or 1 performed by Bob in a separated region B --or, to emphasize the banality of the phenomena, two ways of peeling a banana, resulting in one of two tastes. The imagined bananas of Bananaworld are non-standard, with operational or phenomenal probabilistic correlations for peelings and tastes that lie outside the polytope of local correlations. The 'no go' theorems tell us that we can't shoe-horn these correlations into a classical correlation polytope, which has the structure of a simplex, by supposing that something has been left out of the story, without giving up fundamental principles that define what we mean by a physical system. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are shown to be generic features of correlations that lie outside the local correlation polytope. As far as the conceptual problems are concerned, we might as well talk about bananas.

Jeffrey Bub

2013-01-08

186

Quantum Mechanics and Closed Timelike Curves

General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal region of space-time are investigated. If the correspondence principle is true, then all generalizations of quantum mechanics on acausal manifolds are not renormalizable. Therefore quantum mechanics can only be defined on global hyperbolic manifolds and all general relativity solutions exhibiting time travel are unphysical.

Florin Moldoveanu

2007-04-23

187

Bohmian particle trajectories contradict quantum mechanics

The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to avoid contradictions with quantum mechanics. There are correlations between particle positions at different times which cannot be reproduced with real particle trajectories. A simple rearrangement of an experimental test of the Bell-CHSH inequality demonstrates this.

Michael Zirpel

2009-03-23

188

Quantum Mechanics - Fundamentals and Applications to Technology

Explore the relationship between quantum mechanics and information-age applications This volume takes an altogether unique approach to quantum mechanics. Providing an in-depth exposition of quantum mechanics fundamentals, it shows how these concepts are applied to most of today's information technologies, whether they are electronic devices or materials. No other text makes this critical, essential leap from theory to real-world applications.

Jasprit Singh

1996-01-01

189

A Process Model of Quantum Mechanics

A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise through a non-uniform interpolation process. Standard non-relativistic quantum mechanics emerges under the limit of infinite information (the causal space grows to infinity) and infinitesimal scale (the separation between points goes to zero). The model has the potential to address several paradoxes in quantum mechanics while remaining computationally powerful.

William Sulis

2014-04-21

190

Quantum Statistical Mechanics. III. Equilibrium Probability

Given are a first principles derivation and formulation of the probabilistic concepts that underly equilibrium quantum statistical mechanics. The transition to non-equilibrium probability is traversed briefly.

Phil Attard

2014-04-10

191

PT symmetry in relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

In nonrelativistic quantum mechanics and in relativistic quantum field theory, the time coordinate t is a parameter and thus the time-reversal operator T does not actually reverse the sign of t. In contrast, in the five-dimensional approach to relativistic quantum mechanics introduced by Feynman, time t is a quantum-mechanical operator. In this paper it is shown how one can use this five-dimensional approach to extend T and PT symmetry from nonrelativistic to relativistic quantum mechanics and implement time-reversal as an operation that effects TtT=-t just as P effects PxP=-x, with PT thus effecting PTx?PT=-x?. Some illustrative relativistic quantum-mechanical models are constructed whose associated Hamiltonians are non-Hermitian but PT symmetric, and it is shown that for each such Hamiltonian the energy eigenvalues are all real.

Bender, Carl M.; Mannheim, Philip D.

2011-11-01

192

NASA Astrophysics Data System (ADS)

We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.

Oss, Stefano; Rosi, Tommaso

2015-04-01

193

Testing quantum mechanics: a statistical approach

As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited, how can we be sure that we are observing quantum behavior? This tutorial highlights some of the difficulties in such experimental tests of quantum mechanics, using optomechanics as the central example, and discusses how the issues can be resolved using techniques from statistics and insights from quantum information theory.

Mankei Tsang

2014-01-27

194

The spacetime approach to quantum mechanics

Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schrödinger-Heisenberg formulation that utilizes states on spacelike surfaces because it assigns probabilities to different sets of alternatives. In a sum-over-histories formulation, alternatives at definite moments of time are more restricted than in usual quantum mechanics because

James B. Hartle

1993-01-01

195

Quaternionic Formulation of Supersymmetric Quantum Mechanics

Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with the results of quantum mechanics.

Seema Rawat; O. P. S. Negi

2007-03-18

196

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions no such change Theory: Electrodynamics (1865) light is a moving disturbance in the electromagnetic field the laws

197

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification from the interaction energy Thursday, June 4, 2009 #12;String Theory: A different kind of unification

198

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Friday, June 19, 2009 #12;String Theory Origins We introduced string theory as a possible solution to our

199

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification that is naturally solved by string theory Strings vibrating in a variety of ways give rise to particles of different

200

Probability in modal interpretations of quantum mechanics

Probability in modal interpretations of quantum mechanics Dennis Dieks Institute for the History interpretations have the ambition to construe quantum mechanics as an ob- jective, man-independent description in modal interpretations, and to this end we make a comparison with many-worlds alternatives. An overall

Seevinck, Michiel

201

METHODOLOGICAL NOTES: Conceptual problems in quantum mechanics

This review is devoted to a discussion of the interpretation of quantum mechanics. The heuristic role and limitations of the principle of observability and of operationalism are discussed. It is shown that the probabilistic approach to quantum mechanics is essential as a way of reconciling the conflicting concepts of particle and wave. The reason why the reduction of the wave

V. P. Demutskii; R. V. Polovin

1992-01-01

202

Uncertainty and complementarity in axiomatic quantum mechanics

In this work an investigation of the uncertainty principle and the complementarity principle is carried through. A study of the physical content of these principles and their representation in the conventional Hilbert space formulation of quantum mechanics forms a natural starting point for this analysis. Thereafter is presented more general axiomatic framework for quantum mechanics, namely, a probability function formulation

Pekka J. Lahti

1980-01-01

203

PERSPECTIVE Quantum Mechanics of Black Holes

PERSPECTIVE Quantum Mechanics of Black Holes Edward Witten The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived

204

Macroscopicity of Mechanical Quantum Superposition States

NASA Astrophysics Data System (ADS)

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

Nimmrichter, Stefan; Hornberger, Klaus

2013-04-01

205

An entropic picture of emergent quantum mechanics

Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on space. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant h from Boltzmann's constant k.

D. Acosta; P. Fernandez de Cordoba; J. M. Isidro; J. L. G. Santander

2011-09-20

206

An entropic picture of emergent quantum mechanics

Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on space. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant h from Boltzmann's constant k.

Acosta, D; Isidro, J M; Santander, J L G

2011-01-01

207

Polymer Quantum Mechanics and its Continuum Limit

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

Alejandro Corichi; Tatjana Vukasinac; Jose A. Zapata

2007-08-22

208

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

209

Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology

We investigate the origin of the arrow of time in quantum mechanics in the context of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured subsystems incorporates a fundamental arrow of time. Extending discussions of Aharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a generalized quantum mechanics for cosmology that utilizes both an initial and a final density matrix to give a time-neutral formulation without a fundamental arrow of time. Time asymmetries can arise for particular universes from differences between their initial and final conditions. Theories for both would be a goal of quantum cosmology. A special initial condition and a final condition of indifference would be sufficient to explain the observed time asymmetries of the universe. In this essay we ask under what circumstances a completely time symmetric universe, with T-symmetric initial and final condition, could be consistent with the time asymmetries of the limited domain of our experience. We discuss the ap...

Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B.

1993-01-01

210

The cognitive life of mechanical molecular models.

The use of physical models of molecular structures as research tools has been central to the development of biochemistry and molecular biology. Intriguingly, it has received little attention from scholars of science. In this paper, I argue that these physical models are not mere three-dimensional representations but that they are in fact very special research tools: they are cognitive augmentations. Despite the fact that they are external props, these models serve as cognitive tools that augment and extend the modeler's cognitive capacities and performance in molecular modeling tasks. This cognitive enhancement is obtained because of the way the modeler interacts with these models, the models' materiality contributing to the solving of the molecule's structure. Furthermore, I argue that these material models and their component parts were designed, built and used specifically to serve as cognitive facilitators and cognitive augmentations. PMID:23910718

Charbonneau, Mathieu

2013-07-30

211

The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.

Aalok Pandya

2008-09-08

212

Weyl Geometries, Fisher Information and Quantum Entropy in Quantum Mechanics

NASA Astrophysics Data System (ADS)

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

Fiscaletti, Davide; Licata, Ignazio

2012-11-01

213

Kinetic potentials in quantum mechanics

NASA Astrophysics Data System (ADS)

Suppose that the Hamiltonian H=-?+vf(r) represents the energy of a particle which moves in an attractive central potential and obeys nonrelativistic quantum mechanics. The discrete eigenvalues Enl=Fnl(v) of H may be expressed as a Legendre transformation Fnl(v)=mins?0(s+vf¯nl(s)), n=1,2,3,..., l=0,1,2,..., where the ``kinetic potentials'' f¯nl(s) associated with f(r) are defined by f¯nl(s) =infDnl sup??Dnl, ???=1 ? ?(r) f ([?,-??)/s]1/2r)?(r)d3r, and Dnl is an n-dimensional subspace of L2(R3) labeled by Ylm(?,?), m=0, and contained in the domain D(H) of H. If the potential has the form f(r)=?Ni=1 g(i)( f(i)(r)) then in many interesting cases it turns out that the corresponding kinetic potentials can be closely approximated by ?Ni=1 g(i)( f¯nl(i)(s)). This nice behavior of the kinetic potentials leads to a constructive global approximation theory for Schrödinger eigenvalues. As an illustration, detailed recipes are provided for arbitrary linear combinations of power-law potentials and the log potential. For the linear plus Coulomb potential and the quartic anharmonic oscillator the approximate eigenvalues are compared to accurate values found by numerical integration.

Hall, Richard L.

1984-09-01

214

Operational Axioms for Quantum Mechanics

The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of "physical experiment" and from five simple Postulates concerning "experimental accessibility and simplicity". For the infinite dimensional case, on the other hand, a C*-algebra representation of physical transformations is derived, starting from just four of the five Postulates via a Gelfand-Naimark-Segal (GNS) construction. The present paper simplifies and sharpens the previous derivation in version 1. The main ingredient of the axiomatization is the postulated existence of "faithful states" that allows one to calibrate the experimental apparatus. Such notion is at the basis of the operational definitions of the scalar product and of the "transposed" of a physical transformation. What is new in the present paper with respect to quant-ph/0603011 is the operational deduction of an involution corresponding to the "complex-conjugation" for effects, whose extension to transformations allows to define the "adjoint" of a transformation when the extension is composition-preserving.

Giacomo Mauro D'Ariano

2006-12-08

215

Operational Axioms for Quantum Mechanics

The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of physical experiment and from five simple Postulates concerning experimental accessibility and simplicity. For the infinite dimensional case, on the other hand, a C*-algebra representation of physical transformations is derived, starting from just four of the five Postulates via a Gelfand-Naimark-Segal (GNS) construction. The present paper simplifies and sharpens the previous derivation in Ref. [1]. The main ingredient of the axiomatization is the postulated existence of faithful states that allows one to calibrate the experimental apparatus. Such notion is at the basis of the operational definitions of the scalar product and of the transposed of a physical transformation. What is new in the present paper with respect to Ref. [1], is the operational deduction of an involution corresponding to the complex-conjugation for effects, whose extension to transformations allows to define the adjoint of a transformation when the extension is composition-preserving. The existence of such composition-preserving extension among possible extensions is analyzed.

D'Ariano, Giacomo Mauro [QUIT Group, Dipartimento di Fisica 'A. Volta', via Bassi 6, I-27100 Pavia (Italy); Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL 60208 (United States)

2007-02-21

216

Four-dimensional understanding of quantum mechanics

In this paper I will try to convince that quantum mechanics does not have to lead to indeterminism, but is just a natural consequence of four-dimensional nature of our world - that for example particles shouldn't be imagined as 'moving points' in space, but as their trajectories in the spacetime like in optimizing action formulation of Lagrangian mechanics. There will be analyzed simplified model - Boltzmann distribution among trajectories occurs to give quantum mechanic like behavior - for example electron moving in proton's potential would make some concrete trajectory which average exactly to the probability distribution of the quantum mechanical ground state. We will use this model to build intuition about quantum mechanics and discuss its generalizations to get some effective approximation of physics. We will see that topological excitations of the simplest model obtained this way already creates known from physics particle structure, their decay modes and electromagnetic/gravitational interactions between them.

Jarek Duda

2009-10-14

217

Canonical distribution and incompleteness of quantum mechanics

The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical ensembles is presented as a consequence of the existence of probabilistic processes which are not accounted for by quantum mechanics. The paper provides a new analytical derivation of canonical distribution for macrosystems which takes into account subquantum processes. The paper discusses the possibility of the experimental study of a probability which is beyond quantum mechanics.

V. A. Skrebnev

2014-05-05

218

A Quantum Mechanical Travelling Salesman

A quantum simulation of a travelling salesman is described. A vector space for a graph is defined together with a sequence of operators which transform a special initial state into a superposition states representing Hamiltonian tours. The quantum amplitude for any tour is a function of the classical cost of travelling along the edges in that tour. Tours with the largest quantum amplitude may be different than those with the smallest classically-computed cost.

Ravindra N. Rao

2011-08-23

219

Quantum Mechanics: Interpretation and Philosophy

-- the uncertainty principle -- superposition -- collapse of the wavefunction -- the measurement problem #12;Quantum to be fundamentally beyond our means (uncertainly principle: these are incompatible physical properties) #12;the

Nielsen, Steven O.

220

Playing Games with Quantum Mechanics

We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence. We call such games playable. By focusing on the notion of playability for games we can more clearly see the distinction between classical and quantum games and tackle the thorny issue of what it means to quantize a game. The approach we take can more properly be thought of as gaming the quantum rather than quantizing a game and we find that in this perspective we can think of a complete quantum game, for a given set of preferences, as representing a single family of quantum games with many different playable versions. The versions of Quantum Prisoners Dilemma presented in the literature can therefore be thought of specific instances of the single family of Quantum Prisoner's Dilemma with respect to a particular measurement. The conditions for equilibrium are given for playable quantum games both in terms of expected outcomes and a geometric approach. We discuss how any quantum game can be simulated with a classical game played with classical coins as far as the strategy selections and expected outcomes are concerned.

Simon J. D. Phoenix; Faisal Shah Khan

2012-02-22

221

Visual Quantum Mechanics: Online Interactive Programs

NSDL National Science Digital Library

The Visual Quantum Mechanics project, from the Physics Education Group of Kansas State University's Department of Physics, develops innovative ways to "introduce quantum physics to high school and college students who do not have a background in modern physics or higher level math." Funded by the National Science Foundation, this resource for educators provides interactive computer visualizations and animations that introduce quantum mechanics. The interactive programs (which require Shockwave) include a spectroscopy lab suite, a probability illustrator, an energy band creator, quantum tunneling, a color creator (a Java version is also available), a wave function sketcher, a wave packet explorer, an energy diagram explorer, a diffraction suite, and a hydrogen spectroscopy program. These online demonstrations should prove to be excellent visual, hands-on teaching aids when introducing concepts involving quantum mechanics. Users can download Shockwave at the site.

222

Quantum Mechanical Search and Harmonic Perturbation

Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some important technology advances, such as masers, lasers, nuclear magnetic resonance, etc., originated from it. Here we add quantum computation to this list with a theoretical demonstration. Based on harmonic perturbation, a quantum mechanical algorithm is devised to search the ground state of a given Hamiltonian. The intrinsic complexity of the algorithm is continuous and parametric in both time T and energy E. More precisely, the probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is optimal. As harmonic perturbation provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers.

