Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation
NASA Astrophysics Data System (ADS)
Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter
2013-08-01
The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.
Biological applications of hybrid quantum mechanics/molecular mechanics calculation.
Kang, Jiyoung; Hagiwara, Yohsuke; Tateno, Masaru
2012-01-01
Since in most cases biological macromolecular systems including solvent water molecules are remarkably large, the computational costs of performing ab initio calculations for the entire structures are prohibitive. Accordingly, QM calculations that are jointed with MM calculations are crucial to evaluate the long-range electrostatic interactions, which significantly affect the electronic structures of biological macromolecules. A UNIX-shell-based interface program connecting the quantum mechanics (QMs) and molecular mechanics (MMs) calculation engines, GAMESS and AMBER, was developed in our lab. The system was applied to a metalloenzyme, azurin, and PU.1-DNA complex; thereby, the significance of the environmental effects on the electronic structures of the site of interest was elucidated. Subsequently, hybrid QM/MM molecular dynamics (MD) simulation using the calculation system was employed for investigation of mechanisms of hydrolysis (editing reaction) in leucyl-tRNA synthetase complexed with the misaminoacylated tRNA(Leu), and a novel mechanism of the enzymatic reaction was revealed. Thus, our interface program can play a critical role as a powerful tool for state-of-the-art sophisticated hybrid ab initio QM/MM MD simulations of large systems, such as biological macromolecules. PMID:22536015
NASA Astrophysics Data System (ADS)
Leong, Max Kangchien
A method of combined quantum mechanics/molecular mechanics has been developed to model larger organometallic and metallobiochemical systems where neither quantum mechanics nor molecular mechanics, applied separately, can solve the problem. An electronically transparent interface, which allows charge transfers between the quantum and classical fragments, is devised and realized by employing a special iterative procedure of double (intrafragment and interfragment) self-consistent calculations. The combined QM/MM scheme was successfully applied to model iron picket-fence porphyrin, vitamin B12, aquocobalamin, and vitamin B12 coenzyme molecules.
Thellamurege, Nandun M; Cui, Fengchao; Li, Hui
2013-08-28
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
Ibrahim, Mahmoud A A
2011-10-24
The performance of semiempirical molecular-orbital methods--MNDO, MNDO-d, AM1, RM1, PM3 and PM6--in describing halogen bonding was evaluated, and the results were compared with molecular mechanical (MM) and quantum mechanical (QM) data. Three types of performance were assessed: (1) geometrical optimizations and binding energy calculations for 27 halogen-containing molecules complexed with various Lewis bases (Two of the tested methods, AM1 and RM1, gave results that agree with the QM data.); (2) charge distribution calculations for halobenzene molecules, determined by calculating the solvation free energies of the molecules relative to benzene in explicit and implicit generalized Born (GB) solvents (None of the methods gave results that agree with the experimental data.); and (3) appropriateness of the semiempirical methods in the hybrid quantum-mechanical/molecular-mechanical (QM/MM) scheme, investigated by studying the molecular inhibition of CK2 protein by eight halobenzimidazole and -benzotriazole derivatives using hybrid QM/MM molecular-dynamics (MD) simulations with the inhibitor described at the QM level by the AM1 method and the rest of the system described at the MM level. The pure MM approach with inclusion of an extra point of positive charge on the halogen atom approach gave better results than the hybrid QM/MM approach involving the AM1 method. Also, in comparison with the pure MM-GBSA (generalized Born surface area) binding energies and experimental data, the calculated QM/MM-GBSA binding energies of the inhibitors were improved by replacing the G(GB,QM/MM) solvation term with the corresponding G(GB,MM) term. PMID:21942911
Roopam Khare; Steven L. Mielke; Jeffrey T. Paci; Sulin Zhang; Roberto Ballarini; George C. Schatz; Ted Belytschko
2007-01-01
Coupled quantum mechanical\\/molecular mechanical (QM\\/MM) calculations were used to study the effects of large defects and cracks on the mechanical properties of carbon nanotubes and graphene sheets. The semi-empirical method PM3 was used to treat the QM subdomains and a Tersoff-Brenner potential was used for the molecular mechanics; some of the QM calculations were also done using density functional theory
Caratzoulas, S.; Vlachos, Dion G.
2011-01-01
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.
Tvaroška, Igor
2015-02-11
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
Arafet, Kemel; Ferrer, Silvia; Moliner, Vicent
2015-06-01
Cruzain is a primary cysteine protease expressed by the protozoan parasite Trypanosoma cruzi during Chagas disease infection, and thus, the development of inhibitors of this protein is a promising target for designing an effective therapy against the disease. In this paper, the mechanism of inhibition of cruzain by two different irreversible peptidyl halomethyl ketones (PHK) inhibitors has been studied by means of hybrid quantum mechanics/molecular mechanics-molecular dynamics (MD) simulations to obtain a complete representation of the possible free energy reaction paths. These have been traced on free energy surfaces in terms of the potential of mean force computed at AM1d/MM and DFT/MM levels of theory. An analysis of the possible reaction mechanisms of the inhibition process has been performed showing that the nucleophilic attack of an active site cysteine, Cys25, on a carbon atom of the inhibitor and the cleavage of the halogen-carbon bond take place in a single step. PClK appears to be much more favorable than PFK from a kinetic point of view. This result would be in agreement with experimental studies in other papain-like enzymes. A deeper analysis of the results suggests that the origin of the differences between PClK and PFK can be the different stabilizing interactions established between the inhibitors and the residues of the active site of the protein. Any attempt to explore the viability of the inhibition process through a stepwise mechanism involving the formation of a thiohemiketal intermediate and a three-membered sulfonium intermediate has been unsuccessful. Nevertheless, a mechanism through a protonated thiohemiketal, with participation of His159 as a proton donor, appears to be feasible despite showing higher free energy barriers. Our results suggest that PClK can be used as a starting point to develop a proper inhibitor of cruzain. PMID:25965914
Yang, Seongeun; Cho, Minhaeng
2009-10-01
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 H(2)O is modeled with the TIP3P water. The atomic partial charges are obtained from the Lowdin population analysis, which gives consistent IR spectral profiles irrespective of the basis sets used. The simulated VCD spectrum by a polyproline II(P(II))-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 P(II) conformer is much lower than the other ones at all basis levels used. The simulated VCD spectrum of alpha-helix averaged over five trajectories has the reverse sign pattern compared to the P(II) spectrum and is found to be consistent with the previously observed spectral features of alpha-helical polypeptides. The sign patterns of the beta-strand VCD spectrum are qualitatively similar to the experimental spectra of beta-sheet rich proteins. The VCD spectra obtained from the trajectories containing several extended conformers such as beta and P(II) are not clearly distinguishable from the beta-strand-dominant spectra. It is interesting that the P(II) 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 P(II) 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. PMID:19814574
NASA Astrophysics Data System (ADS)
Philipp, Dean Michael
Methodology is discussed for mixed ab initio quantum mechanics/molecular mechanics modeling of systems where the quantum mechanics (QM) and molecular mechanics (MM) regions are within the same molecule. The ab initio QM calculations are at the restricted Hartree-Fock level using the pseudospectral method of the Jaguar program while the MM part is treated with the OPLS force fields implemented in the IMPACT program. The interface between the QM and MM regions, in particular, is elaborated upon, as it is dealt with by ``breaking'' bonds at the boundaries and using Boys-localized orbitals found from model molecules in place of the bonds. These orbitals are kept frozen during QM calculations. The mixed modeling presented here can be used for single point energy calculations and geometry optimizations. Results from tests of the method to find relative conformational energies and geometries of alanine tetrapeptides are presented along with comparisons to pure QM and pure MM calculations.