Jie-Hong R. Jiang; Dah-Wei Chiou; Cheng-En Wu

2007-09-14

223

Strange Bedfellows: Quantum Mechanics and Data Mining

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

Weinstein, Marvin; /SLAC

2009-12-16

224

Is quantum field theory a generalization of quantum mechanics?

We construct a mathematical model analogous to quantum field theory, but without the notion of vacuum and without measurable physical quantities. This model is a direct mathematical generalization of scattering theory in quantum mechanics to path integrals with multidimensional trajectories (whose mathematical interpretation has been given in a previous paper). In this model the normal ordering of operators in the Fock space is replaced by the Weyl-Moyal algebra. This model shows to be useful in proof of various results in quantum field theory: one first proves these results in the mathematical model and then "translates" them into the usual language of quantum field theory by more or less "ugly" procedures.

A. V. Stoyanovsky

2009-09-10

225

Quantum Semiotics: A Sign Language for Quantum Mechanics

Semiotics is the language of signs which has been used effectively in various disciplines of human scientific endeavor. It gives a beautiful and rich structure of language to express the basic tenets of any scientific discipline. In this article we attempt to develop from first principles such an axiomatic structure of semiotics for Quantum Mechanics. This would be a further enrichment to the already existing well understood mathematical structure of Quantum Mechanics but may give new insights and understanding to the theory and may help understand more lucidly the fundamentality of Nature which Quantum Theory attempts to explain.

Prashant

2006-01-01

226

Quantum Mechanics and the Brain

In this paper we discuss possible quantum effects in the brain. We start with a historical review of what some prominent physicists have said about it. We then dis- cuss some proposals that quantum superpositions may be used by the brain. Although decoherence effects in the brain are believed to be too strong to allow quan- tum computations, we describe

Patrick Suppes; J. Acacio de Barros

2007-01-01

227

Local quantum mechanics with finite Planck mass

In this paper the motion of quantum particles with initial mass m is investigated. The quantum mechanics equation is formulated and solved. It is shown that the wave function contains the component which is depended on the gravitation fine structure constant

M Kozlowski; J. Marciak -Kozlowska; M. pelc

2007-04-20

228

Quantum Mechanics and Multiply Connected Spaces

t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of the fact that Quantum Theory is actually a theory in multiply connected space while Classical Theory operates in simply connected space.

B. G. Sidharth

2006-05-16

229

Quantum Mechanics and the Generalized Uncertainty Principle

The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.

Jang Young Bang; Micheal S. Berger

2006-11-30

230

The Compton effect: Transition to quantum mechanics

The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite

R. H. Stuewer

2000-01-01

231

Quantum mechanics and the generalized uncertainty principle

The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.

Bang, Jang Young; Berger, Micheal S. [Physics Department, Indiana University, Bloomington, Indiana 47405 (United States)

2006-12-15

232

Superconformal Quantum Mechanics from M2-branes

We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a number of exotic and enlightening properties which do not occur in higher dimensional field theories. We see that superfield and superspace formalism is available for $\\mathcal{N}\\le 8$ superconformal mechanical models. We then discuss the M2-branes with a focus on the world-volume descriptions of the multiple M2-branes which are superconformal three-dimensional Chern-Simons matter theories. Finally we argue that the two topics are connected in M-theoretical construction by considering the multiple M2-branes wrapped around a compact Riemann surface and study the emerging IR quantum mechanics. We establish that the resulting quantum mechanics realizes a set of novel $\\mathcal{N}\\ge 8$ superconformal quantum mechanical models which have not been reached so far. Also we discus...

Okazaki, Tadashi

2015-01-01

233

Beyond Quantum Mechanics and General Relativity

In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.

Andrea Gregori

2010-02-24

234

Relative-State Formulation of Quantum Mechanics

NSDL National Science Digital Library

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

Barrett, Jeffrey Alan

235

Supersymmetric q-deformed quantum mechanics

A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.

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

2012-06-27

236

Quantum mechanical streamlines. I - Square potential barrier

NASA Technical Reports Server (NTRS)

Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.

1974-01-01

237

Many-Worlds Interpretation of Quantum Mechanics

NSDL National Science Digital Library

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

Vaidman, Lev

238

Lecture Notes in Quantum Mechanics Doron Cohen

formula Â· Fermi golden rule Â· Markovian master equations Â· Cross section / Born Â· The adiabatic equation Â· Spherical geometry, phase shifts Â· Cross section, optical theorem, resonances Quantum mechanics in practice

Cohen, Doron

239

On a New Form of Quantum Mechanics (II)

The correspondence of a new form of quantum mechanics based on a quantum version of the action principle, which was proposed earlier [arXiv:0807.3508], with the ordinary quantum mechanics is established. New potentialities of the quantum action principle in the interpretation of quantum mechanics are considered.

N. Gorobey; A. Lukyanenko; I. Lukyanenko

2009-12-16

240

CLNS 96/1399 Peculiarities of Quantum Mechanics

CLNS 96/1399 Peculiarities of Quantum Mechanics: Origins and Meaning Yuri F. Orlov Floyd R. Newman, specifically quantum, features of quantum mechanics --- quanÂ tum nonlocality, indeterminism, interference are quantum observables themselves and are represented in quantum mechanics by density matrices of pure states

241

Quantum mechanics in de Sitter space

We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however of the order of the ratio between the length scale of the quantum mechanical system and the de Sitter radius, and therefore exceedingly small. Nevertheless, the existence of effects due to the large scale curvature of spacetime in atomic experiments has a theoretical relevance.

Subir Ghosh; Salvatore Mignemi

2011-01-25

242

2T Physics and Quantum Mechanics

We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit described by the same Hamiltonian. One of these formulations is used as a basis for a complementation of the usual quantum mechanics when in the presence of gravity.

W. Chagas-Filho

2008-02-20

243

Nonequilibrium quantum statistical mechanics and thermodynamics

The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different reversible and irreversible thermodynamic processes are studied from the point of view of quantum statistical mechanics. Special emphasis is put on new adiabatic theorems for steady states close to and far from equilibrium, and on investigating cyclic thermodynamic processes using an extension of Floquet theory.

Walid K. Abou Salem

2006-01-23

244

The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of probability in Quantum Mechanics and its interpretations. We give yet another interpretation to the notion of Faraday lines and loops as the locus of probability flow. Also, the possibilities of visualization of spectra of area operators by means of classical geometric forms and conventional Quantum Mechanics are explored.

Aalok Pandya

2009-01-19

245

Interpretations of Quantum Mechanics: a critical survey

This brief survey analyzes the epistemological implications about the role of observer in the interpretations of Quantum Mechanics. As we know, the goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. In the same time, there are implicit and hidden assumptions about his role. In fact, most interpretations taking as ontic level one of these fundamental concepts as information, physical law and matter bring us to new problematical questions. We think, that no interpretation of the quantum theory can avoid this intrusion until we do not clarify the nature of observer.

Michele Caponigro

2008-11-24

246

Testing foundations of quantum mechanics with photons

The foundational ideas of quantum mechanics continue to give rise to counterintuitive theories and physical effects that are in conflict with a classical description of Nature. Experiments with light at the single photon level have historically been at the forefront of tests of fundamental quantum theory and new developments in photonics engineering continue to enable new experiments. Here we review recent photonic experiments to test two foundational themes in quantum mechanics: wave-particle duality, central to recent complementarity and delayed-choice experiments; and Bell nonlocality where recent theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different photonics experiments.

Peter Shadbolt; Jonathan C. F. Matthews; Anthony Laing; Jeremy L. O'Brien

2015-01-15

247

Simple New Axioms for Quantum Mechanics

The space P of pure states of any physical system, classical or quantum, is identified as a Poisson space with a transition probability. The latter is a function p: PxP -> [0,1]; in addition, a Poisson bracket is defined for functions on P. These two structures are connected through unitarity. Classical and quantum mechanics are each characterized by a simple axiom on the transition probability p. Unitarity then determines the Poisson bracket of quantum mechanics up to a multiplicative constant (identified with Planck's constant). Superselection rules are naturally incorporated.

N. P. Landsman

1996-04-10

248

Projection evolution in quantum mechanics

We propose a model of time evolution of quantum objects which unites the unitary evolution and the measurement procedures. The model allows to treat the time on equal footing with other dynamical variables.

A. Gozdz; M. Pietrow; M. Debicki

2005-08-08

249

The Möbius Symmetry of Quantum Mechanics

The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under $D$--dimensional M\\"obius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global M\\"obius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the M\\"obius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.

Alon E. Faraggi; Marco Matone

2015-02-16

250

On reconciling quantum mechanics and local realism

NASA Astrophysics Data System (ADS)

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

Graft, Donald A.

2013-10-01

251

Quantum mechanics as "space-time statistical mechanics"?

In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time configurations. It is argued that this could perhaps be accomplished by giving up the assumption that the objective ``state'' of a system is independent of a future measurement performed on the system. This idea is then applied in an example of quantum state estimation on a qubit system.

Anders Månsson

2005-01-24

252

Statistical mechanics based on fractional classical and quantum mechanics

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., E-mail: mewalid@yahoo.com [Physics Department, LRPPS Laboratory, Ouargla University, Ouargla 30000 (Algeria)

2014-03-15

253

Quantum mechanics: last stop for reductionism

The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a complex vector space, used in quantum mechanics.

Gabriele Carcassi

2012-03-16

254

Quantum mechanics as applied mathematical statistics

Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

Skala, L., E-mail: Lubomir.Skala@mff.cuni.cz [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic); University of Waterloo, Department of Applied Mathematics, Waterloo, Ontario, Canada N2L 3G1 (Canada); Cizek, J. [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic); University of Waterloo, Department of Applied Mathematics, Waterloo, Ontario, Canada N2L 3G1 (Canada); Kapsa, V. [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic)

2011-05-15

255

Quantum mechanism of Biological Search

We wish to suggest an algorithm for biological search including DNA search. Our argument supposes that biological search be performed by quantum search.If we assume this, we can naturally answer the following long lasting puzzles such that "Why does DNA use the helix structure?" and "How can the evolution in biological system occur?".

Younghun Kwon

2006-05-09

256

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

257

Failure of Standard Quantum Mechanics for the Description of Compound Quantum Entities

Failure of Standard Quantum Mechanics for the Description of Compound Quantum Entities Diederik that proves that two separated quantum entities cannot be described by means of standard quantum mechanics of this result indicates a failure of standard quantum mechanics, and not just some peculiar shortcoming due

Aerts, Diederik

258

Canonical Relational Quantum Mechanics from Information Theory

In this paper we construct a theory of quantum mechanics based on Shannon information theory. We define a few principles regarding information-based frames of reference, including explicitly the concept of information covariance, and show how an ensemble of all possible physical states can be setup on the basis of the accessible information in the local frame of reference. In the next step the Bayesian principle of maximum entropy is utilized in order to constrain the dynamics. We then show, with the aid of Lisi's universal action reservoir approach, that the dynamics is equivalent to that of quantum mechanics. Thereby we show that quantum mechanics emerges when classical physics is subject to incomplete information. We also show that the proposed theory is relational and that it in fact is a path integral version of Rovelli's relational quantum mechanics. Furthermore we give a discussion on the relation between the proposed theory and quantum mechanics, in particular the role of observation and correspondence to classical physics is addressed. In addition to this we derive a general form of entropy associated with the information covariance of the local reference frame. Finally we give a discussion and some open problems.

Joakim Munkhammar

2011-01-07

259

A quantum information approach to statistical mechanics

We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in different dimensions, different types of many-body interactions, different symmetries, etc) can be mapped to the partition function of a single model. Second, we give efficient quantum algorithms to estimate the partition function of various classical spin models, such as the Ising or the Potts model. The proofs of these two results are based on a mapping from partition functions to quantum states and to quantum circuits, respectively. Finally, we show how classical spin models can be used to describe certain fluctuating lattices appearing in models of discrete quantum gravity.

Gemma De las Cuevas

2013-12-20

260

Foundations of quantum mechanics: decoherence and interpretation

In this paper we review Castagnino's contributions to the foundations of quantum mechanics. First, we recall his work on quantum decoherence in closed systems, and the proposal of a general framework for decoherence from which the phenomenon acquires a conceptually clear meaning. Then, we introduce his contribution to the hard field of the interpretation of quantum mechanics: the modal-Hamiltonian interpretation solves many of the interpretive problems of the theory, and manifests its physical relevance in its application to many traditional models of the practice of physics. In the third part of this work we describe the ontological picture of the quantum world that emerges from the modal-Hamiltonian interpretation, stressing the philosophical step toward a deep understanding of the reference of the theory.

Olimpia Lombardi; Juan Sebastián Ardenghi; Sebastian Fortin; Martin Narvaja

2010-09-02

261

Levitated Quantum Nano-Magneto-Mechanical Systems

NASA Astrophysics Data System (ADS)

Quantum nanomechanical sysems have attracted much attention as they provide new macroscopic platforms for the study of quantum mechanics but may also have applications in ultra-sensitive sensing, high precision measurements and in quantum computing. In this work we study the control and cooling of a quantum nanomechanical system which is magnetically levitated via the Meissner effect. Supercurrents in nano-sized superconducting loops give rise to a motional restoring force (trap), when placed in an highly inhomogenous magnetic field and can yield complete trapping of all translational and rotational motions of the levitated nano-object with motional oscillation frequencies ?˜10-100MHz. As the supercurrents experience little damping this system will possess unprecendented motional quality factors, with Qmotion˜10^9-10^13, and motional superposition states may remain coherent for days. We describe how to execute sideband cooling through inductive coupling to a nearby flux qubit, cooling the mechanical motion close to the ground state.

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

2011-03-01

262

Collapse challenge for interpretations of quantum mechanics

The collapse challenge for interpretations of quantum mechanics is to build from first principles and your preferred interpretation a complete, observer-free quantum model of the described experiment (involving a photon and two screens), together with a formal analysis that completely explains the experimental result. The challenge is explained in detail, and discussed in the light of the Copenhagen interpretation and the decoherence setting.

Arnold Neumaier

2005-05-23

263

On Time. 6b: Quantum Mechanical Time

The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure of time. This corresponds to a change of logic at the microphysical level. We show that the resulting logic is a quantum logic. This provides a natural and rigorous explanation of quantum interference. This structured-time interpretation of quantum mechanics is briefly compared with various other interpretations of q.m.

C. K. Raju

2008-08-09

264

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

265

On the missing axiom of Quantum Mechanics

The debate on the nature of quantum probabilities in relation to Quantum Non Locality has elevated Quantum Mechanics to the level of an "Operational Epistemic Theory". In such context the quantum superposition principle has an extraneous non epistemic nature. This leads us to seek purely operational foundations for Quantum Mechanics, from which to derive the current mathematical axiomatization based on Hilbert spaces. In the present work I present a set of axioms of purely operational nature, based on a general definition of "the experiment", the operational/epistemic archetype of information retrieval from reality. As we will see, this starting point logically entails a series of notions [state, conditional state, local state, pure state, faithful state, instrument, propensity (i.e. "effect"), dynamical and informational equivalence, dynamical and informational compatibility, predictability, discriminability, programmability, locality, a-causality, rank of the state, maximally chaotic state, maximally entangled state, informationally complete propensity, etc. ], along with a set of rules (addition, convex combination, partial orderings, ...), which, far from being of quantum origin as often considered, instead constitute the universal "syntactic manual" of the operational/epistemic approach. The missing ingredient is, of course, the quantum superposition axiom for probability amplitudes: for this I propose some substitute candidates of purely operational/epistemic nature.