P. K. Biswas
We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical QM-molecular-mechanical MM calculations. To remedy the nonphysical QM\\/MM Coulomb interaction at short distances arising from a point electrostatic potential ESP charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge
P. K. Biswas; V. Gogonea
2005-01-01
We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical (QM)-molecular-mechanical (MM) calculations. To remedy the nonphysical QM\\/MM Coulomb interaction at short distances arising from a point electrostatic potential (ESP) charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge
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
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.
Ortega-Carrasco, Elisabeth; Lledós, Agustí; Maréchal, Jean-Didier
2014-01-01
In recent years, the design of artificial metalloenzymes obtained by the insertion of homogeneous catalysts into biological macromolecules has become a major field of research. These hybrids, and the corresponding X-ray structures of several of them, are offering opportunities to better understand the synergy between organometallic and biological subsystems. In this work, we investigate the resting state and activation process of a hybrid inspired by an oxidative haemoenzyme but presenting an unexpected reactivity and structural features. An extensive series of quantum mechanics/molecular mechanics calculations show that the resting state and the activation processes of the novel enzyme differ from naturally occurring haemoenzymes in terms of the electronic state of the metal, participation of the first coordination sphere of the metal and the dynamic process. This study presents novel insights into the sensitivity of the association between organometallic and biological partners and illustrates the molecular challenge that represents the design of efficient enzymes based on this strategy. PMID:24829279
NASA Astrophysics Data System (ADS)
Jeon, Jonggu; Cho, Minhaeng
2010-06-01
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.
Zeng Xiancheng; Hu Hao; Hu Xiangqian; Yang Weitao [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States)
2009-04-28
A quantum mechanical/molecular mechanical minimum free energy path (QM/MM-MFEP) method was developed to calculate the redox free energies of large systems in solution with greatly enhanced efficiency for conformation sampling. The QM/MM-MFEP method describes the thermodynamics of a system on the potential of mean force surface of the solute degrees of freedom. The molecular dynamics (MD) sampling is only carried out with the QM subsystem fixed. It thus avoids 'on-the-fly' QM calculations and thus overcomes the high computational cost in the direct QM/MM MD sampling. In the applications to two metal complexes in aqueous solution, the new QM/MM-MFEP method yielded redox free energies in good agreement with those calculated from the direct QM/MM MD method. Two larger biologically important redox molecules, lumichrome and riboflavin, were further investigated to demonstrate the efficiency of the method. The enhanced efficiency and uncompromised accuracy are especially significant for biochemical systems. The QM/MM-MFEP method thus provides an efficient approach to free energy simulation of complex electron transfer reactions.
Jensen, Lasse; van Duijnen, Piet Th
2005-08-15
In this work we have investigated the first hyperpolarizability of pNA in 1,4-dioxane solution using a quantum mechanics/molecular mechanics (QM/MM) model. The particular model adopted is the recently developed discrete solvent reaction field (DRF) model. The DRF model is a polarizable QM/MM model in which the QM part is treated using time-dependent density-functional theory and local-field effects are incorporated. This allows for direct computation of molecular effective properties which can be compared with experimental results. The solvation shift for the first hyperpolarizability is calculated to be 30% which is in good agreement with the experimental results. However, the calculated values, both in the gas phase and in solution, are by a factor of 2 larger than the experimental ones. This is in contrast to the calculation of the first hyperpolarizability for several small molecules in the gas phase where fair agreement is found with experimental. The inclusion of local-field effects in the calculations was found to be crucial and neglecting them led to results which are significantly larger. To test the DRF model the refractive index of liquid 1,4-dioxane was also calculated and found to be in good agreement with experiment. PMID:16229570
Altun, Ahmet; Yokoyama, Shozo; Morokuma, Keiji
2009-01-01
We have investigated the protonation state and photoabsorption spectrum of Schiff-base (SB) nitrogen bound 11-cis-retinal in human blue and mouse UV cone visual pigments as well as in bovine rhodopsin by hybrid quantum mechanical/molecular mechanical (QM/MM) calculations. We have employed both multireference (MRCISD+Q, MR-SORCI+Q, and MR-DDCI2+Q) and single reference (TD-B3LYP and RI-CC2) QM methods. The calculated ground-state and vertical excitation energies show that UV-sensitive pigments have deprotonated SB nitrogen, while violet-sensitive pigments have protonated SB nitrogen, in agreement with some indirect experimental evidence. A significant blue shift of the absorption maxima of violet-sensitive pigments relative to rhodopsins arises from the increase in bond length alternation of the polyene chain of 11-cis-retinal induced by polarizing fields of these pigments. The main counterion is Glu113 in both violet-sensitive vertebrate pigments and bovine rhodopsin. Neither Glu113 nor the remaining pigment has a significant influence on the first excitation energy of 11-cis-retinal in the UV-sensitive pigments that have deprotonated SB nitrogen. There is no charge transfer between the SB and ?-ionone terminals of 11-cis-retinal in the ground and first excited states. PMID:19630373
NASA Astrophysics Data System (ADS)
Jung, Jaewoon; Re, Suyong; Sugita, Yuji; Ten-no, Seiichiro
2013-01-01
The nudged elastic band (NEB) and string methods are widely used to obtain the reaction path of chemical reactions and phase transitions. In these methods, however, it is difficult to define an accurate Lagrangian to generate the conservative forces. On the other hand, the constrained optimization with locally updated planes (CO-LUP) scheme defines target function properly and suitable for micro-iteration optimizations in quantum mechanical/molecular mechanical (QM/MM) systems, which uses the efficient second order QM optimization. However, the method does have problems of inaccurate estimation of reactions and inappropriate accumulation of images around the energy minimum. We introduce three modifications into the CO-LUP scheme to overcome these problems: (1) An improved tangent estimation of the reaction path, which is used in the NEB method, (2) redistribution of images using an energy-weighted interpolation before updating local tangents, and (3) reduction of the number of constraints, in particular translation/rotation constraints, for improved convergence. First, we test the method on the isomerization of alanine dipeptide without QM/MM calculation, showing that the method is comparable to the string method both in accuracy and efficiency. Next, we apply the method for defining the reaction paths of the rearrangement reaction catalyzed by chorismate mutase (CM) and of the phosphoryl transfer reaction catalyzed by cAMP-dependent protein kinase (PKA) using generalized hybrid orbital QM/MM calculations. The reaction energy barrier of CM is in high agreement with the experimental value. The path of PKA reveals that the enzyme reaction is associative and there is a late transfer of the substrate proton to Asp 166, which is in agreement with the recently published result using the NEB method.