Giacomo Mauro D'Ariano

2005-07-30

266

Improving students' understanding of quantum mechanics

NASA Astrophysics Data System (ADS)

Learning quantum mechanics is especially challenging, in part due to the abstract nature of the subject. We have been conducting investigations of the difficulties that students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) as well as tools for peer-instruction. The goal of QuILTs and peer-instruction tools is to actively engage students in the learning process and to help them build links between the formalism and the conceptual aspects of quantum physics without compromising the technical content. They focus on helping students integrate qualitative and quantitative understanding, confront and resolve their misconceptions and difficulties, and discriminate between concepts that are often confused. In this talk, I will give examples from my research in physics education of how students' prior knowledge relevant for quantum mechanics can be assessed, and how learning tools can be designed to help students develop a robust knowledge structure and critical thinking skills.

Singh, Chandralekha

2011-03-01

267

CLNS 96/1443 Peculiarities of Quantum Mechanics

CLNS 96/1443 REVISED Peculiarities of Quantum Mechanics: Origins and Meaning 1 Yuri F. Orlov Floyd The most peculiar, specifically quantum, features of quantum mechanics --- quanÂ tum nonlocality mechanics 1 This paper, to be presented to the Nordic Symposium on Basic Problems in Quantum Physics, June

268

QM/MM methods have been developed as a computationally feasible solution to QM simulation of chemical processes, such as enzyme-catalyzed reactions, within a more approximate MM representation of the condensed-phase environment. However, there has been no independent method for checking the quality of this representation, especially for highly nonisotropic protein environments such as those surrounding enzyme active sites. Hence, the validity of QM/MM methods is largely untested. Here we use the possibility of performing all-QM calculations at the semiempirical PM3 level with a linear-scaling method (MOZYME) to assess the performance of a QM/MM method (PM3/AMBER94 force field). Using two model pathways for the hydride-ion transfer reaction of the enzyme dihydrofolate reductase studied previously (Titmuss et al., Chem Phys Lett 2000, 320, 169-176), we have analyzed the reaction energy contributions (QM, QM/MM, and MM) from the QM/MM results and compared them with analogous-region components calculated via an energy partitioning scheme implemented into MOZYME. This analysis further divided the MOZYME components into Coulomb, resonance and exchange energy terms. For the model in which the MM coordinates are kept fixed during the reaction, we find that the MOZYME and QM/MM total energy profiles agree very well, but that there are significant differences in the energy components. Most significantly there is a large change (approximately 16 kcal/mol) in the MOZYME MM component due to polarization of the MM region surrounding the active site, and which arises mostly from MM atoms close to (<10 A) the active-site QM region, which is not modelled explicitly by our QM/MM method. However, for the model where the MM coordinates are allowed to vary during the reaction, we find large differences in the MOZYME and QM/MM total energy profiles, with a discrepancy of 52 kcal/mol between the relative reaction (product-reactant) energies. This is largely due to a difference in the MM energies of 58 kcal/mol, of which we can attribute approximately 40 kcal/mol to geometry effects in the MM region and the remainder, as before, to MM region polarization. Contrary to the fixed-geometry model, there is no correlation of the MM energy changes with distance from the QM region, nor are they contributed by only a few residues. Overall, the results suggest that merely extending the size of the QM region in the QM/MM calculation is not a universal solution to the MOZYME- and QM/MM-method differences. They also suggest that attaching physical significance to MOZYME Coulomb, resonance and exchange components is problematic. Although we conclude that it would be possible to reparameterize the QM/MM force field to reproduce MOZYME energies, a better way to account for both the effects of the protein environment and known deficiencies in semiempirical methods would be to parameterize the force field based on data from DFT or ab initio QM linear-scaling calculations. Such a force field could be used efficiently in MD simulations to calculate free energies. PMID:12214314

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

2002-11-15

269

The statistical origins of quantum mechanics

It is shown that Schroedinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle mechanics by replacing all observables by statistical averages. The second is a local conservation law of probability with a probability current which takes the form of a gradient. The third is a principle of maximal disorder as realized by the requirement of minimal Fisher information. The rule for calculating expectation values is obtained from a fourth postulate, the requirement of energy conservation in the mean. The fact that all these basic relations of quantum theory may be derived from premises which are statistical in character is interpreted as a strong argument in favor of the statistical interpretation of quantum mechanics. The structures of quantum theory and classical statistical theories are compared and some fundamental differences are identified.

U. Klein

2011-03-08

270

Quantum mechanics and consciousness: fact and fiction

This article was written in response to a request from an editor of American Vedantist. It is shown that the idea that consciousness is essential to understanding quantum mechanics arises from logical fallacies. This may be welcome news to those who share the author's annoyance at consciousness being dragged into discussions of physics, but beware: The same fallacies may underlie the reader's own way of making sense of quantum mechanics. The article ends up embracing a Vedantic world view, for two reasons. For one, such a world view seems to the author to be the most sensible alternative to a materialistic one. For another, quantum mechanics is inconsistent with a materialistic world view but makes perfect sense within a Vedantic framework of thought.

Ulrich Mohrhoff

2014-08-03

271

Multichannel framework for singular quantum mechanics

A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.

Camblong, Horacio E., E-mail: camblong@usfca.edu [Department of Physics and Astronomy, University of San Francisco, San Francisco, CA 94117-1080 (United States); Epele, Luis N., E-mail: epele@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Fanchiotti, Huner, E-mail: huner@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina)] [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); García Canal, Carlos A., E-mail: garcia@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Ordóñez, Carlos R., E-mail: ordonez@uh.edu [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States)

2014-01-15

272

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

273

Mossbauer neutrinos in quantum mechanics and quantum field theory

We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence, and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detection cross section, including localization and Lamb-Mossbauer terms, cannot be predicted in quantum mechanics and have to be put in by hand.

Joachim Kopp

2009-06-12

274

Entangled state representations in noncommutative quantum mechanics

We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called entangled state representations. Furthermore, we derive unitary transformations between the new representations and the ordinary one used in noncommutative quantum mechanics (NCQM) and obtain eigenfunctions of some basic operators in these representations. To show the potential applications of the entangled state representations, a two-dimensional harmonic oscillator on the noncommutative plane with both coordinate-coordinate and momentum-momentum couplings is exactly solved.

S. C. Jing; Q. Y. Liu; H. Y. Fan

2005-03-30

275

Equivariant Localization for Supersymmetric Quantum Mechanics

We apply equivariant localization to supersymmetric quantum mechanics and show that the partition function localizes on the instantons of the theory. Our construction of equivariant cohomology for SUSY quantum mechanics is different than the ones that already exist in the literature. A hidden bosonic symmetry is made explicit and the supersymmetry is extended. New bosonic symmetry is the square of the new fermionic symmetry. The D term is now the parameter of the bosonic symmetry. This construction provides us with an equivariant complex together with a Cartan differential and makes the use of localization principle possible.

Levent Akant

2005-05-30

276

Relativistic quantum mechanics and the Bohmian interpretation

Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role, provides a viable interpretation of relativistic quantum mechanics. We formulate the Bohmian interpretation of many-particle wave functions in a Lorentz-covariant way. In contrast with the nonrelativistic case, the relativistic Bohmian interpretation may lead to measurable predictions on particle positions even when the conventional interpretation does not lead to such predictions.

H. Nikolic

2005-04-04

277

Two basic Uncertainty Relations in Quantum Mechanics

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

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

2011-04-07

278

First-Person Plural Quantum Mechanics

Doing justice to quantum mechanics calls for a deeper examination of the relations between our experience, its objects, and its subjects than either third-person interpretations or the first-person singular interpretation of the QBist permit. The metaphysical space opened by Bohr's employment of the "Kantian wedge" between the objective world, about which we can communicate, and the world "in itself" allows quantum mechanics to unfold its metaphysical potential. This in turn makes it possible to go a long way towards bridging the epistemological gap between the empirical and transcendental conceptions of reality.

Ulrich Mohrhoff

2014-10-22

279

A new introductory quantum mechanics curriculum

NASA Astrophysics Data System (ADS)

The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum-mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of the interpretive aspects of quantum mechanics and quantum information theory. This paper gives an overview of the resources available from the IOP website. The core text includes around 80 articles which are co-authored by leading experts, arranged in themes, and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is included in the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways, from being supplemental to existing courses to forming a complete programme.

Kohnle, Antje; Bozhinova, Inna; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth

2014-01-01

280

Partitions and Objective Indefiniteness in Quantum Mechanics

Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM--which shows that the mathematical framework of QM is a type of logical system over the complex numbers. And then we show how the machinery of QM can be transported the other way down to the set-like vector spaces over Z_2 showing how the classical logical finite probability calculus (in a "non-commutative" version) is a type of "quantum mechanics" over Z_2, i.e., over sets. In this way, we try to make sense out of objective indefiniteness and thus to interpret quantum mechanics.

David Ellerman

2014-03-24

281

A proof of von Neumann's postulate in Quantum Mechanics

A Clifford algebraic analysis is explained. It gives proof of von Neumann's postulate on quantum measurement. It is of basic significance to explain the problem of quantum wave function reduction in quantum mechanics.

Conte, Elio [Department of Pharmacology and Human Physiology, TIRES-Center for Innovative Technologies for Signal Detection and Processing, Department of Physics, University of Bari (Italy) and School of Advanced International Studies for Applied Theoretical and Non Linear Methodologies of Physics, Bari (Italy)

2010-05-04

282

Can quantum mechanics fool the cosmic censor?

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

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

2009-05-15

283

Quantum statistical mechanics, L-series, Anabelian Geometry

Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Adem Lectures, Mexico City, January 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12 Mechanics, L-series and Anabelian Geometry, arXiv:1009.0736 Matilde Marcolli Quantum statistical mechanics

Marcolli, Matilde

284

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

285

CPT and Quantum Mechanics Tests with Kaons

In this review we first discuss the theoretical motivations for possible CPT violation and deviations from ordinary quantum-mechanical behavior of field-theoretic systems in the context of an extended class of quantum-gravity models. Then we proceed to a description of precision tests of CPT symmetry using mainly neutral kaons. We emphasize the possibly unique role of neutral meson factories in providing specific tests of models where the quantum-mechanical CPT operator is not well-defined, leading to modifications of Einstein-Podolsky-Rosen particle correlators. Finally, we present tests of CPT, T, and CP using charged kaons, and in particular K_l4 decays, which are interesting due to the high statistics attainable in experiments.

Jose Bernabeu; John Ellis; Nick E. Mavromatos; Dimitri V. Nanopoulos; Joannis Papavassiliou

2006-07-28

286

A Euclidean formulation of relativistic quantum mechanics

In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear operators on a Hilbert space, it has many of the advantages of quantum mechanics. One interesting feature of this approach is that matrix elements of operators in normalizable states on the physical Hilbert space can be calculated directly using the Euclidean Green functions without performing an analytic continuation. The formalism is summarized in this paper. We discuss the motivation, advantages and difficulties in using this formalism. We discuss how to compute bound states, scattering cross sections, and finite Poincare transformations without using analytic continuation. A toy model is used to demonstrate how matrix elements of exp(-beta H) in normalizable states can be used to construct-sharp momentum transition matrix elements.

Philip Kopp; Wayne Polyzou

2011-06-21

287

Quantum mechanics and the time travel paradox

The closed causal chains arising from backward time travel do not lead to paradoxes if they are self consistent. This raises the question as to how physics ensures that only self-consistent loops are possible. We show that, for one particular case at least, the condition of self consistency is ensured by the interference of quantum mechanical amplitudes associated with the loop. If this can be applied to all loops then we have a mechanism by which inconsistent loops eliminate themselves.

David T. Pegg

2005-06-17

288

Is Quantum Mechanics needed to explain consciousness ?

In this short comment to a recent contribution by E. Manousakis [1] it is argued that the reported agreement between the measured time evolution of conscious states during binocular rivalry and predictions derived from quantum mechanical formalisms does not require any direct effect of QM. The recursive consumption analysis process in the Ouroboros Model can yield the same behavior.

Knud Thomsen

2007-11-13

289

Quantum Mechanical Effects in Gravitational Collapse

In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schr\\"odinger formalism. The Functional Schr\\"odinger formalism allows us to investigate the time-dependent evolutions of the quantum mechanical effects, which is beyond the scope of the usual methods used to investigate the quantum mechanical corrections of gravitational collapse. Utilizing the time-dependent nature of the Functional Schr\\"odinger formalism, we study the quantization of a spherically symmetric domain wall from the view point of an asymptotic and infalling observer, in the absence of radiation. To build a more realistic picture, we then study the time-dependent nature of the induced radiation during the collapse using a semi-classical approach. Using the domain wall and the induced radiation, we then study the time-dependent evolution of the entropy of the domain wall. Finally we make some remarks about the possible inclusion of backreaction into the system.

Eric Greenwood

2010-01-12

290

Spin & statistics in nonrelativistic quantum mechanics, II

Recently a sufficient and necessary condition for Pauli's spin-statistics connection in nonrelativistic quantum mechanics has been established [1]. The two-dimensional part of this result is extended to n-particle systems and reformulated and further simplified in a more geometric language.

Bernd Kuckert; Jens Mund

2005-01-01

291

The geometric semantics of algebraic quantum mechanics

In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.

John Alex Cruz Morales; Boris Zilber

2014-10-27

292

BiHermitian supersymmetric quantum mechanics

BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the

Roberto Zucchini

2007-01-01

293

Comparison of Classical and Quantum Mechanical Uncertainties.

ERIC Educational Resources Information Center

Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)

Peslak, John, Jr.

1979-01-01

294

QBism and Locality in Quantum Mechanics

NASA Astrophysics Data System (ADS)

A critique to the article by C.A. Fuchs, N.D. Mermin, and R.Schack, "An introduction to QBism with and application to the locality of quantum mechanics" that appeared in Am. J. Phys. 82 (8), 749-754 (2014)

Nauenberg, Michael

2015-03-01

295

Holism, Physical Theories and Quantum Mechanics

Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.

M. P. Seevinck

2005-02-04

296

Summer 2011 Black Holes and Quantum Mechanics

to reject the notion of black holes that his theory of general relativity and gravity, published more than, explains the development of a string theoretic interpretation of black holes where quantum mechanics a precise description of a black hole, which is described holographically in terms of a theory living

297

Solvable potentials from supersymmetric quantum mechanics

A recurrence relation of Riccati-type differential equations known in supersymmetric quantum mechanics is investigated to find exactly solvable potentials. Taking some simple {\\it ans\\"atze}, we find new classes of solvable potentials as well as reproducing the known shape-invariant ones.

Soh, D S; Kim, S P; Soh, Dong Sup; Cho, Kyung Hyun; Kim, Sang Pyo

1995-01-01

298

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

299

Time and the foundations of quantum mechanics

NASA Astrophysics Data System (ADS)

Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of `time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on re ection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.

Pashby, Thomas

300

The Compton effect: Transition to quantum mechanics

NASA Astrophysics Data System (ADS)

The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite Robert A. Millikan's confirmation of Einstein's equation of the photoelectric effect in 1915. I then follow in some detail the experimental and theoretical research program that Arthur Holly Compton pursued between 1916 and 1922 at the University of Minnesota, the Westinghouse Lamp Company, the Cavendish Laboratory, and Washington University that culminated in his discovery of the Compton effect. Surprisingly, Compton was not influenced directly by Einstein's light-quantum hypothesis, in contrast to Peter Debye and H.A. Kramers, who discovered the quantum theory of scattering independently. I close by discussing the most significant response to that discovery, the Bohr-Kramers-Slater theory of 1924, its experimental refutation, and its influence on the emerging new quantum mechanics.

Stuewer, R. H.

2000-11-01

301

Deformation Quantization: From Quantum Mechanics to Quantum Field Theory

The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to quantum field theory. Also, we discuss some of the conceptual advantages of DQ and how DQ may be related to algebraic quantum field theory. Additionally, our previous results are summarized which includes the construction of the Fedosov star-product on dS/AdS. One of the goals of these results was to verify that DQ gave the same results as previous analyses of these spaces. Another was to verify that the formal series used in the conventional treatment converged by obtaining exact and nonperturbative results for these spaces.

P. Tillman

2006-10-31

302

Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics

Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics S. Albeverio, a new rigorous, but not probabilistic, Lagrangian version of nonrelativistic quantum mechanics is given in SchrÃ¶dinger's Euclidean quantum mechanics."1 There, a proba- bilistic i.e., "Euclidean" generalization

Zambrini, Jean-Claude

303

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

NSDL National Science Digital Library

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

304

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

305

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

306

Relativistic quantum mechanics with trapped ions

NASA Astrophysics Data System (ADS)

We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. Firstly, we study the bidimensional relativistic scattering of single Dirac particles by a linear potential. Secondly, we explore the case of a Dirac particle in a magnetic field and its topological properties. Finally, we analyze the problem of two Dirac particles that are coupled by a controllable and confining potential. The latter interaction may be useful to study important phenomena such as the confinement and asymptotic freedom of quarks.

Lamata, L.; Casanova, J.; Gerritsma, R.; Roos, C. F.; García-Ripoll, J. J.; Solano, E.

2011-09-01

307

Limits to the Universality of Quantum Mechanics

Niels Bohr's arguments indicating the non-applicability of quantum methodology to the study of the ultimate details of life given in his book "Atomic physics and human knowledge" conflict with the commonly held opposite view. The bases for the usual beliefs are examined and shown to have little validity. Significant differences do exist between the living organism and the type of system studied successfully in the physics laboratory. Dealing with living organisms in quantum-mechanical terms with the same degree of rigour as is normal for non-living systems would seem not to be possible without considering also questions of the origins of life and of the universe.

Brian D. Josephson

2011-10-08

308

Emergence of quantum mechanics from a sub-quantum statistical mechanics

NASA Astrophysics Data System (ADS)

A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wavefunctions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" non-locality.

Grössing, Gerhard

2014-07-01

309

The Objective Inde...niteness Interpretation of Quantum Mechanics

The Objective Inde...niteness Interpretation of Quantum Mechanics David Ellerman University of California at Riverside Draft (not for quotation) May 28, 2013 Abstract Quantum mechanics (QM models indef- inite elements that become more de...nite as distinctions are made. If quantum mechanics

WÃ¼thrich, Christian

310

Predicting crystal structure by merging data mining with quantum mechanics

ARTICLES Predicting crystal structure by merging data mining with quantum mechanics CHRISTOPHER C@mit.edu Published online: 9 July 2006; doi:10.1038/nmat1691 Modern methods of quantum mechanics have proved with quantum mechanics if an algorithm to direct the search through the large space of possible structures

Ceder, Gerbrand

311

How to Teach the Postulates of Quantum Mechanics without Enigma.

ERIC Educational Resources Information Center

Shows how a statistical approach can help students accept postulates of quantum mechanics. The approach, which also makes students aware of the philosophical/humanistic implications of quantum mechanics, involves the following sequence: (1) important experiments in quantum mechanics; (2) conventional statistical interpretation; (3) mathematical…

Teixeira-Dias, Jose J. C.

1983-01-01

312

Operational Axioms for Quantum Mechanics Giacomo Mauro D'Ariano

Operational Axioms for Quantum Mechanics Giacomo Mauro D'Ariano QUIT Group, Dipartimento di Fisica is derived. Undeniably the axioms of Quantum Mechanics are of a highly abstract and mathematical nature of Quantum Mechanics, its "physical" axioms-- if they exist--must be of very general nature: they must even

D'Ariano, Giacomo Mauro

313

Quantum statistical mechanics, L-series, Anabelian Geometry

Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Colloquium, Harvard University, March 24, 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12 as partition functions of physical systems Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian

Marcolli, Matilde

314

Quantum statistical mechanics, L-series, Anabelian Geometry

Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Beijing, August 2013 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;joint work with Gunther Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;Number fields: finite

Marcolli, Matilde

315

ADDENDUM: Chaos in Bohmian quantum mechanics

NASA Astrophysics Data System (ADS)

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 erratum published by the same authors (Parmenter and Valentine 1996 Phys. Lett. A 213 319) that recognized the error made in their previous calculations. The authors realized that, when correctly calculated, 'aperiodic trajectories with well defined boundaries...have vanishing Lyapunov exponents', i.e., they are not chaotic. We want to supplement our paper with a reference to this erratum. The generic calculation of Lyapunov exponents in Bohmian quantum systems remains an original contribution of our paper (section 2).

Efthymiopoulos, C.; Contopoulos, G.

2006-06-01

316

Quantum mechanics on phase space and teleportation

NASA Astrophysics Data System (ADS)

The formalism of quantum mechanics on phase space is used to describe the standard protocol of quantum teleportation with continuous variables in order to partially investigate the interplay between this formalism and quantum information. Instead of the Wigner quasi-probability distributions used in the standard protocol, we use positive definite true probability densities which account for unsharp measurements through a proper wave function representing a non-ideal quantum measuring device. This is based on a result of Schroeck and may be taken on any relativistic or nonrelativistic phase space. The obtained formula is similar to a known formula in quantum optics, but contains the effect of the measuring device. It has been applied in three cases. In the first case, the two measuring devices, corresponding to the two entangled parts shared by Alice and Bob, are not entangled and described by two identical Gaussian wave functions with respect to the Heisenberg group. They lead to a probability density identical to the function which is analyzed and compared with the Wigner formalism. A new expression of the teleportation fidelity for a coherent state in terms of the quadrature variances is obtained. In the second case, these two measuring devices are entangled in a two-mode squeezed vacuum state. In the third case, two Gaussian states are combined in an entangled squeezed state. The overall observation is that the state of the measuring devices shared by Alice and Bob influences the fidelity of teleportation through their unsharpness and entanglement.

Messamah, Juba; Schroeck, Franklin E.; Hachemane, Mahmoud; Smida, Abdallah; Hamici, Amel H.

2015-03-01

317

Does Quantum Mechanics Save Free Will?

According to the widely accepted opinion, classical (statistical) physics does not support objective indeterminism, since the statistical laws of classical physics allow a deterministic hidden background, while --- as Arthur Fine writes polemizing with Gr\\"unbaum --- "{\\sl the antilibertarian position finds little room to breathe in a statistical world if we take laws of the quantum theory as exemplars of the statistical laws in such a world. So, it appears that, contrary to what Gr\\"unbaum claims, the libertarians' 'could have done otherwise' does indeed find support from indeterminism if we take the indeterministic laws to be of the sort found in the quantum theory.}" In this paper I will show that, quite the contrary, quantum mechanics does not save free will. For instance, the EPR experiments are compatible with a deterministic world. They admit a deterministic local hidden parameter description if the deterministic model is 'allowed' to describe not only the measurement outcomes, but also the outcomes of the 'decisions' whether this or that measurement will be performed. So, the derivation of the freedom of the will from quantum mechanics is a tautology: from the assumption that the world is indeterministic it is derived that the world cannot be deterministic.

Laszlo E. Szabo

1995-06-28

318

Does quantum mechanics require non-locality?

Non-commutative properties of single quanta must violate the limit of Bell's theorem, but not the boundary of Tsirelson's theorem. This is a consequence of three basic principles: superposition (every quantum is in many states at the same time), correspondence (only the net state of interference is real), and uncertainty (conjugate variables have inversely proportional spectra). The two conditions have only been verified with entangled pairs of quanta. It is not possible to perform incompatible measurements on the same entity. Hence, the principles of quantum mechanics cannot be verified directly. At least one of them could be wrong. Though, as shown by EPR, this can only be true if non-locality is at work. In light of the latest developments in quantum theory, even that assumption is insufficient. Non-local effects are either unable to cross Bell's limit, or forced to violate Tsirelson's bound. New layers of hidden variables are required to maintain belief in action-at-a-distance, but the three principles cannot be rejected in any case. Therefore, quantum mechanics is immune to this challenge. The hypothesis of non-locality is superfluous.

Ghenadie N. Mardari

2014-10-29

319

Events and the Ontology of Quantum Mechanics

In the first part of the paper I argue that an ontology of events is precise, flexible and general enough so as to cover the three main alternative formulations of quantum mechanics as well as theories advocating an antirealistic view of the wave function. Since these formulations advocate a primitive ontology of entities living in four-dimensional spacetime, they are good candidates to connect that quantum image with the manifest image of the world. However, to the extent that some form of realism about the wave function is also necessary, one needs to endorse also the idea that the wave function refers to some kind of power. In the second part, I discuss some difficulties raised by the recent proposal that in Bohmian mechanics this power is holistically possessed by all the particles in the universe.

Dorato, Mauro

2015-01-01

320

The preparation of states in quantum mechanics

The important problem of how to prepare a quantum mechanical system, $S$, in a specific initial state of interest - e.g., for the purposes of some experiment - is addressed. Three distinct methods of state preparation are described. One of these methods has the attractive feature that it enables one to prepare $S$ in a preassigned initial state with certainty; i.e., the probability of success in preparing $S$ in a given state is unity. This method relies on coupling $S$ to an open quantum-mechanical environment, $E$, in such a way that the dynamics of $S \\vee E$ pulls the state of $S$ towards an "attractor", which is the desired initial state of $S$. This method is analyzed in detail.

Juerg Froehlich; Baptiste Schubnel

2014-09-28

321

Beyond relativity and quantum mechanics: space physics

NASA Astrophysics Data System (ADS)

Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.

Lindner, Henry H.

2011-09-01

322

Chiral quantum mechanics (CQM) for antihydrogen systems

A first deception of QM on antiH already appears in one-center integrals for two-center systems (G. Van Hooydonk, physics/0511115). In reality, full QM is a theory for chiral systems but the QM establishment was wrong footed with a permutation of reference frames. With chiral quantum mechanics (CQM), the theoretical ban on natural antiH must be lifted as soon as possible.

G. Van Hooydonk

2005-12-03

323

Small Black Holes and Superconformal Quantum Mechanics

NASA Astrophysics Data System (ADS)

Recently, Gaiotto, Strominger and Yin have proposed a holographic representation of the microstates of certain N = 2 black holes as chiral primaries of a superconformal quantum mechanics living on D0-branes in the attractor geometry. We show that their proposal can be succesfully applied to `small' black holes which are dual to Dabholkar-Harvey states and have vanishing horizon area in the leading supergravity approximation.

Raeymaekers, Joris

2005-12-01

324

The human story behind Everettian quantum mechanics

Hugh Everett III (1930–1982) was an unappealing character with a remarkable mind. His Princeton doctoral thesis on the foundations of physics transformed our understanding of quantum–mechanical reality, and he made original contributions to military operations research and to game theory. His domestic life was less inspiring; he died young after a lifetime of over-indulgence in food, alcohol, tobacco and sex,

Alastair Wilson

325

Statistical-mechanical description of quantum entanglement

We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable states. We further study this system using statistical mechanical methods. Finally, we apply our techniques to Werner states of two qubits and obtain a sufficient criterion for separability.

J. K. Korbicz; F. Hulpke; A. Osterloh; M. Lewenstein

2008-08-27

326

Quantum Mechanics on Manifolds and Topological Effects

A unique classification of the topological effects associated to quantum mechanics on manifolds is obtained on the basis of\\u000a the invariance under diffeomorphisms and the realization of the Lie–Rinehart relations between the generators of the diffeomorphism\\u000a group and the algebra of C\\u000a ? functions on the manifold. This leads to a unique (“Lie–Rinehart”) C\\u000a *-algebra as observable algebra; its regular

Giovanni Morchio; Franco Strocchi

2007-01-01

327

Physical Interpretations of Nilpotent Quantum Mechanics

Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization, and related issues.

Peter Rowlands

2010-04-09

328

A tossed coin as quantum mechanical object

Comprehensive and physically consistent model of a tossed coin is presented in terms of geometric algebra. The model clearly shows that there is nothing elementary particle specific in the half-spin quantum mechanical formalism. It also demonstrates what really is behind this formalism, feasibly reveals the probabilistic meaning of wave function and shows that arithmetic of packed objects, namely wave functions and Pauli matrices, reduces the amount of available information.

Alexander M. Soiguine

2014-08-28

329

Modern Quantum Mechanics Experiments for Undergraduates

NSDL National Science Digital Library

Authored by Mark Beck of Whitman College's Department of Physics, this site provides information about simplified quantum mechanics experiments such as the Grangier experiment and single photon interference. Included are a general description, an overview, course materials, experiments, external links and notes. Each experiment or lesson provides instructions and other need information such as images, charts or graphs. This series of resources could be used to enhance or create curricula in the field.

Beck, Mark

330

Quantum Mechanics - Fundamentals and Applications to Technology

NASA Astrophysics Data System (ADS)

Explore the relationship between quantum mechanics and information-age applications This volume takes an altogether unique approach to quantum mechanics. Providing an in-depth exposition of quantum mechanics fundamentals, it shows how these concepts are applied to most of today's information technologies, whether they are electronic devices or materials. No other text makes this critical, essential leap from theory to real-world applications. The book's lively discussion of the mathematics involved fits right in with contemporary multidisciplinary trends in education: Once the basic formulation has been derived in a given chapter, the connection to important technological problems is summarily described. The many helpful features include * Twenty-eight application-oriented sections that focus on lasers, transistors, magnetic memories, superconductors, nuclear magnetic resonance (NMR), and other important technology-driving materials and devices * One hundred solved examples, with an emphasis on numerical results and the connection between the physics and its applications * End-of-chapter problems that ground the student in both fundamental and applied concepts * Numerous figures and tables to clarify the various topics and provide a global view of the problems under discussion * Over two hundred illustrations to highlight problems and text A book for the information age, Quantum Mechanics: Fundamentals and Applications to Technology promises to become a standard in departments of electrical engineering, applied physics, and materials science, as well as physics. It is an excellent text for senior undergraduate and graduate students, and a helpful reference for practicing scientists, engineers, and chemists in the semiconductor and electronic industries.

Singh, Jasprit

1996-10-01

331

Entanglement, superselection rules and supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

In this paper we show that the energy eigenstates of supersymmetric quantum mechanics (SUSYQM) with non-definite “fermion” number are entangled states. They are “physical states” of the model provided that observables with odd number of spin variables are allowed in the theory like it happens in the Jaynes-Cummings model. Those states generalize the so-called “spin-spring” states of the Jaynes-Cummings model which have played an important role in the study of entanglement.

Cattaruzza, E.; Gozzi, E.; Pagani, C.

2014-07-01

332

Relativistic Non-Hermitian Quantum Mechanics

We develop relativistic wave equations in the framework of the new non-hermitian ${\\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\\cal PT}$-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 $\\cal{PT}$ symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is non-zero.The ${\\cal PT}$-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a non-interacting theory it violates ${\\cal P}$ and ${\\cal T}$ 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 new possibilities permitted by the non-hermiticity parameter $m_2$.

Katherine Jones-Smith; Harsh Mathur

2014-07-01

333

Combining abstract to laboratory projected quantum states a general analysis of headline quantum phenomena is presented. Standard representation mode is replaced; instead quantum states sustained by elementary material constituents occupy its place. Renouncing to assign leading roles to language originated in classical physics when describing genuine quantum processes, together with sustainment concept most, if not all weirdness associated to Quantum Mechanics vanishes.

O. Tapia

2014-04-02

334

Philosophy of Quantum Mechanics Quantum theory is arguably the most accurate scientific theory ever

1 PHIL 245: Philosophy of Quantum Mechanics Quantum theory is arguably the most accurate scientific of a quantum world has been hotly disputed since the theorys inception. Many very distinct models of a quantum?; the quantum eraser; instrumentalism; realism Week 3 Collapse Views "Realistic" collapse theories have been

Callender, Craig

335

Quantum mechanics, by itself, implies perception of a classical world

Several versions of reality can simultaneously exist in the states of quantum mechanics, but we perceive only one classical version. The question is whether the mathematics of quantum mechanics, by itself, implies we perceive only one classical version. Zurek has used a method involving the environment, redundancy, decoherence and quantum Darwinism to show that quantum mechanics does indeed imply this result, but the argument is quite complex. Here we give a simpler method based on linearity.