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
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.
Mayes, Heather B; Tian, Jianhui; Nolte, Michael W; Shanks, Brent H; Beckham, Gregg T; Gnanakaran, S; Broadbelt, Linda J
2014-02-27
In the last several decades, significant efforts have been conducted to understand the fundamental reactivity of glucose derived from plant biomass in various chemical environments for conversion to renewable fuels and chemicals. For reactions of glucose in water, it is known that inorganic salts naturally present in biomass alter the product distribution in various deconstruction processes. However, the molecular-level interactions of alkali metal ions and glucose are unknown. These interactions are of physiological interest as well, for example, as they relate to cation-glucose cotransport. Here, we employ quantum mechanics (QM) to understand the interaction of a prevalent alkali metal, sodium, with glucose from a structural and thermodynamic perspective. The effect on ?-glucose is subtle: a sodium ion perturbs bond lengths and atomic partial charges less than rotating a hydroxymethyl group. In contrast, the presence of a sodium ion significantly perturbs the partial charges of ?-glucose anomeric and ring oxygens. Molecular dynamics (MD) simulations provide dynamic sampling in explicit water, and both the QM and the MD results show that sodium ions associate at many positions with respect to glucose with reasonably equivalent propensity. This promiscuous binding nature of Na(+) suggests that computational studies of glucose reactions in the presence of inorganic salts need to ensure thorough sampling of the cation positions, in addition to sampling glucose rotamers. The effect of NaCl on the relative populations of the anomers is experimentally quantified with light polarimetry. These results support the computational findings that Na(+) interacts similarly with ?- and ?-glucose. PMID:24308866
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
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.
Yokoyama, Shozo
Color Tuning in Short Wavelength-Sensitive Human and Mouse Visual Pigments: Ab initio Quantum-retinal in human blue and mouse UV cone visual pigments as well as in bovine rhodopsin by hybrid quantum mechanical energies show that UV-sensitive pigments have deprotonated SB nitrogen, while violet-sensitive pigments
Maria Andrea Mroginski; Franz Mark; Walter Thiel; Peter Hildebrandt
2007-01-01
We have established a quantum mechanics (QM)\\/molecular mechanics (MM) hybrid method for calculating the Raman spectra of protein-bound cofactors using the ?-subunit of C-phycocyanin containing a phycocyanobilin (PCB) chromophore as a test case. The PCB cofactor was described with density functional theory, whereas the protein matrix was treated with the CHARMM force field. The Hessian matrix of the QM region
Dokainish, Hisham M; Gauld, James W
2013-03-12
The catalytic mechanism of MsrA in Mycobacterium tuberculosis, in which S-methionine sulfoxide (Met-O) is reduced to methionine (Met), has been investigated using docking, molecular dynamics (MD) simulations, and ONIOM (quantum mechanics/molecular mechanics) methods. In addition, the roles of specific active site residues, including an aspartyl (Asp87) near the recycling cysteine, tyrosyls (Tyr44 and Tyr92), and glutamyl (Glu52), have been examined, as well as the general effects of the protein and active site on the nature and properties of mechanistic intermediates. The mechanism is initiated by the transfer of a proton from the catalytic cysteine's thiol (Cys13SH) via a bridging water to the R group carboxylate of Glu52. The now anionic sulfur of Cys13 nucleophilically attacks the substrate's sulfur with concomitant transfer of a proton from Glu52 to the sulfoxide oxygen, generating a sulfurane. The active site enhances the proton affinity of the sulfurane oxygen, which can readily accept a proton from the phenolic hydroxyls of Tyr44 or Tyr92 to give a sulfonium cation. Subsequently, Asp87 and the recycling cysteine (Cys154) can facilitate nucleophilic attack of a solvent water at the Cys13S center of the sulfonium to give a sulfenic acid (Cys13SOH) and Met. For the subsequent reduction of Cys13SOH with intramolecular disulfide bond formation, Asp87 can help facilitate nucleophilic attack of Cys154S at the sulfur of Cys13SOH by deprotonating its thiol. This reduction is found likely to occur readily upon suitable positioning of the active site hydrogen bond network and the sulfur centers of both Cys13 and Cys154. The calculated rate-limiting barrier is in good agreement with experiment. PMID:23418817
Quesne, Matthew G; Latifi, Reza; Gonzalez-Ovalle, Luis E; Kumar, Devesh; de?Visser, Sam P
2014-01-01
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
Altun, Ahmet; Yokoyama, Shozo
2009-01-01
We have investigated photoabsorption spectra of bovine rhodopsin and its mutants (E122Q and E113Q) by hybrid quantum mechanical/molecular mechanical (QM/MM) calculations as well as retinal in vacuo by pure QM calculations, employing multireference (MR) ab initio and TD-B3LYP methods. The sophisticated MR-SORCI+Q and MRCISD+Q methods extrapolated with respect to adopted approximations can reproduce the experimental absorption maxima of retinal very well. The relatively inexpensive MR-DDCI2+Q method gives absorption maxima blue-shifted by ca. 65 nm from experimental values; however, this error is systematic and thus MR-DDCI2+Q can be used to estimate spectral shifts. In MR calculations, the ground state energy of retinal at B3LYP geometry is significantly lower than that at CASSCF geometry. Therefore, B3LYP geometry is more reliable than CASSCF geometry, which has blue-shift error as large as 100 nm in the gas phase. The effect of ground state geometry on the excitation energies is less critical in the polarizing field of protein environments. At the B3LYP geometry, there is no significant charge transfer upon vertical excitation to the S1 excited state either from Glu113 to retinal or from Schiff-base terminal to ?-ionone ring through the polyene chain. All-trans to 11-cis isomerization of retinal in the gas phase has no influence on the calculated S1 absorbing state, in agreement with experiment. The shoulder of the experimental absorption spectrum of retinal in vacuo at the S1 absorbing band appears to be the second electronic transition (S2) in our calculations, contrary to previous tentative assignment to vibrational state of S1 or to the S1 band of a retinal isomer. PMID:19367945
Ion, Bogdan F; Bushnell, Eric A C; Luna, Phil De; Gauld, James W
2012-01-01
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(?)=NH(2)+ 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(?)=NH(2)+ 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 ?-NH(2) 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
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
Karasulu, Bora; Patil, Mahendra; Thiel, Walter
2013-09-11
We report classical molecular dynamics (MD) simulations and combined quantum mechanics/molecular mechanics (QM/MM) calculations to elucidate the catalytic mechanism of the rate-determining amine oxidation step in the lysine-specific demethylase 1 (LSD1)-catalyzed demethylation of the histone tail lysine (H3K4), with flavin adenine dinucleotide (FAD) acting as cofactor. The oxidation of substrate lysine (sLys) involves the cleavage of an ?-CH bond accompanied by the transfer of a hydride ion equivalent to FAD, leading to an imine intermediate. This hydride transfer pathway is shown to be clearly favored for sLys oxidation over other proposed mechanisms, including the radical (or single-electron transfer) route as well as carbanion and polar-nucleophilic mechanisms. MD simulations on six NVT ensembles (covering different protonation states of sLys and K661 as well as the K661M mutant) identify two possible orientations of the reacting sLys and FAD subunits (called "downward" and "upward"). Calculations at the QM(B3LYP-D/6-31G*)/CHARMM22 level provide molecular-level insights into the mechanism, helping to understand how LSD1 achieves the activation of the rather inert methyl-CH bond in a metal-free environment. Factors such as proper alignment of sLys (downward orientation), transition-state stabilization (due to the protein environment and favorable orbital interactions), and product stabilization via adduct formation are found to be crucial for facilitating the oxidative ?-CH bond cleavage. The current study also sheds light on the role of important active-site residues (Y761, K661, and W695) and of the conserved water-bridge motif. The steric influence of Y761 helps to position the reaction partners properly, K661 is predicted to get deprotonated prior to substrate binding and to act as an active-site base that accepts a proton from sLys to enable the subsequent amine oxidation, and the water bridge that is stabilized by K661 and W695 mediates this proton transfer. PMID:23988016
Capoferri, Luigi; Lodola, Alessio; Rivara, Silvia; Mor, Marco
2015-03-23
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
Löytynoja, T; Niskanen, J; Jänkälä, K; Vahtras, O; Rinkevicius, Z; Ågren, H
2014-11-20
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
Ballarini, Roberto
of large defects and cracks on the mechanical properties of carbon nanotubes and graphene sheets. The semi.50.Ah, 81.07.De I. INTRODUCTION Due to their favorable mechanical properties, carbon nanotubes CNTs-quantities of perfect CNTs or graphene sheets may prove challenging; in practice, mechanical properties will often
Woods, Christopher J; Shaw, Katherine E; Mulholland, Adrian J
2015-01-22
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
NASA Astrophysics Data System (ADS)
Ngaojampa, C.; Nimmanpipug, P.; Yu, L. D.; Anuntalabhochai, S.; Lee, V. S.
2011-02-01
In order to promote understanding of the fundamentals of ultra-low-energy ion interaction with DNA, molecular dynamics simulations using combined quantum-mechanics/molecular-mechanics of poly-AT and poly-GC A-DNA double strands irradiated by <200 eV carbon ions were performed to investigate the molecular implications of mutation bias. The simulations were focused on the responses of the DNA backbones and nitrogenous bases to irradiation. Analyses of the root mean square displacements of the backbones and non-hydrogen atoms of base rings of the simulated DNA structure after irradiation revealed a potential preference of DNA double strand separation, dependent on the irradiating energy. The results show that for the backbones, the large difference in the displacement between poly-GC and poly-AT in the initial time period could be the reason for the backbone breakage; for the nitrogenous base pairs, A-T is 30% more sensitive or vulnerable to ion irradiation than G-C, demonstrating a preferential, instead of random, effect of irradiation-induced mutation.
Chaskar, Prasad; Zoete, Vincent; Röhrig, Ute F
2014-11-24
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
Dong, Minghui; Liu, Haiyan
2008-08-21
The Escherichia coli peptide deformylase (PDF) and Bacillus thermoproteolyticus thermolysin (TLN) are two representative metal-requiring peptidases having remarkably similar active centers but distinctively different metal preferences. Zinc is a competent catalytic cofactor for TLN but not for PDF. Reaction pathways and the associated energetics for both enzymes were determined using combined semiempirical and ab initio quantum mechanical/molecular mechanical modeling, without presuming reaction coordinates. The results confirmed that both enzymes catalyze via the same chemical steps, and reproduced their different preferences for zinc or iron as competent cofactors. Further analyses indicated that different feasibility of the nucleophilic attack step leads to different metal preferences of the two enzymes. In TLN, the substrate is strongly activated and can serve as the fifth coordination ligand of zinc prior to the chemical steps. In PDF, the substrate carbonyl is activated by the chemical step itself, and becomes the fifth coordination partner of zinc only in a later stage of the nucleophilic attack. These leads to a much more difficult nucleophilic attack in PDF than in TLN. Different from some earlier suggestions, zinc has no difficulty in accepting an activated substrate as the fifth ligand to switch from tetra- to penta-coordination in either PDF or TLN. When iron replaces zinc, its stronger interaction with the hydroxide ligand may lead to higher activation barrier in TLN. In PDF, the stronger interactions of iron with ligands allow iron-substrate coordination to take place either before or at a very early stage of the chemical step, leading to effective catalysis. Our calculations also show combined semiempirical and ab initio quantum mechanical modeling can be efficient approaches to explore complicated reaction pathways in enzyme systems. PMID:18651766
Monari, Antonio; Rivail, Jean-Louis; Assfeld, Xavier
2013-02-19
Molecular mechanics methods can efficiently compute the macroscopic properties of a large molecular system but cannot represent the electronic changes that occur during a chemical reaction or an electronic transition. Quantum mechanical methods can accurately simulate these processes, but they require considerably greater computational resources. Because electronic changes typically occur in a limited part of the system, such as the solute in a molecular solution or the substrate within the active site of enzymatic reactions, researchers can limit the quantum computation to this part of the system. Researchers take into account the influence of the surroundings by embedding this quantum computation into a calculation of the whole system described at the molecular mechanical level, a strategy known as the mixed quantum mechanics/molecular mechanics (QM/MM) approach. The accuracy of this embedding varies according to the types of interactions included, whether they are purely mechanical or classically electrostatic. This embedding can also introduce the induced polarization of the surroundings. The difficulty in QM/MM calculations comes from the splitting of the system into two parts, which requires severing the chemical bonds that link the quantum mechanical subsystem to the classical subsystem. Typically, researchers replace the quantoclassical atoms, those at the boundary between the subsystems, with a monovalent link atom. For example, researchers might add a hydrogen atom when a C-C bond is cut. This Account describes another approach, the Local Self Consistent Field (LSCF), which was developed in our laboratory. LSCF links the quantum mechanical portion of the molecule to the classical portion using a strictly localized bond orbital extracted from a small model molecule for each bond. In this scenario, the quantoclassical atom has an apparent nuclear charge of +1. To achieve correct bond lengths and force constants, we must take into account the inner shell of the atom: for an sp(3) carbon atom, we consider the two core 1s electrons and treat that carbon as an atom with three electrons. This results in an LSCF+3 model. Similarly, a nitrogen atom with a lone pair of electrons available for conjugation is treated as an atom with five electrons (LSCF+5). This approach is particularly well suited to splitting peptide bonds and other bonds that include carbon or nitrogen atoms. To embed the induced polarization within the calculation, researchers must use a polarizable force field. However, because the parameters of the usual force fields include an average of the induction effects, researchers typically can obtain satisfactory results without explicitly introducing the polarization. When considering electronic transitions, researchers must take into account the changes in the electronic polarization. One approach is to simulate the electronic cloud of the surroundings by a continuum whose dielectric constant is equal to the square of the refractive index. This Electronic Response of the Surroundings (ERS) methodology allows researchers to model the changes in induced polarization easily. We illustrate this approach by modeling the electronic absorption of tryptophan in human serum albumin (HSA). PMID:23249409
Sekharan, Sivakumar; Yokoyama, Shozo; Morokuma, Keiji
2011-12-29