Casey Blood

2012-06-12

336

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

337

Neutrino oscillations: quantum mechanics vs. quantum field theory

NASA Astrophysics Data System (ADS)

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

2010-04-01

338

Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory

I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.

H. Nikolic

2006-10-12

339

Optimal guidance law in quantum mechanics

NASA Astrophysics Data System (ADS)

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 ???.

Yang, Ciann-Dong; Cheng, Lieh-Lieh

2013-11-01

340

An approach to nonstandard quantum mechanics

We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to non-relativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the M{\\o}ller wave operators and the S-Matrix.

Andreas Raab

2006-12-27

341

Copenhagen Interpretation of Quantum Mechanics Is Incorrect

(A point-by-point response to a comment (quant-ph/0509130) on our paper (quant-ph/0509089) is added as Appendix C. We find the comment incorrect.) Einstein's criticism of the Copenhagen interpretation of quantum mechanics is an important part of his legacy. Although most physicists consider Einstein's criticism technically unfounded, we show that the Copenhagen interpretation is actually incorrect, since Born's probability explanation of the wave function is incorrect due to a false assumption on "continuous probabilities" in modern probability theory. "Continuous probability" means a "probability measure" that can take every value in a subinterval of the unit interval (0, 1). We prove that such "continuous probabilities" are invalid. Since Bell's inequality also assumes "continuous probabilities", the result of the experimental test of Bell's inequality is not evidence supporting the Copenhagen interpretation. Although successful applications of quantum mechanics and explanation of quantum phenomena do not necessarily rely on the Copenhagen interpretation, the question asked by Einstein 70 years ago, i.e., whether a complete description of reality exists, still remains open.

Guang-Liang Li; Victor O. K. Li

2005-09-23

342

The Mathematical Basis for Deterministic Quantum Mechanics

NASA Astrophysics Data System (ADS)

If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.

't Hooft, G.

2007-09-01

343

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

344

Advances in relativistic molecular quantum mechanics

NASA Astrophysics Data System (ADS)

A quantum mechanical equation H?=E? is composed of three components, viz., Hamiltonian H, wave function ?, and property E(?), each of which is confronted with fundamental issues in the relativistic regime, e.g., (1) What is the most appropriate relativistic many-body Hamiltonian? How to solve the resulting equation? (2) How does the relativistic wave function behave at the coalescence of two electrons? How to do relativistic explicit correlation? (3) How to formulate relativistic properties properly?, to name just a few. It is shown here that the charge-conjugated contraction of Fermion operators, dictated by the charge conjugation symmetry, allows for a bottom-up construction of a relativistic Hamiltonian that is in line with the principles of quantum electrodynamics (QED). Various approximate but accurate forms of the Hamiltonian can be obtained based entirely on physical arguments. In particular, the exact two-component Hamiltonians can be formulated in a general way to cast electric and magnetic fields, as well as electron self-energy and vacuum polarization, into a unified framework. While such algebraic two-component Hamiltonians are incompatible with explicit correlation, four-component relativistic explicitly correlated approaches can indeed be made fully parallel to the nonrelativistic counterparts by virtue of the ‘extended no-pair projection’ and the coalescence conditions. These findings open up new avenues for future developments of relativistic molecular quantum mechanics. In particular, ‘molecular QED’ will soon become an active and exciting field.

Liu, Wenjian

2014-04-01

345

Quantum Field Theory for Mathematicians Hamiltonian Mechanics and Symplectic Geometry

Quantum Field Theory for Mathematicians Â· Hamiltonian Mechanics and Symplectic Geometry Integral Quantization Â Supersymmetric Quantum Mechanics Â Introduction to Scattering Theory Â· Classical Field Theory Â· Relativistic Fields, PoincarÂ´e Group and Wigner Classification Â· Free Quantum Fields

Woit, Peter

346

Quantum gears: a simple mechanical system in the quantum Angus MacKinnon

Quantum gears: a simple mechanical system in the quantum regime Angus MacKinnon Blackett Laboratory. The quantum mechanics of a simple mechanical system is considered. A group of gears can serve as a model molecules. An expression is derived for the quantisation of the dynamics of a 2Âgear system. The general

MacKinnon, Angus

347

FIG. 1: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. FIG. 2: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. 1 #12;FIG. 3: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect

Nielsen, Steven O.

348

Bhomian Mechanics vs. Standard Quantum Mechanics: a Difference in Experimental Predictions

Standard Quantum Mechanics (QM) predicts an anti-intuitive fenomenon here referred to as "quantum autoscattering", which is excluded by Bhomian Mechanics. The scheme of a gedanken experiment testing the QM prediction is briefly discussed.

Artur Szczepanski

2010-02-08

349

Quantum Mechanics of a Rotating Billiard

Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, $\\lambda = 2E/\\omega^{2}$ where E is the energy of the particle inside the billiard and $\\omega$ is the angular frequency of rotation of billiard. We study the system classically and quantum mechanically in view of obtaining a correspondence in the two descriptions. Classical phase space in Poincar\\'{e} surface of section shows transition from regular to chaotic motion as the parameter $\\lambda$ is decreased. In the Quantum counterpart, the spectral statistics shows a transition from Poisson to Wigner distribution as the system turns chaotic with decrease in $\\lambda$. The wavefunction statistics however show breakdown of time-reversal symmetry as $\\lambda$ decreases.

Nandan Jha; Sudhir R. Jain

2014-06-12

350

Quantum Mechanics in Terms of Realism

We expound an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new interpretation is formulated in the language of epistemological realism. It involves a change in some basic physical concepts. The $\\psi $ function is no longer interpreted as a probability amplitude of the observed behavior of elementary particles but as an objective physical field representing the particles themselves. The particles are thus extended objects whose extension varies in time according to the variation of $\\psi $. They are considered as fundamental regions of space with some kind of nonlocality. Special consideration is given to the Heisenberg relations, the reduction process, the problem of measurement, Schr\\"odinger's cat, Wigner's friend, the Einstein-Podolsky-Rosen correlations, field quantization and quantum-statistical distributions.

Arthur Jabs

2015-02-02

351

Measurement and Ergodicity in Quantum Mechanics

The experimental realization of successive non-demolition measurements on single microscopic systems brings up the question of ergodicity in Quantum Mechanics (QM). We investigate whether time averages over one realization of a single system are related to QM averages over an ensemble of similarly prepared systems. We adopt a generalization of von Neumann model of measurement, coupling the system to $N$ "probes" --with a strength that is at our disposal-- and detecting the latter. The model parallels the procedure followed in experiments on Quantum Electrodynamic cavities. The modification of the probability of the observable eigenvalues due to the coupling to the probes can be computed analytically and the results compare qualitatively well with those obtained numerically by the experimental groups. We find that the problem is not ergodic, except in the case of an eigenstate of the observable being studied.

Mariano Bauer; Pier A. Mello

2015-04-03

352

Path integration in relativistic quantum mechanics

The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.

Ian H. Redmount; Wai-Mo Suen

1992-10-28

353

Quantum-Mechanical Model of Spacetime

We consider a possibility to construct a quantum-mechanical model of spacetime, where Planck size quantum black holes act as the fundamental constituents of space and time. Spacetime is assumed to be a graph, where black holes lie on the vertices. Our model implies that area has a discrete spectrum with equal spacing. At macroscopic length scales our model reproduces Einstein's field equation with a vanishing cosmological constant as a sort of thermodynamical equation of state of spacetime and matter fields. In the low temperature limit, where most black holes are assumed to be in the ground state, our model implies the Unruh and the Hawking effects, whereas in the high temperature limit we find, among other things, that black hole entropy depends logarithmically on the event horizon area, instead of being proportional to the area.

Jarmo Makela

2007-06-20

354

Adaptive Perturbation Theory I: Quantum Mechanics

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be treatable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, H, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. This paper introduces the method in the context of the pure anharmonic oscillator and then goes on to apply it to the case of tunneling between both symmetric and asymmetric minima. It concludes with an introduction to the extension of these methods to the discussion of a quantum field theory. A more complete discussion of this issue will be given in the second paper in this series, and it will show how to use the method of adaptive perturbation theory to non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.

Weinstein, Marvin; /SLAC

2005-10-19

355

Quantum selfish gene (biological evolution in terms of quantum mechanics)

I propose to treat the biological evolution of genoms by means of quantum mechanical tools. We start with the concept of meta- gene, which specifies the "selfish gene" of R.Dawkins. Meta- gene encodes the abstract living unity, which can live relatively independently of the others, and can contain a few real creatures. Each population of living creatures we treat as the wave function on meta- genes, which module squared is the total number of creatures with the given meta-gene, and the phase is the sum of "aspirations" to change the classical states of meta- genes. Each individual life thus becomes one of possible outcomes of the virtual quantum measurement of this function. The evolution of genomes is described by the unitary operator in the space of psi-functions or by Kossovsky-Lindblad equation in the case of open biosystems. This operator contains all the information about specific conditions under which individuals are, and how "aspirations" of their meta- genes may be implemented at the biochemical level. We show the example of quantum description of the population with two parts of meta-gene: "wolves" and "deer", which can be simultaneously in the same abstract living unity. "Selfish gene" reconciled with the notion of individuality of alive beings that gives possibility to consider evolutionary scenarios and their possible physical causes from the single position.

Yuri I. Ozhigov

2013-12-07

356

Probability Representation of Quantum Mechanics: Comments and Bibliography

The probability representation of states in standard quantum mechanics where the quantum states are associated with fair probability distributions (instead of wave function or density matrix) is shortly commented and bibliography related to the probability representation is given.

V. I. Man'ko; O. V. Pilyavets; V. G. Zborovskii

2006-10-17

357

5.74 Introductory Quantum Mechanics II, Spring 2003

Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...

Tokmakoff, Andrei

358

5.74 Introductory Quantum Mechanics II, Spring 2005

Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...

Tokmakoff, Andrei

359

5.74 Introductory Quantum Mechanics II, Spring 2007

Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...

Tokmakoff, Andrei

360

The Multiverse Interpretation of Quantum Mechanics

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

Raphael Bousso; Leonard Susskind

2011-07-22

361

Clocks And Dynamics In Quantum Mechanics

We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of quantum uncertainty lies with the absence of infinities or infinitesimals in observational data and that our concept of time derives from observing changing data (events). We argue that the fundamentally important content of the Superposition Principle is not the "probability amplitude" of posterior state observation but future state availability conditional only on prior information. Since event detection also implies posterior conditions (e.g. a specific type of detectable event occurred) as well as prior conditions, the probabilities of detected outcomes are also conditional on properties of the posterior properties of the observation. Such posterior conditions cannot affect the prior state availabilities and this implies violation of counter-factual definiteness. A component of a quantum system may be chosen to represent a clock and changes in other components can then be expected to be correlated with clocks with which they are entangled. Instead of traditional time-dependent equations of motion we provide a specific mechanism whereby evolution of data is instead quasi-causally related to the relative \\availability\\ of states and equations of motion are expressed in terms of quantized clock variables. We also suggest that time-reversal symmetry-breaking in weak interactions is an artifice of a conventional choice of co-ordinate time-function. Analysis of a "free" particle suggests that conventional co-ordinate space-time emerges from how we measure the separation of objects and events.

Michael York

2014-07-11

362

Wigner Measures in Noncommutative Quantum Mechanics

We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner measure, for a Gaussian to be a noncommutative Wigner measure, and derive certain properties of the marginal distributions which are not shared by ordinary Wigner measures. Moreover, we derive the Robertson-Schr\\"odinger uncertainty principle. Finally, we show explicitly how the set of noncommutative Wigner measures relates to the sets of Liouville and (commutative) Wigner measures.

C. Bastos; N. C. Dias; J. N. Prata

2009-07-25

363

Improved lattice actions for supersymmetric quantum mechanics

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

Sebastian Schierenberg; Falk Bruckmann

2012-10-19

364

Euclidean Quantum Mechanics and Universal Nonlinear Filtering

An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr\\"odinger equation.

Bhashyam Balaji

2008-09-25

365

Vector Models in PT Quantum Mechanics

We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by Bender and Kalveks, wherein the E2 algebra was examined; here we consider the E3 algebra representing a particle on a sphere, and identify the critical value of coupling constant which marks the transition from real to imaginary eigenvalues. Next we analyze a model with SO(3) symmetry, and in the process extend the application of the Wigner-Eckart theorem to a non-Hermitian setting.

Katherine Jones-Smith; Rudolph Kalveks

2013-04-21

366

Perspectives: Quantum Mechanics on Phase Space

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

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

2006-06-27

367

Counting Trees in Supersymmetric Quantum Mechanics

We study the supersymmetric ground states of the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in four-dimensional N=2 systems. The ground state degeneracy may be written as a multi-dimensional contour integral, and the enumeration of poles can be simply phrased as counting bipartite trees. We solve this combinatorics problem, thereby obtaining exact formulas for the degeneracies of an infinite class of models. We also develop an algorithm to compute the angular momentum of the ground states, and present explicit expressions for the refined indices of theories where one rank is small.

Cordova, Clay

2015-01-01

368

Non-representative quantum mechanical weak values

The operational definition of a weak value for a quantum mechanical system involves the limit of the weak measurement strength tending to zero. I study how this limit compares to the situation for the undisturbed (no weak measurement) system. Under certain conditions, which I investigate, this limit is discontinuous in the sense that it does not merge smoothly to the Hilbert space description of the undisturbed system. Hence, in these discontinuous cases, the weak value does not represent the undisturbed system. As a result, conclusions drawn from such weak values regarding the properties of the studied system cannot be upheld. Examples are given.

B. E. Y. Svensson

2015-03-06

369

Fragment quantum mechanical calculation of proteins and its applications.