Since Vogt's discovery of A(3)-retinal or 3-hydroxyretinal in insects in 1983 and Matsui's discovery of A(4)-retinal or 4-hydroxyretinal in firefly squid in 1988, hydroxyretinal-protein interactions mediating vision have remained largely unexplored. In the present study, A(3)- and A(4)-retinals are theoretically incorporated into squid and bovine visual pigments by use of the hybrid quantum mechanics/molecular mechanics [SORCI+Q//B3LYP/6-31G(d):Amber96] method, and insights into structure, enantioselectivity, and spectroscopy are gathered and presented for the first time. Contrary to general perception, our findings rule out the formation of a hydrogen bond between the hydroxyl-bearing ?-ionone ring portion of retinal and opsin. Compared to A(1)-pigments, A(3)- and A(4)-pigments exhibit slightly blue-shifted absorption maxima due to increase in bond-length alternation of the hydroxyretinal. We suggest that (i) the binding site of firefly squid (Watasenia scintillans) opsin is very similar to that of the Japanese common squid (Todarodes pacificus) opsin; (ii) the molecular mechanism of spectral tuning in small white butterflies involve sites S116 and T185 and breaking of a hydrogen bond between sites E180 and T185; and finally (iii) A(3)-retinal may have occurred during the conversion of A(1)- to A(2)-retinal and insects may have acquired them, in order to absorb light in the blue-green wavelength region and to speed up the G-protein signaling cascade. PMID:22087641
Wang, Binju; Li, Chunsen; Dubey, Kshatresh Dutta; Shaik, Sason
2015-06-17
Quantum mechanical/molecular mechanical calculations address the longstanding-question of a "second oxidant" in P450 enzymes wherein the proton-shuttle, which leads to formation of the "primary-oxidant" Compound I (Cpd I), was severed by mutating the crucial residue (in P450cam: Threonine-252-to-Alanine, hence T252A). Investigating the oxidant candidates Cpd I, ferric hydroperoxide, and ferric hydrogen peroxide (Fe(III)(O2H2)), and their reactions, generates reactivity networks which enable us to rule out a "second oxidant" and at the same time identify an additional coupling pathway that is responsible for the epoxidation of 5-methylenylcamphor by the T252A mutant. In this "second-coupling pathway", the reaction starts with the Fe(III)(O2H2) intermediate, which transforms to Cpd I via a O-O homolysis/H-abstraction mechanism. The persistence of Fe(III)(O2H2) and its oxidative reactivity are shown to be determined by interplay of substrate and protein. The substrate 5-methylenylcamphor prevents H2O2 release, while the protein controls the Fe(III)(O2H2) conversion to Cpd I by nailing-through hydrogen-bonding interactions-the conformation of the HO(•) radical produced during O-O homolysis. This conformation prevents HO(•) attack on the porphyrin's meso position, as in heme oxygenase, and prefers H-abstraction from Fe(IV)OH thereby generating H2O + Cpd I. Cpd I then performs substrate oxidations. Camphor cannot prevent H2O2 release and hence the T252A mutant does not oxidize camphor. This "second pathway" transpires also during H2O2 shunting of the cycle of wild-type P450cam, where the additional hydrogen-bonding with Thr252 prevents H2O2 release, and contributes to a successful Cpd I formation. The present results lead to a revised catalytic cycle of Cytochrome P450cam. PMID:26011529
NASA Astrophysics Data System (ADS)
Ishida, Toyokazu
2008-09-01
In this study, we investigated the electronic character of protein environment in enzymatic processes by performing all-electron QM calculations based on the fragment molecular orbital (FMO) method. By introducing a new computational strategy combining all-electron QM analysis with ab initio QM/MM modeling, we investigated the details of molecular interaction energy between a reactive substrate and amino acid residues at a catalytic site. For a practical application, we selected the chorismate mutase catalyzed reaction as an example. Because the computational time required to perform all-electron QM reaction path searches was very large, we employed the ab initio QM/MM modeling technique to construct reliable reaction profiles and performed all-electron FMO calculations for the selected geometries. The main focus of the paper is to analyze the details of electrostatic stabilization, which is considered to be the major feature of enzymatic catalyses, and to clarify how the electronic structure of proteins is polarized in response to the change in electron distribution of the substrate. By performing interaction energy decomposition analysis from a quantum chemical viewpoint, we clarified the relationship between the location of amino acid residues on the protein domain and the degree of electronic polarization of each residue. In particular, in the enzymatic transition state, Arg7, Glu78, and Arg90 are highly polarized in response to the delocalized electronic character of the substrate, and as a result, a large amount of electrostatic stabilization energy is stored in the molecular interaction between the enzyme and the substrate and supplied for transition state stabilization.
Ardèvol, Albert; Rovira, Carme
2015-06-24
Carbohydrate-active enzymes such as glycoside hydrolases (GHs) and glycosyltransferases (GTs) are of growing importance as drug targets. The development of efficient competitive inhibitors and chaperones to treat diseases related to these enzymes requires a detailed knowledge of their mechanisms of action. In recent years, sophisticated first-principles modeling approaches have significantly advanced in our understanding of the catalytic mechanisms of GHs and GTs, not only the molecular details of chemical reactions but also the significant implications that just the conformational dynamics of a sugar ring can have on these mechanisms. Here we provide an overview of the progress that has been made in the past decade, combining molecular dynamics simulations with density functional theory to solve these sweet mysteries of nature. PMID:25970019
Patel, Chandan; Garrec, Julian; Dupont, Céline; Dumont, Elise
2013-01-15
Naturally occurring intrastrand oxidative cross-link lesions have proven to be a potent source of endogenous DNA damage. Among the variety of lesions that can be formed and have been identified, G[8-5]C damage (in which the C8 atom of a guanine is covalently bonded to the C5 atom of a nearby cytosine belonging to the same strand) occurs with a low incidence yet takes on special importance because of its high mutagenicity. Hybrid Car-Parrinello molecular dynamics simulations, rooted in density functional theory and coupled to molecular mechanics, have been performed to shed light on the cyclization process. The activation free energy of the reacting subsystem embedded in a solvated dodecamer is estimated to be ?12.4 kcal/mol, which is ?3 kcal/mol higher than the value for the prototypical G[8-5m]T lesion inferred employing the same theoretical framework [Garrec, J., Patel, C., Rothlisberger, U., and Dumont, E. (2012) J. Am. Chem. Soc.134, 2111-2119]. This study also situates the G[8-5m]mC lesion at an intermediate activation free energy (?10.5 kcal/mol). The order of reactivity in DNA (T(•) > mC(•) > C(•)) is reversed compared to that in the reacting subsystems in the gas phase (C(•) > mC(•) > T(•)), stressing the crucial role of the solvated B-helix environment. The results of our simulations also characterize a more severe distortion for G[8-5]C than for methylene-bridged intrastrand cross-links. PMID:23256602
NSDL National Science Digital Library
De Raedt, Hans
This website contains a number of descriptions of quantum mechanical phenomena, using 3D animations to illustrate the physics. The goal is to introduce basic concepts and phenomena using simulations rather than complex mathematics. The time-dependence of quantum systems is a focus of this material.