Conspectus The desire to study molecular systems that are much larger than what the current state-of-the-art ab initio or density functional theory methods could handle has naturally led to the development of novel approximate methods, including semiempirical approaches, reduced-scaling methods, and fragmentation methods. The major computational limitation of ab initio methods is the scaling problem, because the cost of ab initio calculation scales nth power or worse with system size. In the past decade, the fragmentation approach based on chemical locality has opened a new door for developing linear-scaling quantum mechanical (QM) methods for large systems and for applications to large molecular systems such as biomolecules. The fragmentation approach is highly attractive from a computational standpoint. First, the ab initio calculation of individual fragments can be conducted almost independently, which makes it suitable for massively parallel computations. Second, the electron properties, such as density and energy, are typically combined in a linear fashion to reproduce those for the entire molecular system, which makes the overall computation scale linearly with the size of the system. In this Account, two fragmentation methods and their applications to macromolecules are described. They are the electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method and the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. The EE-GMFCC method is developed from the MFCC approach, which was initially used to obtain accurate protein-ligand QM interaction energies. The main idea of the MFCC approach is that a pair of conjugate caps (concaps) is inserted at the location where the subsystem is divided by cutting the chemical bond. In addition, the pair of concaps is fused to form molecular species such that the overcounted effect from added concaps can be properly removed. By introducing the electrostatic embedding field in each fragment calculation and two-body interaction energy correction on top of the MFCC approach, the EE-GMFCC method is capable of accurately reproducing the QM molecular properties (such as the dipole moment, electron density, and electrostatic potential), the total energy, and the electrostatic solvation energy from full system calculations for proteins. On the other hand, the AF-QM/MM method was used for the efficient QM calculation of protein nuclear magnetic resonance (NMR) parameters, including the chemical shift, chemical shift anisotropy tensor, and spin-spin coupling constant. In the AF-QM/MM approach, each amino acid and all the residues in its vicinity are automatically assigned as the QM region through a distance cutoff for each residue-centric QM/MM calculation. Local chemical properties of the central residue can be obtained from individual QM/MM calculations. The AF-QM/MM approach precisely reproduces the NMR chemical shifts of proteins in the gas phase from full system QM calculations. Furthermore, via the incorporation of implicit and explicit solvent models, the protein NMR chemical shifts calculated by the AF-QM/MM method are in excellent agreement with experimental values. The applications of the AF-QM/MM method may also be extended to more general biological systems such as DNA/RNA and protein-ligand complexes. PMID:24851673

He, Xiao; Zhu, Tong; Wang, Xianwei; Liu, Jinfeng; Zhang, John Z H

2014-09-16

370

Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new general continuous eigenvalue equation and a general discrete eigenvalue equation in quantum mechanics, and discover that a eigenvalue of quantum mechanics is just an extreme value of an operator in possibility distribution, the eigenvalue f is just classical observable quantity. A general classical statistical uncertain relation is further given, the general classical statistical uncertain relation is generally generalized to quantum uncertainty principle, the two lost conditions in classical uncertain relation and quantum uncertainty principle, respectively, are found. We generally expound the relations among uncertainty principle, singularity and condensed matter stability, discover that quantum uncertainty principle prevents from the appearance of singularity of the electromagnetic potential between nucleus and electrons, and give the failure conditions of quantum uncertainty principle. Finally, we discover that the classical limit of quantum mechanics is classical statistical mechanics, the classical statistical mechanics may further be degenerated to classical mechanics, and we discover that only saying that the classical limit of quantum mechanics is classical mechanics is mistake. As application examples, we deduce both Shrodinger equation and state superposition principle, deduce that there exist decoherent factor from a general mathematical representation of state superposition principle, and the consistent difficulty between statistical interpretation of quantum mechanics and determinant property of classical mechanics is overcome.

Y. C. Huang; F. C. Ma; N. Zhang

2005-06-13

371

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

372

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 at the present time. Examination of QM in n-space, as well as relativistic QM equations does not change this conclusion.

Mario Rabinowitz

2006-02-22

373

Materials* Yan Wang** and Teresa L. Hein American University In this paper we will present our experiences using a portion of the materials developed by the Visual Quantum Mechanics (VQM) project1 as part of our materials were utilized in a new second-tier introductory course for non-science majors at American

Larkin, Teresa L.

374

A quantum protective mechanism in photosynthesis.

Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life. PMID:25732807

Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk

2015-01-01

375

A quantum protective mechanism in photosynthesis

Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life. PMID:25732807

Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk

2015-01-01

376

Mechanical momentum in nonequilibrium quantum electrodynamics

The reformulation of field theory in which self-energy processes are no longer present [Annals of Physics, {\\bf311} (2004), 314.], [ Progr. Theor. Phys., {\\bf 109} (2003), 881.], [Trends in Statistical Physics {\\bf 3} (2000), 115.] provides an adequate tool to transform Swinger-Dyson equations into a kinetic description outside any approximation scheme. Usual approaches in quantum electrodynamics (QED) are unable to cope with the mechanical momentum of the electron and replace it by the canonical momentum. The use of that unphysical momentum is responsible for the divergences that are removed by the renormalization procedure in the $S$-matrix theory. The connection between distribution functions in terms of the canonical and those in terms of the mechanical momentum is now provided by a dressing operator [Annals of Physics, {\\bf314} (2004), 10] that allows the elimination of the above divergences, as the first steps are illustrated here.

Michel de Haan

2006-10-23

377

A quantum protective mechanism in photosynthesis

NASA Astrophysics Data System (ADS)

Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life.

Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk

2015-03-01

378

NASA Astrophysics Data System (ADS)

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

Sakata, Tetsuya; Kawashima, Yukio; Nakano, Haruyuki

2011-01-01

379

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

380

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

381

A note on the Landauer principle in quantum statistical mechanics

A note on the Landauer principle in quantum statistical mechanics Vojkan Jaksi´c1 and Claude results concerning the derivation of the Landauer bound from the first principles of statistical mechanics and proof of the Landauer principle in the context of quantum statistical mechanics has led to a number

Boyer, Edmond

382

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

383

Quantum Mechanical Study of Nanoscale MOSFET

NASA Technical Reports Server (NTRS)

The steady state characteristics of MOSFETS that are of practical Interest are the drive current, off-current, dope of drain current versus drain voltage, and threshold voltage. In this section, we show that quantum mechanical simulations yield significantly different results from drift-diffusion based methods. These differences arise because of the following quantum mechanical features: (I) polysilicon gate depletion in a manner opposite to the classical case (II) dependence of the resonant levels in the channel on the gate voltage, (III) tunneling of charge across the gate oxide and from source to drain, (IV) quasi-ballistic flow of electrons. Conclusions dI/dV versus V does not increase in a manner commensurate with the increase in number of subbands. - The increase in dI/dV with bias is much smaller then the increase in the number of subbands - a consequence of bragg reflection. Our calculations show an increase in transmission with length of contact, as seen in experiments. It is desirable for molecular electronics applications to have a small contact area, yet large coupling. In this case, the circumferential dependence of the nanotube wave function dictates: - Transmission in armchair tubes saturates around unity - Transmission in zigzag tubes saturates at two.

Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan

2001-01-01

384

A bilocal picture of quantum mechanics

NASA Astrophysics Data System (ADS)

A new, bilocal picture of quantum mechanics is developed. We show that Born’s rule supports a virtual probability for a particle to arrive, as a wave, at any two locations (but no more). We discuss two ways to implement twin detectors suitable for detecting bilocal arrivals. The bilocal picture sheds light on currents in quantum mechanics. We find there are two types of bilocal current density, whose polar form and related mean velocities are given. In the bilocal context, the definitions of both current types simplify. In the unilocal case, the two types become the usual current and a fluctuation current. Their respective mean velocity fields are the usual de Broglie–Madelung–Bohm velocity and the imaginary (osmotic) velocity. We obtain a new, probabilistic Schrödinger equation for the bilocal probability by itself, solve the example of a free particle, develop the dyadic stationary states, and find that the von Neumann equation for time-varying density of states follows directly from the new equation. We also show how to include the electromagnetic potentials in this probabilistic Schrödinger equation.

Withers, L. P., Jr.; Narducci, F. A.

2015-04-01

385

Surveying Instructors' Attitudes and Approaches to Teaching Quantum Mechanics

NASA Astrophysics Data System (ADS)

Understanding instructors' attitudes and approaches to teaching quantum mechanics can be helpful in developing research-based learning tools. Here we discuss the findings from a survey in which 13 instructors reflected on issues related to quantum mechanics teaching. Topics included opinions about the goals of a quantum mechanics course, general challenges in teaching the subject, students' preparation for the course, comparison between their own learning of quantum mechanics vs. how they teach it and the extent to which contemporary topics are incorporated into the syllabus.

Siddiqui, Shabnam; Singh, Chandralekha

2010-10-01

386

Quantum selfish gene (biological evolution in terms of quantum mechanics)

I propose to treat the biological evolution of genoms by means of quantum mechanical tools. We start with the concept of meta- gene, which specifies the "selfish gene" of R.Dawkins. Meta- gene encodes the abstract living unity, which can live relatively independently of the others, and can contain a few real creatures. Each population of living creatures we treat as the wave function on meta- genes, which module squared is the total number of creatures with the given meta-gene, and the phase is the sum of "aspirations" to change the classical states of meta- genes. Each individual life thus becomes one of possible outcomes of the virtual quantum measurement of this function. The evolution of genomes is described by the unitary operator in the space of psi-functions or by Kossovsky-Lindblad equation in the case of open biosystems. This operator contains all the information about specific conditions under which individuals are, and how "aspirations" of their meta- genes may be implemented at the biochemical lev...

Ozhigov, Yuri I

2014-01-01

387

Supmech, an algebraic scheme of mechanics integrating noncommutative symplectic geometry and noncommutative probability, subsumes quantum and classical mechanics and permits consistent treatment of interaction of quantum and classical systems. Quantum measurements are treated in this framework; the von Neumann reduction rule (generally postulated) is derived and interpreted in physical terms.

Tulsi Dass

2006-12-29

388

Three attempts at two axioms for quantum mechanics

The axioms of nonrelativistic quantum mechanics lack clear physical meaning. In particular, they say nothing about nonlocality. Yet quantum mechanics is not only nonlocal, it is twice nonlocal: there are nonlocal quantum correlations, and there is the Aharonov-Bohm effect, which implies that an electric or magnetic field h e r e may act on an electron t h e r e. Can we invert the logical hierarchy? That is, can we adopt nonlocality as an axiom for quantum mechanics and derive quantum mechanics from this axiom and an additional axiom of causality? Three versions of these two axioms lead to three different theories, characterized by "maximal nonlocal correlations", "jamming" and "modular energy". Where is quantum mechanics in these theories?

Daniel Rohrlich

2011-11-04

389

Fundamental phenomena of quantum mechanics explored with neutron interferometers

Ongoing fascination with quantum mechanics keeps driving the development of the wide field of quantum-optics, including its neutron-optics branch. Application of neutron-optical methods and, especially, neutron interferometry and polarimetry has a long-standing tradition for experimental investigations of fundamental quantum phenomena. We give an overview of related experimental efforts made in recent years.

J. Klepp; S. Sponar; Y. Hasegawa

2014-07-11

390

Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics

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

V. Jaksic; Y. Ogata; C. -A. Pillet; R. Seiringer

2012-07-16

391

This investigation presents the characterization of structural and dynamical properties of uranyl tricarbonate in aqueous solution employing an extended hybrid quantum mechanical/molecular mechanical (QM/MM) approach. It is shown that the inclusion of explicit solvent molecules in the quantum chemical treatment is essential to mimic the complex interaction occurring in an aqueous environment. Thus, in contrast to gas phase cluster calculations on a quantum chemical level proposing a 6-fold coordination of the three carbonates, the QMCF MD simulation proposes a 5-fold coordination. An extensive comparison of the simulation results to structural and dynamical data available in the literature was found to be in excellent agreement. Furthermore, this work is the first theoretical study on a quantum chemical level of theory able to observe the conversion of carbonate (CO?²?) to bicarbonate (HCO??) in the equatorial coordination sphere of the uranyl ion. From a comparison of the free energy ?G values for the unprotonated educt [UO?(CO?)?]?? and the protonated [UO?(CO?)?(HCO?)]³?, it could be concluded that the reaction equilibrium is strongly shifted toward the product state confirming the benignity for the observed protonation reaction. Structural properties and the three-dimensional arrangement of carbonate ligands were analyzed via pair-, three-body, and angular distributions, the dynamical properties were evaluated by hydrogen-bond correlation functions and vibrational power spectra. PMID:25157847

Tirler, Andreas O; Hofer, Thomas S

2014-11-13

392

Reciprocal relativity of noninertial frames: quantum mechanics

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

Stephen G. Low

2007-03-23

393

Quantum mechanics, strong emergence and ontological non-reducibility

We show that a new interpretation of quantum mechanics, in which the notion of event is defined without reference to measurement or observers, allows to construct a quantum general ontology based on systems, states and events. Unlike the Copenhagen interpretation, it does not resort to elements of a classical ontology. The quantum ontology in turn allows us to recognize that a typical behavior of quantum systems exhibits strong emergence and ontological non-reducibility. Such phenomena are not exceptional but natural, and are rooted in the basic mathematical structure of quantum mechanics.

Gambini, Rodolfo; Pullin, Jorge

2015-01-01

394

Symmetry as a foundational concept in Quantum Mechanics

Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a fundamental concept in the construction of physical systems. Based on this idea, we propose a series of postulates for describing quantum systems, and establish their relation and correspondence with axioms of standard quantum mechanics. Through some examples we show that this reformulation helps better understand some of ambiguities of standard description. Nonetheless its application is not limited to explaining confusing concept and it may be a necessary step toward a consistent model of quantum cosmology and gravity.

Ziaeepour, Houri

2015-01-01

395

Quantum mechanics, strong emergence and ontological non-reducibility

We show that a new interpretation of quantum mechanics, in which the notion of event is defined without reference to measurement or observers, allows to construct a quantum general ontology based on systems, states and events. Unlike the Copenhagen interpretation, it does not resort to elements of a classical ontology. The quantum ontology in turn allows us to recognize that a typical behavior of quantum systems exhibits strong emergence and ontological non-reducibility. Such phenomena are not exceptional but natural, and are rooted in the basic mathematical structure of quantum mechanics.

Rodolfo Gambini; Lucia Lewowicz; Jorge Pullin

2015-02-12

396

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

397

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

398

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

399

Quantum mechanics of a generalised rigid body

We consider the quantum version of Arnold's generalisation of a rigid body in classical mechanics. Thus, we quantise the motion on an arbitrary Lie group manifold of a particle whose classical trajectories correspond to the geodesics of any one-sided-invariant metric. We show how the derivation of the spectrum of energy eigenstates can be simplified by making use of automorphisms of the Lie algebra and (for groups of Type I) by methods of harmonic analysis. As examples, we consider all connected and simply-connected Lie groups up to dimension 3. This includes the universal cover of the archetypical rigid body, along with a number of new exactly-solvable models. We also discuss a possible application to the topical problem of quantising a perfect fluid.

Gripaios, Ben

2015-01-01

400

Quantum mechanics of a generalised rigid body

We consider the quantum version of Arnold's generalisation of a rigid body in classical mechanics. Thus, we quantise the motion on an arbitrary Lie group manifold of a particle whose classical trajectories correspond to the geodesics of any one-sided-invariant metric. We show how the derivation of the spectrum of energy eigenstates can be simplified by making use of automorphisms of the Lie algebra and (for groups of Type I) by methods of harmonic analysis. As examples, we consider all connected and simply-connected Lie groups up to dimension 3. This includes the universal cover of the archetypical rigid body, along with a number of new exactly-solvable models. We also discuss a possible application to the topical problem of quantising a perfect fluid.

Ben Gripaios; Dave Sutherland

2015-04-06

401

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

402

Quantum Information Theory Quantum mechanics makes probabilistic predictions about experiments lead to the development of a theory of quantum information that generalises previous notions distribution. Â· Information theory: noisy quantum states, purifications, von Neumann entropy, data compression

Burton, Geoffrey R.

403

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

404

A Causal Net Approach to Relativistic Quantum Mechanics

In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.

R. D. Bateson

2012-05-13

405

Hidden-Variables Models of Quantum Mechanics (Noncontextual and Contextual)

In the following discussion of hidden variables models of quantum mechanics the ? Hilbert space formulation of quantum mechanics\\u000a and the standard interpretation of its notation and concepts will be taken to be initially understood, even though challenges\\u000a to the standard interpretation are implicit in the proposals of ? hidden variables.\\u000a \\u000a Very soon after the formulation of the new quantum

Abner Shimony

406

Developing and Evaluating Animations for Teaching Quantum Mechanics Concepts

ERIC Educational Resources Information Center

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

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

2010-01-01

407

Chem 7940 Quantum Mechanics II Spring 2011 Chemistry 7940

Chem 7940 Quantum Mechanics II Spring 2011 Chemistry 7940 Problem Set 4 Spring 2011 Due: in class frequency in the two limits and -E0/ , i.e., k 0. 1 of 3 #12;Chem 7940 Quantum Mechanics II Spring change sign? (iii) Show that the diagonal coupling matrix elements +| d d |+ and -| d d |- (8

408

Environment-Induced Decoherence in Noncommutative Quantum Mechanics

We address the question of the appearence of ordinary quantum mechanics in the context of noncommutative quantum mechanics. We obtain the noncommutative extension of the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators. We consider the particular case of an Ohmic regime.

Joao Nuno Prata; Nuno Costa Dias

2006-12-02

409

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

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

Shan Yu; Danko Nikolic

2010-01-01

410

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

411

In Defense of a Heuristic Interpretation of Quantum Mechanics

ERIC Educational Resources Information Center

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

Healy, Eamonn F.

2010-01-01

412

Design and Validation of the Quantum Mechanics Conceptual Survey

ERIC Educational Resources Information Center

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

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

2010-01-01

413

New Potentials for Old: The Darboux Transformation in Quantum Mechanics

ERIC Educational Resources Information Center

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

Williams, Brian Wesley; Celius, Tevye C.

2008-01-01

414

Quaternionic quantum mechanics allows non-local boxes

We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows one to rule out quaternionic quantum mechanics using assumptions about communication complexity or information causality.

Matthew McKague

2009-11-09

415

Quantum Mechanics from Periodic Dynamics: the bosonic case

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

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

2010-05-04

416

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 $K_L \\rightarrow 2\\pi$ and $K_{L,S}$ semileptonic decays at LEAR or a $\\phi$ factory.

John Ellis; N. E. Mavromatos; D. V. Nanopoulos

1992-07-29

417

Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems

ERIC Educational Resources Information Center

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

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

2009-01-01

418

Depicting qudit quantum mechanics and mutually unbiased qudit theories

We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these theories in detail: qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits. The calculus allows us to analyze the structure of qudit stabilizer quantum mechanics and provides a geometrical picture of qudit stabilizer theory using D-toruses, which generalizes the Bloch sphere picture for qubit stabilizer quantum mechanics. We also use our framework to describe generalizations of Spekkens toy theory to higher dimensional systems. This gives a novel proof that qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits are operationally equivalent in three dimensions. The qudit pictorial calculus is a useful tool to study quantum foundations, understand the relationship between qubit and qudit quantum mechanics, and provide a novel, high level description of quantum information protocols.

André Ranchin

2014-12-30

419

A quantum mechanical version of Price's theorem for Gaussian states

This paper is concerned with integro-differential identities which are known in statistical signal processing as Price's theorem for expectations of nonlinear functions of jointly Gaussian random variables. We revisit these relations for classical variables by using the Frechet differentiation with respect to covariance matrices, and then show that Price's theorem carries over to a quantum mechanical setting. The quantum counterpart of the theorem is established for Gaussian quantum states in the framework of the Weyl functional calculus for quantum variables satisfying the Heisenberg canonical commutation relations. The quantum mechanical version of Price's theorem relates the Frechet derivative of the generalized moment of such variables with respect to the real part of their quantum covariance matrix with other moments. As an illustrative example, we consider these relations for quadratic-exponential moments which are relevant to risk-sensitive quantum control.

Igor G. Vladimirov

2014-09-15

420

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

421

BYU PHYS 731 Statistical Mechanics Chapter 7: Sethna Professor Manuel Berrondo Quantum Statistical #12;BYU PHYS 731 Statistical Mechanics Chapter 7: Sethna Professor Manuel Berrondo Quantum ensembles: = n pn |n n| density matrix 2 #12;BYU PHYS 731 Statistical Mechanics Chapter 7: Sethna Professor

Hart, Gus

422

Chirality, quantum mechanics, and biological determinism

NASA Astrophysics Data System (ADS)

The holy grail of astrobiology is the discovery of a second sample of life that has emerged de novo, independently of life on Earth (as opposed to extraterrestrial life that shares a common origin with terrestrial life via a panspermia process). It would then be possible to separate aspects of biology that are lawlike and expected from those that are accidental and contingent, and thus to address the question of whether the laws of nature are intrinsically bio-friendly. The popular assumption that life is an almost inevitable product of physics and chemistry, and therefore widespread in the universe, is known as biological determinism. It remains an open question whether biological determinism is correct, as there is little direct evidence in its favour from fundamental physics. Homochirality is a deep property of known life, and provides an important test case for the competing ideas of contingency versus lawfulness - or chance versus necessity. Conceivably, a chiral signature is imprinted on life by fundamental physics via parity-violating mixing of the weak and electromagnetic interactions. If so, homochirality would be universal and lawlike. On the other hand, it may be the result of chance: a random molecular accident during the pre-biotic phase. If the latter explanation is correct, one could expect that a second sample of life may have opposite chiral signature even if it resembled known life in its basic biochemistry. There is thus a curious obverse relationship between chirality and biogenesis in relation to biological determinism. If the chiral signature of life is the product of chance, we may hope to discover "mirror life" (i.e. organisms with opposite chiral signature) as evidence of a second genesis, and the latter would establish that life's emergence from non-life is quasi-deterministic. On the other hand, if the chiral signature is determined by fundamental physics, then it may be much harder to establish an independent origin for extraterrestrial life with biochemical make-up resembling that of known life. Whilst the experimental search for a second sample of life - possibly by detecting a chiral "anomaly" - continues, some theoretical investigations may be pursued to narrow down the options. Chiral determinism would be an intrinsically quantum process. There are hints that quantum mechanics plays a key role in biology, but the claim remains contentious. Here I review some of the evidence for quantum aspects of biology. I also summarize some proposals for testing biological determinism by seeking evidence for a multiple genesis events on Earth, and for identifying extant "alien microbes" - micro-organisms descended from an independent origin from familiar life.

Davies, P. C. W.

2006-08-01

423

Information Security and Quantum Mechanics: Security of Quantum Protocols

The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is found that unitary bases are central to both encryption of quantum information, as well as the generation of states used in generalized quantum key distribution (which are called mutually unbiased bases). A one-to-one correspondence between certain unitary bases and mutually unbiased bases is found. Finally, a new protocol for making anonymous classical broadcasts is given along with a security proof. An experimental procedure to implement this protocol is also given. In order to prove these new results, some new bounds for accessible information of quantum sources are obtained.

P. Oscar Boykin

2002-10-28

424

QUANTUM STATISTICAL MECHANICS OVER FUNCTION FIELDS CATERINA CONSANI AND MATILDE MARCOLLI

QUANTUM STATISTICAL MECHANICS OVER FUNCTION FIELDS CATERINA CONSANI AND MATILDE MARCOLLI 1 interplay between quantum statistical mechanics and arithmetic. In the case of number fields, the symmetries]. Moreover, very recently Benoit Jacob constructed an interesting quantum statistical mechanical system

Marcolli, Matilde

425

Calendar effects in quantum mechanics in view of interactive holography

NASA Astrophysics Data System (ADS)

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

Berkovich, Simon

2013-04-01

426

Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics

NASA Astrophysics Data System (ADS)

In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called quantum annealing. The most typical instance is quantum adiabatic computation based on the adiabatic theorem. The quantum adiabatic computation as discussed in the other chapter, unfortunately, has a crucial bottleneck for a part of the optimization problems. We here introduce several recent trials to overcome such a weakpoint by use of developments in statistical mechanics. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.

Ohzeki, Masayuki

2013-09-01

427

Is Holographic Entropy and Gravity the result of Quantum Mechanics?

In this paper we suggest a connection between quantum mechanics and Verlinde's recently proposed entropic force theory for the laws of Newton. We propose an entropy based on the quantum mechanical probability density distribution. With the assumption that the holographic principle holds we propose that our suggested quantum entropy generalizes the Bekenstein entropy used by Verlinde in his approach. Based on this assumption we suggest that Verlinde's entropic theory of gravity has a quantum mechanical origin. We establish a reformulation of the Newtonian potential for gravity based on this quantum mechanical entropy. We also discuss the notion of observation and the correspondence to classical physics. Finally we give a discussion, a number of open problems and some concluding remarks.

Joakim Munkhammar

2010-03-09

428

Is string interaction the origin of quantum mechanics?

NASA Astrophysics Data System (ADS)

String theory was developed by demanding consistency with quantum mechanics. In this paper we wish to reverse the reasoning. We pretend that open string field theory is a fully consistent definition of the theory - it is at least a self-consistent sector. Then we find in its structure that the rules of quantum mechanics emerge from the non-commutative nature of the basic string joining/splitting interactions. Thus, rather than assuming the quantum commutation rules among the usual canonical variables we derive them from the physical process of string interactions. Morally we could apply such an argument to M-theory to cover quantum mechanics for all physics. If string or M-theory really underlies all physics, it seems that the door has been opened to an explanation of the origins of quantum mechanics from the physical processes point of view.

Bars, Itzhak; Rychkov, Dmitry

2014-12-01

429

Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

NASA Astrophysics Data System (ADS)

This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.

Plotnitsky, Arkady

2014-12-01

430

Statistical Mechanics of Quantum-Classical Systems with Holonomic Constraints

The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained system arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear response function of constrained quantum-classical systems contains non-trivial additional terms which are absent in the response of unconstrained systems.

Alessandro Sergi

2005-11-15

431

A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation

The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief introduction to quantum computation, covering such topics as elementary quantum computing devices, wiring diagrams, the no-cloning theorem, quantum teleportation, Shor's algorithm, Grover's algorithm. Many examples are given. A table of contents as well as an index are provided for readers who wish to "pick and choose." Since this paper is intended for a diverse audience, it is written in an informal style at varying levels of difficulty and sophistication from the very elementary to the more advanced.

Samuel J. Lomonaco; jr

2000-07-17

432

High-efficiency quantum state transfer and quantum memory using a mechanical oscillator

NASA Astrophysics Data System (ADS)

We analyze an optomechanical system that can be used to efficiently transfer a quantum state between an optical cavity and a distant mechanical oscillator coupled to a second optical cavity. We show that for a moderate mechanical Q factor it is possible to achieve a transfer efficiency of 99.4 % by using adjustable cavity damping rates and destructive interference. We also show that the quantum mechanical oscillator can be used as a quantum memory device with an efficiency of 96 % employing a pulsed optomechanical coupling. Although the mechanical dissipation slightly decreases the efficiency, its effect can be significantly reduced by designing a high-Q mechanical oscillator.

Sete, Eyob A.; Eleuch, H.

2015-03-01

433

Potentiality and Contradiction in Quantum Mechanics

Following J.-Y.B\\'eziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in \\cite{are14}. Our conclusion was that such states are \\ita{contraries} (\\ita{i.e.} both can be false, but both cannot be true), contradicting previous analyzes that have led to different results, such as those claiming that those states represent \\ita{contradictory} properties (\\ita{i. e.} they must have opposite truth values). In this chapter we bring the issue once again into the center of the stage, but now discussing the metaphysical presuppositions which underlie each kind of analysis and which lead to each kind of result, discussing in particular the idea that superpositions represent potential contradictions. We shall argue that the analysis according to which states in superposition are contrary rather than contradictory is still more plausible.

Jonas R. B. Arenhart; Décio Krause

2014-06-07

434

Linking Quantum Mechanics to Freshman Physics

NASA Astrophysics Data System (ADS)

First-year quantum mechanics can be linked to introductory physics. One example is the Mossbauer effect, which is explained using a simple solution to Schrodinger's equation involving the Dirac delta function. Generalization to N coupled harmonic oscillators shows that the equality of the forces exerted by winner and loser in the game of "tug-of-war" is only an approximation because Newton's third law of motion is not valid (unless phonon momentum is considered). Another example is a treatment of the Gaussian wavepacket which involves less algebra than found in standard textbooks, yet shows that the peak moves according to the familiar equation of motion x = vt + (1/2)at^2 when the applied force is uniform. Finally, a rendition of "Turkey in the Straw" on the viola illustrates Heisenberg's uncertainty principle, which can be written in the less mysterious form, f=(N+-.1)/T , where N cycles are counted in T seconds. Students experience this uncertainty as they try to measure the frequency of a stretched slinky.

Vandegrift, Guy

1998-10-01

435

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. PMID:24491259

Shim, Irene; Lindow, Morten; Ørum, Henrik

2014-01-01

436

The representation of numbers in quantum mechanics.

Earlier work on modular arithmetic of k-ary representations of length L of the natural numbers in quantum mechanics is extended here to k-ary representations of all natural numbers, and to integers and rational numbers. Since the length L is indeterminate, representations of states and operators using creation and annihilation operators for bosons and fermions are defined. Emphasis is on definitions and properties of operators corresponding to the basic operations whose properties are given by the axioms for each type of number. The importance of the requirement of efficient implementability for physical models of the axioms is emphasized. Based on this, successor operations for each value of j corresponding to addition of k {l_brace}j-1{r_brace} if j>0 and k {l_brace}j{r_brace} if j<0 are defined. It follows from the efficient implementability of these successors, which is the case for all computers, that implementation of the addition and multiplication operators, which are defined in terms of polynomially many iterations of the successors, should be efficient. This is not the case for definitions based on the successor for j=1 only. This is the only successor defined in the usual axioms of arithmetic.

Benioff, P.; Physics

2002-12-01

437

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

438

The structure of supersymmetry in ${\\cal PT}$ symmetric quantum mechanics

The structure of supersymmetry is analyzed systematically in ${\\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\\cal PT}$ symmetric quantum mechanical theories. We show that there is a richer structure present in these theories compared to the conventional theories associated with Hermitian Hamiltonians. We bring out various properties associated with these supersymmetric systems and generalize such quantum mechanical theories to higher dimensions as well as to the case of one dimensional shape invariant potentials.

D. Bazeia; Ashok Das; L. Greenwood; L. Losano

2009-03-17

439

The actual content of quantum theoretical kinematics and mechanics

NASA Technical Reports Server (NTRS)

First, exact definitions are supplied for the terms: position, velocity, energy, etc. (of the electron, for instance), such that they are valid also in quantum mechanics. Canonically conjugated variables are determined simultaneously only with a characteristic uncertainty. This uncertainty is the intrinsic reason for the occurrence of statistical relations in quantum mechanics. Mathematical formulation is made possible by the Dirac-Jordan theory. Beginning from the basic principles thus obtained, macroscopic processes are understood from the viewpoint of quantum mechanics. Several imaginary experiments are discussed to elucidate the theory.

Heisenberg, W.

1983-01-01

440

Is there a measurement-only version of quantum mechanics?

Tensor universality often implies that multi-partite quantum-state processing is determined by what happens in totally disentangled cases. In independent systems relative time direction for the parts is arbitrary. This hints that time may be linked to entanglement and measurements and that there may be a measurement-only version of quantum mechanics. One-way quantum computation suggests that this may be possible.

George Svetlichny

2009-03-24

441

Quantum mechanical fragment methods based on partitioning atoms or partitioning coordinates.