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 5 problems LAST NAME FIRST NAME #12 with the effective electron mass at the band edges. #12;Applied quantum mechanics 3 (c) Write a computer program
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 8 problems LAST NAME FIRST NAME #12;Applied quantum mechanics 3 (b) If the electron is in a semiconductor and has an effective mass m * 0.07 m
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 1 problems LAST NAME FIRST NAME #12 happens to the beat frequency if the airplane moves in an arc? #12;Applied quantum mechanics 3 Problem 1
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 10 problems LAST NAME FIRST NAME #12 ( ) L/( )= L/ #12;Applied quantum mechanics 3 (d) Use the results of (b) an (c) to draw the electron
Quantum Mechanics II (Undergraduate)
Nickrent, Daniel L.
Quantum Mechanics II (Undergraduate) Applications of Quantum Mechanics Spring, 2014 Physics 440 TEXTBOOK: Introduction to Quantum Mechanics (Second Edition), by David J. Griffiths, and QUNET's wikibook to apply quantum mechanics to some fundamental and important problems such as: better understanding
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 6 problems LAST NAME FIRST NAME #12 --- and that for a Poisson distribution of such photons #12; 1 2 n ---------------- Applied quantum mechanics 3 (c) Apply conditions is the quantum mechanical result m t 2 2 d d x xd d V x = the same Newton's second law in which
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 6 problems LAST NAME FIRST NAME #12 of the system. (b) Find . (c) Find and show that . Under what conditions is the quantum mechanical result( ) td d A t( ) t A td d A /= A B i 2 --- A^ B^,[ ] A^ B^ Et 2 --- n n 1 2 --- #12;Applied quantum
Bender, Carl M; DeKieviet, Maarten; Klevansky, S. P.
2013-01-01
-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter–antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics. PMID:23509390
Introduction: quantum resonances Classical and quantum mechanics
Ramond, Thierry
: quantum resonances Classical and quantum mechanics Microlocal analysis Resonances associated;..... . .... . .... . ..... . .... . .... . .... . ..... . .... . .... . .... . ..... . .... . .... . .... . ..... . .... . ..... . .... . .... . Introduction: quantum resonances Classical and quantum mechanics Microlocal analysis Resonances associated with homoclinic orbits Outline Introduction: quantum resonances Classical and quantum mechanics Microlocal
Bohmian mechanics contradicts quantum mechanics
Neumaier, Arnold
Bohmian mechanics contradicts quantum mechanics Arnold Neumaier Institut fur Mathematik, Universit://solon.cma.univie.ac.at/#24;neum/ Abstract. It is shown that, for a harmonic oscillator in the ground state, Bohmian mechanics and quantum mechanics predict values of opposite sign for certain time correlations. The discrepancy can
Quantum Mechanics Measurements, Mutually
Gruner, Daniel S.
Quantum Mechanics Measurements, Mutually Unbiased Bases and Finite Geometry Or why six is the first) #12;Quantum Mechanics for Dummies Finite dimensional quantum states are represented by trace one,1 -icS1,1[ ] #12;Quantum systems evolve and are measured. The evolution of a quantum system using
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 5 problems LAST NAME FIRST NAME #12 + --------------------------------------------- k = t 10/= t 1= Ek 2t kxL( ) 2t 2kxL( )cos+cos= t 10/= t 1= t 0.2= #12;Applied quantum mechanics 3 (c) Write a computer program to plot the electron density of states for a square lat- tice
Nikolai Laskin
2000-01-01
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Lévy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Lévy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and
A. L. Stewart; G. Scolarici; L. Solombrino
1963-01-01
We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two alternative descriptions of a quantum
Quantum Mechanics + Open Systems
Steinhoff, Heinz-Jürgen
Quantum Mechanics + Open Systems = Thermodynamics ? Jochen Gemmer T¨ubingen, 09.02.2006 #12., World Scientific) #12;Fundamental Law or Emergent Description? Quantum Mechanics i t = (- 2 2m + V or Emergent Description? Quantum Mechanics i t = (- 2 2m + V ) "Heisenberg Cut" Classical Mechanics: m d2
Chapin, Kimberly R.
1997-01-01
The role of time in quantum mechanics has been and is still very controversial. The purpose of this paper was to explore the historical interpretation of time in quantum mechanics, to determine the current status of this ...
Introduction to Quantum Mechanics
Eduardo J. S. Villaseñor
2008-04-23
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.
NASA Astrophysics Data System (ADS)
Laskin, Nikolai
2000-06-01
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the non-relativistic fractional quantum-mechanical particle has been found, and the Levy wave packet has been introduced into quantum mechanics. We have derived a free particle quantum-mechanical propagator using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been established. We also discuss the relationships between fractional and the well-known Feynman path integrals approaches to quantum mechanics.
Park, Jae Woo; Rhee, Young Min
2012-09-13
The excited state dynamics of the blue fluorescent protein (BFP) and its variants, azurite, EBFP1.2, and EBFP2.0, are studied using molecular dynamics (MD) simulations on potential energy surfaces (PESs) generated with the interpolated mechanics-molecular mechanics (IM/MM) scheme. This IM/MM strategy adopts the interpolated PES for an important area of the complex and the conventional force field for the remaining part. We focus on the internal rotation dynamics of the chromophore unit, which is directly related to its fluorescence property, and analyze the time evolutions of the nonrotated chromophore fractions based on trajectories over 10 ?s of aggregate simulation time. The characteristics obtained from the calculated time progresses of the nonrotated chromophore fractions in BFP and other variants agree well with experimentally observed properties. The results show that the MD simulation with an IM/MM potential is an attractive approach for studying excited state dynamics of fluorescent proteins in consideration of its efficiency and reliability. We also attempt to investigate the detailed roles that the mutated residues play in delaying the excited state chromophore twisting and thus improving the fluorescence property, and discuss the contributions by the Coulombic and the steric interactions between the chromophore and the mutated residues. PMID:22891786
Fractals and quantum mechanics
NASA Astrophysics Data System (ADS)
Laskin, Nick
2000-12-01
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Lévy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Lévy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrödinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical particle has been established, and the Lévy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a free particle quantum-mechanical kernel using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a free particle in a square infinite potential well, the fractional "Bohr atom" and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics.
Fractals and quantum mechanics.
Laskin, Nick
2000-12-01
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical particle has been established, and the Levy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a free particle quantum-mechanical kernel using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a free particle in a square infinite potential well, the fractional "Bohr atom" and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics. (c) 2000 American Institute of Physics. PMID:12779428
NSDL National Science Digital Library
Mabuchi, Hideo
This web site contains resources for a comprehensive quantum mechanics course designed for graduate and advanced undergraduate students at Cal Tech. The course has been revised to include quantum information science, and prepares students for a course in quantum computation. Lecture notes, a syllabus, homework problems with solutions, and exam solutions are available.
Chapin, Kimberly R.