Conspectus The development of more efficient and more accurate ways to represent reactive potential energy surfaces is a requirement for extending the simulation of large systems to more complex systems, longer-time dynamical processes, and more complete statistical mechanical sampling. One way to treat large systems is by direct dynamics fragment methods. Another way is by fitting system-specific analytic potential energy functions with methods adapted to large systems. Here we consider both approaches. First we consider three fragment methods that allow a given monomer to appear in more than one fragment. The first two approaches are the electrostatically embedded many-body (EE-MB) expansion and the electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE), which we have shown to yield quite accurate results even when one restricts the calculations to include only electrostatically embedded dimers. The third fragment method is the electrostatically embedded molecular tailoring approach (EE-MTA), which is more flexible than EE-MB and EE-MB-CE. We show that electrostatic embedding greatly improves the accuracy of these approaches compared with the original unembedded approaches. Quantum mechanical fragment methods share with combined quantum mechanical/molecular mechanical (QM/MM) methods the need to treat a quantum mechanical fragment in the presence of the rest of the system, which is especially challenging for those parts of the rest of the system that are close to the boundary of the quantum mechanical fragment. This is a delicate matter even for fragments that are not covalently bonded to the rest of the system, but it becomes even more difficult when the boundary of the quantum mechanical fragment cuts a bond. We have developed a suite of methods for more realistically treating interactions across such boundaries. These methods include redistributing and balancing the external partial atomic charges and the use of tuned fluorine atoms for capping dangling bonds, and we have shown that they can greatly improve the accuracy. Finally we present a new approach that goes beyond QM/MM by combining the convenience of molecular mechanics with the accuracy of fitting a potential function to electronic structure calculations on a specific system. To make the latter practical for systems with a large number of degrees of freedom, we developed a method to interpolate between local internal-coordinate fits to the potential energy. A key issue for the application to large systems is that rather than assigning the atoms or monomers to fragments, we assign the internal coordinates to reaction, secondary, and tertiary sets. Thus, we make a partition in coordinate space rather than atom space. Fits to the local dependence of the potential energy on tertiary coordinates are arrayed along a preselected reaction coordinate at a sequence of geometries called anchor points; the potential energy function is called an anchor points reactive potential. Electrostatically embedded fragment methods and the anchor points reactive potential, because they are based on treating an entire system by quantum mechanical electronic structure methods but are affordable for large and complex systems, have the potential to open new areas for accurate simulations where combined QM/MM methods are inadequate. PMID:24841937

Wang, Bo; Yang, Ke R; Xu, Xuefei; Isegawa, Miho; Leverentz, Hannah R; Truhlar, Donald G

2014-09-16

442

Removing redundancy in relativistic quantum mechanics

It is proposed that the Dirac equation, as normally interpreted, incorporates intrinsic redundancies whose removal necessarily leads to an enormous gain in calculating power and physical interpretation. Streamlined versions of the Dirac equation can be developed which remove the redundancies and singularities from many areas of quantum physics while giving quantum representations to specific particle states.

Peter Rowlands

2005-07-27

443

"Mysticism" in Quantum Mechanics: The Forgotten Controversy

ERIC Educational Resources Information Center

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

Marin, Juan Miguel

2009-01-01

444

Lectures on Black Hole Quantum Mechanics

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,

Frank Wilczek

1998-01-01

445

On a commutative ring structure in quantum mechanics

In this article, I propose a concept of the $p$-on which is modelled on the multi-photon absorptions in quantum optics. It provides a commutative ring structure in quantum mechanics. Using it, I will give an operator representation of the Riemann $\\zeta$ function.

Shigeki Matsutani

2009-10-10

446

Quantum Mechanics as a Science -Religion Bridge By Stanley Klein

Quantum Mechanics as a Science - Religion Bridge By Stanley Klein (May 1, 2002) Stanley Klein an ideal framework for the science-religion duality. This framework provides a relativistic ontology and science/religion violate our intuitions in the same way. Before setting theological issues of quantum

Klein, Stanley

447

NESS in quantum statistical mechanics VOJKAN JASI C1

NESS in quantum statistical mechanics VOJKAN JASI ´C1 , CLAUDE-ALAIN PILLET2 1 Department@univ-tln.fr In this article we describe the construction of canonical Non-Equilibrium Steady States (NESS) for a small quantum]). Definition 1 Let be a state on O. We say that + is a NESS of V associated to the reference state

Jaksic, Vojkan

448

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

449

Thermal Vacuum Polarization Using the Quantum Mechanical Path Integral

It has been shown how the quantum mechanical path integral can be used to do perturbative calculations in both quantum and thermal field theory to any order of the loop expansion. However, it is not readily apparent how gauge invariance is made manifest in this approach; in this paper we demonstrate how the vacuum polarization in electrodynamics at one-loop order

D. G. C. McKeon

1997-01-01

450

Mechanism of Selective Ammoxidation of Propene to Acrylonitrile on Bismuth Molybdates from Quantum ammoxidation of propene to acrylonitrile by bismuth molybdates, we report quantum mechanical studies (using stages of this industry, acrylonitrile was produced by propene on simple bismuth and molybdenum oxide

Goddard III, William A.

451

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.

F. S. Bemfica; H. O. Girotti

2008-02-11

452

Quantum mechanics helps in learning for more intelligent robot

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

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

2005-06-18

453

Particles, Waves, and the Interpretation of Quantum Mechanics

ERIC Educational Resources Information Center

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

Christoudouleas, N. D.

1975-01-01

454

A Low Temperature Expansion for Matrix Quantum Mechanics

We analyze solutions to loop-truncated Schwinger-Dyson equations in massless N=2 and N=4 Wess-Zumino matrix quantum mechanics at finite temperature, where conventional perturbation theory breaks down due to IR divergences. We find a rather intricate low temperature expansion that involves fractional power scaling in the temperature, based on a consistent "soft collinear" approximation. We conjecture that at least in the N=4 matrix quantum mechanics, such scaling behavior holds to all perturbative orders in the 1/N expansion. We discuss some preliminary results in analyzing the gauged supersymmetric quantum mechanics using Schwinger-Dyson equations, and comment on the connection to metastable microstates of black holes in the holographic dual of BFSS matrix quantum mechanics.

Ying-Hsuan Lin; Shu-Heng Shao; Yifan Wang; Xi Yin

2013-04-08

455

Chemistry 6491: Quantum Mechanics Requirements and Grading Scheme

a minimal understanding of the subject. Pass/fail students are required to take both tests and the final and receive an overall passing grade. Topics Unit I: Fundamentals of Quantum Mechanics (A) Introduction

Sherrill, David

456

Path integral in energy representation in quantum mechanics

In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it is much more better defined than the usual functional integral. We investigate this representation from various directions and compare such approach to quantum mechanics with the standard ones.

P. Putrov

2007-08-30

457

Multi-instantons in large N Matrix Quantum Mechanics

We calculate the multi-instanton corrections to the ground state energy in large $N$ Matrix Quantum Mechanics. We find that they can be obtained, through a non-perturbative difference equation, from the multi-instanton series in conventional Quantum Mechanics, as determined by the exact WKB method. We test our results by verifying that the one-instanton correction controls the large order behavior of the $1/N$ expansion in the quartic potential and in the $c=1$ string.

Marcos Marino; Pavel Putrov

2009-11-16

458

Quantum mechanics and the social sciences: After hermeneutics

NASA Astrophysics Data System (ADS)

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

Heelan, Patrick A.

1995-04-01

459

$\\cN$-FOLD SUPERSYMMETRY IN QUANTUM MECHANICAL MATRIX MODELS

NASA Astrophysics Data System (ADS)

We formulate ?-fold supersymmetry in quantum mechanical matrix models. As an example, we construct general two-by-two Hermitian matrix two-fold supersymmetric quantum mechanical systems. We find that there are two inequivalent such systems, both of which are characterized by two arbitrary scalar functions, and one of which does not reduce to the scalar system. The obtained systems are all weakly quasi-solvable.

Tanaka, Toshiaki

2012-03-01

460

Quantum mechanics, Bayes' theorem and the conjunction fallacy

In the present article we consider the conjunction fallacy, a well known cognitive heuristic experimentally tested in cognitive science, which occurs for intuitive judgments in situations of bounded rationality. We show that the quantum formalism can be used to describe in a very simple way this fallacy in terms of interference effect. We evidence that the quantum formalism leads quite naturally to violations of Bayes' rule when considering the probability of the conjunction of two events. Thus we suggest that in cognitive science the formalism of quantum mechanics can be used to describe a \\textit{quantum regime}, the bounded-rationality regime, where the cognitive heuristics are valid.

R. Franco

2007-05-17

461

Quantum Mechanics and the Origin of Life

NASA Astrophysics Data System (ADS)

The race to build a quantum computer has led to a radical re-evaluation of the concept of information. In this paper I conjecture that life, defined as an information processing and replicating system, may be exploiting the considerable efficiency advantages offered by quantum computation, and that quantum information processing may dramatically shorten the odds for life originating from a random chemical soup. The plausibility of this conjecture rests, however, on life somehow circumventing the decoherence effects of the environment. I offer some speculations on ways in which this might happen.

Davies, Paul

2004-06-01

462

NASA Astrophysics Data System (ADS)

We present an implementation of analytical quantum mechanical molecular gradients within the polarizable embedding (PE) model to allow for efficient geometry optimizations and vibrational analysis of molecules embedded in large, geometrically frozen environments. We consider a variational ansatz for the quantum region, covering (multiconfigurational) self-consistent-field and Kohn-Sham density functional theory. As the first application of the implementation, we consider the internal vibrational Stark effect of the C=O group of acetophenone in different solvents and derive its vibrational linear Stark tuning rate using harmonic frequencies calculated from analytical gradients and computed local electric fields. Comparisons to PE calculations employing an enlarged quantum region as well as to a non-polarizable embedding scheme show that the inclusion of mutual polarization between acetophenone and water is essential in order to capture the structural modifications and the associated frequency shifts observed in water. For more apolar solvents, a proper description of dispersion and exchange-repulsion becomes increasingly important, and the quality of the optimized structures relies to a larger extent on the quality of the Lennard-Jones parameters.

List, Nanna Holmgaard; Beerepoot, Maarten T. P.; Olsen, Jógvan Magnus Haugaard; Gao, Bin; Ruud, Kenneth; Jensen, Hans Jørgen Aagaard; Kongsted, Jacob

2015-01-01

463

Is quantum mechanics based on an invariance principle?

Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are induced by isotropic space dilations. This invariance imposes a change in the laws of classical mechanics that exactly corresponds to the transition to quantum mechanics. The Schroedinger equation appears jointly with a second nonlinear equation describing non-unitary processes. Unitary and non-unitary evolutions are exclusive and appear sequentially in time. The non-unitary equation admits solutions that seem to correspond to the collapse of the wave function.

Leon Brenig

2007-04-27

464

Bohmian Trajectories as the Foundation of Quantum Mechanics

Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schroedinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. Indeed, they succeed in serving that purpose in the context of a theory known as Bohmian mechanics, to which this article is an introduction.

Sheldon Goldstein; Roderich Tumulka; Nino Zanghi

2009-12-14

465

Duality, Mechanical Wave Theory, New Quantum Operators and Nonlinear Equations in Quantum Theory

Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various mechanical equations, and may be derive some new results. It is called the mechanical wave theory. From this we derive new operators which represent more physical quantities. Further, we propose some nonlinear equations and their solutions, which may be probably applied to quantum theory.

Yi-Fang Chang

2010-08-17

466

Quantum network of superconducting qubits through opto-mechanical interface

We propose a scheme to realize quantum networking of superconducting qubits based on the opto-mechanical interface. The superconducting qubits interact with the microwave photons, which then couple to the optical photons through the opto-mechanical interface. The interface generates a quantum link between superconducting qubits and optical flying qubits with tunable pulse shapes and carrier frequencies, enabling transmission of quantum information to other superconducting or atomic qubits. We show that the scheme works under realistic experimental conditions and it also provides a way for fast initialization of the superconducting qubits under 1 K instead of 20 mK operation temperature.

Zhang-qi Yin; W. L. Yang; L. Sun; L. M. Duan

2015-01-08

467

Is Quantum Mechanics Incompatible with Newton's First Law of Motion

Quantum mechanics (QM)clearly violates Newton's First Law of Motion (NFLM) in the quantum domain. This paper examines an apparent incompatibility between the predictions of QM in the classical limit, and that of classical mechanics (CM) with respect to NFLM. In the process, a general argument is made that such a disparity may be found commonly for a wide variety of quantum predictions in the classical limit. The meaning of the classical limit is examined. Critical views regarding QM by Schrodinger, Bohm, Bell, Clauser, and others are presented as a perspective for the motivation of the present work.

Rabinowitz, Mario

2007-01-01

468

From Quantum Mechanics to Quantum Field Theory: The Hopf route

We show that the combinatorial numbers known as {\\em Bell numbers} are generic in quantum physics. This is because they arise in the procedure known as {\\em Normal ordering} of bosons, a procedure which is involved in the evaluation of quantum functions such as the canonical partition function of quantum statistical physics, {\\it inter alia}. In fact, we shall show that an evaluation of the non-interacting partition function for a single boson system is identical to integrating the {\\em exponential generating function} of the Bell numbers, which is a device for encapsulating a combinatorial sequence in a single function. We then introduce a remarkable equality, the Dobinski relation, and use it to indicate why renormalisation is necessary in even the simplest of perturbation expansions for a partition function. Finally we introduce a global algebraic description of this simple model, giving a Hopf algebra, which provides a starting point for extensions to more complex physical systems.

Solomon, Allan I; Blasiak, Pawel; Horzela, Andrzej; Penson, Karol A

2010-01-01

469

Quantum Mechanics in Biology: Photoexcitations in DNA

NASA Astrophysics Data System (ADS)

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

Bittner, Eric R.; Czader, Arkadiusz

470

Bohmian Mechanics with Complex Action: A New Trajectory-Based Formulation of Quantum Mechanics

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

Yair Goldfarb; Ilan Degani; David J. Tannor

2006-04-20

471

OPERA data and The Equivalence Postulate of Quantum Mechanics

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

Alon E. Faraggi

2011-10-24

472

Whether quantum mechanics can be almighty even in information science

We discuss that there is a crucial contradiction within quantum mechanics. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the directions in a spin-1/2 system. The quantum predictions within the formalism of von Neumann's projective measurement cannot coexist with the proposition concerning the existence of the directions. Therefore, we have to give up either the existence of the directions or the formalism of von Neumann's projective measurement. Hence there is a crucial contradiction within the Hilbert space formalism of the quantum theory. This implies that there is no axiomatic system for the quantum theory. This also reveals that we need new physical theories in order to explain the handing of raw experimental data. We discuss that this crucial contradiction makes the quantum-theoretical formulation of Deutsch's algorithm questionable.

Koji Nagata; Tadao Nakamura

2008-11-28

473

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

474

The M\\"obius Symmetry of Quantum Mechanics

The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under $D$--dimensional M\\"obius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global M\\"obius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the M\\"obius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.

Faraggi, Alon E

2015-01-01

475

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

476

Quantum Mechanical Oscillators: NIST-7 and Beyond

NASA Astrophysics Data System (ADS)

Time and its inverse, frequency, are the most precisely measurable of all quantities. We routinely make measurements to a precision of a part in 10^12 in just one second and a part in 10^17 in one day. As a result of this measurement precision, some other units are cast in terms of frequency; e. g., voltage through the Josephson volt and length through the defined speed of light. Additionally, practical measurements are often made with frequency transducers; e. g., quartz resonator film thickness monitors, temperature probes, and pressure sensors. Time and frequency are also very important in modern telecommunications, navigation, and security systems. For all of these reasons, we need very highly accurate and widely available standards of frequency and time. We use ``quantum mechanical oscillators,'' transitions in atoms and molecules, for these standards because their systematic biases can be determined to a high degree and their frequency is reproducible any place in the universe within the known laws of physics. Fortunately, this area of technology and atomic physics is very dynamic, often leading advances in spectroscopic resolution and technology. Standards for time and frequency have improved five orders of magnitude over the last 35 years and there is no end in sight. We will briefly discuss the historical development of atomic beam standards to show how accuracy has evolved. We will then discuss the design and accuracy evaluation of NIST-7, a state-of-the-art thermal-cesium-beam magnetic-resonance spectrometer with optical state preparation and detection, which is the current US primary frequency standard. Development of this standard has been accompanied by major advances in error analysis methodology. When describing NIST-7 in the terms of an atomic frequency standard, we say each systematic bias can ultimately be evaluated to a fractional frequency uncertainty of a few parts in 10^16 which will result in an overall uncertainty in the accuracy of the standard of only a few parts in 10^15. However, when viewed as a spectrometer, this level of performance is equivalent to splitting a line with absolute accuracy of a part in 10^7! This represents unprecedented knowledge of lineshape physics and instrumentation effects. Work is already being conducted on the next several generations of standards ranging from atomic fountains to cooled trapped ions involving optical frequency metrology.

Drullinger, Robert E.

1996-03-01

477