1997-01-01
to describe the quantum mechanical system The first, matrix mechanics, was presented by Heisenberg [31-33] in 1925. The second, wave mechanics, was presented by Schrodinger [34-37] a year later. In 1926, Schrodmger [38] demonstrated the equivalence... can jump &om one state to another. The result is a discontinuous variation in time (i. e. the tune atom) [42]. Throughout the development of quantum mechanics, this atomistic view of time surfaces again and again, For example, In 1925, J. J...
Introduction to Quantum Mechanics
NSDL National Science Digital Library
The Concord Consortium
2011-12-12
The microscopic world is full of phenomena very different from what we see in everyday life. Some of those phenomena can only be explained using quantum mechanics. This activity introduces basic quantum mechanics concepts about electrons that are essential to understanding modern and future technology, especially nanotechnology. Start by exploring probability distribution, then discover the behavior of electrons with a series of simulations.
Geometrization of Quantum Mechanics
J. F. Carinena; J. Clemente-Gallardo; G. Marmo
2007-03-23
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.
Okazaki, Tadashi
2015-01-01
We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N = 16 and N = 12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2) and SU(1,1|6) quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi-Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N = 8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.
Covariant quantum mechanics and quantum symmetries
JanyÂ?ka, Josef
Covariant quantum mechanics and quantum symmetries Josef JanyÅ¸ska 1 , Marco Modugno 2 , Dirk Saller: quantum mechanics, classical mechanics, general relativity, infinitesimal symmetries. 2000 MSC: 81P99, 81Q Introduction 2 2 Covariant quantum mechanics 5 2.1 Classical background
Laskin
2000-09-01
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Levy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and statistical mechanics have been developed via our fractional path integral approach. A fractional generalization of the Schrodinger equation has been found. A relationship between the energy and the momentum of the nonrelativistic quantum-mechanical particle has been established. The equation for the fractional plane wave function has been obtained. We have derived a free particle quantum-mechanical kernel using Fox's H function. A fractional generalization of the Heisenberg uncertainty relation has been established. Fractional statistical mechanics has been developed via the path integral approach. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in terms of the Fox's H function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics. PMID:11088808
Quantum Mechanics Without Observers
W. H. Sulis
2013-03-03
The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process theory and utilizing methods from combinatorial games, interpolation theory and complex systems theory results in a novel realist version of quantum mechanics incorporating quasi-local, nondeterministic hidden variables that are compatible with the no-hidden variable theorems and relativistic invariance, and reproduce the standard results of quantum mechanics to a high degree of accuracy without invoking observers.
Kapustin, Anton [California Institute of Technology, Pasadena, California 91125 (United States)] [California Institute of Technology, Pasadena, California 91125 (United States)
2013-06-15
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
Ontology and Quantum Mechanics
N. D. Hari Dass
2014-06-19
The issue of ontology in quantum mechanics, or equivalently the issue of the reality of the wave function is critically examined within standard quantum theory. It is argued that though no strict ontology is possible within quantum theory, ingenious measurement schemes may still make the notion of a \\emph{FAPP Ontology} i.e ontology for all practical purposes (a phrase coined by John Bell), meaningful and useful.
W G Unruh
2006-01-01
Quantum mechanics is one of the most successful theoretical structures in all of science. Developed between 1925-26 to explain the optical spectrum of atoms, the theory over the succeeding 80 years has been extended, first to quantum field theories, gauge field theories, and now even string theory. It is used every day by thousands of physicists to calculate physical phenomena
Supersymmetry in quantum mechanics
Avinash Khare
1997-01-01
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical\\u000a problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable. In\\u000a this lecture I review the theoretical formulation of supersymmetric quantum mechanics and discuss many of its applications.\\u000a I show that the well-known exactly solvable
QUANTUM MECHANICS II Physics 342
Rosner, Jonathan L.
QUANTUM MECHANICS II Physics 342 KPTC 103 9:00 Â 10:20 a.m. 1 Tues., Thurs. Â Winter Quarter 2011 quantum mechanics at the graduate level. The text for Quantum Mechanics II will be J. J. Sakurai and Jim Napolitano, Modern Quantum Mechanics, Second Edition (Addison-Wesley, San Francisco, 2011). For supplemental
NSDL National Science Digital Library
Zollman, Dean
The Kansas State University Visual Quantum Mechanics project is developing instructional materials about quantum physics for high school and college students. Instructional units and/or courses are being created for high school and college non-science students, pre-medical and biology students, and science and engineering majors. Each set of the teaching-learning materials integrates interactive visualizations with inexpensive materials and written documents in an activity-based environment.
W. Chagas-Filho
2009-05-11
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position or in the momentum representation. As a way to support this complementation, starting from the action that describes conformal gravity in the world-line formalism, we show that there are duality transformations that relate the dynamics in the presence of position dependent vector and tensor fields to the dynamics in the presence of momentum dependent vector and tensor fields.
QUANTUM MECHANICS I Physics 341
Rosner, Jonathan L.
QUANTUM MECHANICS I Physics 341 KPTC 103 9:00 Â 10:20 a.m. 1 Tues., Thurs. Â Fall Quarter 1999 mechanics at the graduate level. The text for Quantum mechanics I and II will be J. J. Sakurai and Jim Napolitano, Modern Quantum Mechanics, Second Edition (Addison- Wesley, 2011). We will cover the first three
From Quantum Mechanics to Thermodynamics?
Steinhoff, Heinz-Jürgen
From Quantum Mechanics to Thermodynamics? Dresden, 22.11.2004 Jochen Gemmer Universit¨at Osnabr Description? Quantum Mechanics i¯h t = (- ¯h2 2m + V ) Classical Mechanics: m d2 dt2 x = - V Thermodynamics: dU = TdS - pdV dS dt > 0 #12;Fundamental Law or Emergent Description? Quantum Mechanics i
Quantum Mechanics in Phase Space
Ali Mohammad Nassimi
2008-06-11
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
Biorthogonal quantum mechanics
NASA Astrophysics Data System (ADS)
Brody, Dorje C.
2014-01-01
The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called ‘biorthogonal quantum mechanics’, is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems.
Argyris Nicolaidis
2012-11-09
We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics.
Interpretation of quantum mechanics
Roland Omnès
1987-01-01
New axioms are proposed for the interpretation of quantum mechanics. They rest on a kind of calculus allowing to select meaningful physical statements and giving rules to check a given physical reasoning containing implications. Measurement theory is reformulated. Laboratoire associé au Centre National de la Recherche Scientifique.
Supersymmetry and quantum mechanics
Fred Cooper; Avinash Khare; Uday Sukhatme
1995-01-01
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of
On Randomness in Quantum Mechanics
Alberto C. de la Torre
2007-07-19
The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.
Epigenetics: Biology's Quantum Mechanics
Jorgensen, Richard A.
2011-01-01
The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene – the molecular biological view and the epigenetic view – are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider. PMID:22639577
Glenn Eric Johnson
2014-12-21
The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the Feynman series for Compton scattering. To have a semi-norm, photon states are constrained to transverse polarizations and for Compton scattering, the constructed cross section deviates at large momentum exchanges from the cross section prediction of the Feynman rules. Discussion includes the incompatibility of canonical quantization with the constructed interacting fields, and the role of interpretations of quantum mechanics in realizing QFT.
Probabilistic Interpretation of Quantum Mechanics
Brigitte Falkenburg; Peter Mittelstaedt
The probabilistic interpretation of quantum mechanics is based on Born's 1926 papers and von Neumann's formal account of quantum\\u000a mechanics in ? Hilbert space. According to Max Born (1882–1970), the quantum mechanical ? wave function ? does not have any\\u000a direct physical meaning, whereas its square ???2 is a probability [1] ? Born rule, probability in quantum mechanics. According to
Quantum Mechanics and Representation Theory Columbia University
Woit, Peter
Quantum Mechanics and Representation Theory Peter Woit Columbia University Texas Tech, November 21 2013 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 1 / 30 #12;Does Anyone Understand Quantum Mechanics? "No One Understands Quantum Mechanics" "I think
Determinism Beneath Quantum Mechanics
Gerard't Hooft
Contrary to common belief, it is not difficult to construct deterministic\\u000amodels where stochastic behavior is correctly described by quantum mechanical\\u000aamplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What\\u000ais difficult however is to obtain a Hamiltonian that is bounded from below, and\\u000awhose ground state is a vacuum that exhibits complicated vacuum fluctuations,\\u000aas in the real world.
Euclidean Relativistic Quantum Mechanics
Philip Kopp; Wayne Polyzou
2013-01-28
We discuss a formulation of exactly Poincar\\'e invariant quantum mechanics where the input is model Euclidean Green functions or their generating functional. We discuss the structure of the models, the construction of the Hilbert space, the construction and transformation properties of single-particle states, and the construction of GeV scale transition matrix elements. A simple model is utilized to demonstrate the feasibility of this approach.
Relativity and quantum mechanics
Hüseyin Yilmaz
1982-01-01
Conditions under which quantum mechanics can be made compatible with the curved space-time of gravitation theories is investigated. A postulate is imposed in the formv=vg wherev is the kinematical Hamilton-Jacobi (geometric optic limit) velocity andvg is the group velocity of the waves. This imposes a severe condition on the possible coordinates in which the Schrödinger form (the coordinate realization) of
Principles of Fractional Quantum Mechanics
Nick Laskin
2010-09-28
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum mechanics, hermiticity of the Hamilton operator, parity conservation law and the current density. Applications of fractional quantum mechanics cover dynamics of a free particle, new representation for a free particle quantum mechanical kernel, infinite potential well, bound state in {\\delta}-potential well, linear potential, fractional Bohr atom and fractional oscillator. We also review fundamentals of the L\\'evy path integral approach to fractional statistical mechanics.
Abstract: Quantum mechanics provides a
Shahriar, Selim
Abstract: Quantum mechanics provides a mechanism for absolutely secure communication between remote parties. For distances greater than 100 kilometers direct quantum communication via optical fiber is not viable, due to fiber losses, and intermediate storage of the quantum information along the trans- mission
Bohmian quantum mechanics with quantum trajectories
NASA Astrophysics Data System (ADS)
Jeong, Yeuncheol
The quantum trajectory method in the hydrodynamical formulation of Madelung-Bohm-Takabayasi quantum mechanics is an example of showing the cognitive importance of scientific illustrations and metaphors, especially, in this case, in computational quantum chemistry and electrical engineering. The method involves several numerical schemes of solving a set of hydrodynamical equations of motion for probability density fluids, based on the propagation of those probability density trajectories. The quantum trajectory method gives rise to, for example, an authentic quantum electron transport theory of motion to, among others, classically-minded applied scientists who probably have less of a commitment to traditional quantum mechanics. They were not the usual audience of quantum mechanics and simply choose to use a non-Copenhagen type interpretation to their advantage. Thus, the metaphysical issues physicists had a trouble with are not the main concern of the scientists. With the advantages of a visual and illustrative trajectory, the quantum theory of motion by Bohm effectively bridges quantum and classical physics, especially, in the mesoscale domain. Without having an abrupt shift in actions and beliefs from the classical to the quantum world, scientists and engineers are able to enjoy human cognitive capacities extended into the quantum mechanical domain.
Octonic relativistic quantum mechanics
V. L. Mironov; S. V. Mironov
2008-04-22
In this paper we represent the generalization of relativistic quantum mechanics on the base of eght-component values "octons", generating associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the eight-component octonic wave function, obtained from the Einshtein relation for energy and momentum, describes particles with spin of 1/2. It is established that the octonic wave function of a particle in the state with defined spin projection has the specific spatial structure in the form of octonic oscillator with two spatial polarizations: longitudinal linear and transversal circular. The relations between bispinor and octonic descriptions of relativistic particles are established. We propose the eight-component spinors, which are octonic generalisation of two-component Pauli spinors and four-component Dirac bispinors. It is shown that proposed eight-component spinors separate the states with different spin projection, different particle-antiparticle state as well as different polarization of the octonic oscillator. We demonstrate that in the frames of octonic relativistic quantum mechanics the second-order equation for octonic wave function can be reformulated in the form of the system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special type of wave functions the second-order equation can be reduced to the single first-order equation, which is analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not create quantum fields.
Gravitomagnetism in quantum mechanics
Adler, Ronald J.; Chen Pisin [Gravity Probe B, Hansen Laboratory for Experimental Physics, Stanford University, Stanford California 94309 (United States); Leung Center for Cosmology and Particle Astrophysics and Department of Physics and Graduate Institute of Astrophysics, National Taiwan University, Taipei, Taiwan 10617 and Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States)
2010-07-15
We give a systematic treatment of the quantum mechanics of a spin zero particle in a combined electromagnetic field and a weak gravitational field that is produced by a slow moving matter source. The analysis is based on the Klein-Gordon equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The Klein-Gordon equation is recast into Schroedinger equation form, which we then analyze in the nonrelativistic limit. We include a discussion of some rather general observable physical effects implied by the Schroedinger equation form, concentrating on gravitomagnetism. Of particular interest is the interaction of the orbital angular momentum of the particle with the gravitomagnetic field.
Diffusion-Schrödinger Quantum Mechanics
NASA Astrophysics Data System (ADS)
Lasukov, V. V.; Lasukova, T. V.; Lasukova, O. V.; Novoselov, V. V.
2014-08-01
A quantum solution of a nonlinear differential equation of diffusion type with a potential term has been found. Diffusion-Schrödinger quantum mechanics can find wide application in quantum biology, biological electronics, synthetic biology, nanomedicine, the quantum theory of consciousness, cosmology, and other fields of science and technology. One consequence of the macroscopic nature of diffusion-Schrödinger quantum mechanics is the possibility of generation of hard photons. The dust plasma in the Universe can generate cosmic rays with ultra-relativistic energies in a galactic magnetic field via a diffusion mechanism.
Advanced Concepts in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Esposito, Giampiero; Marmo, Giuseppe; Miele, Gennaro; Sudarshan, George
2014-11-01
Preface; 1. Introduction: the need for a quantum theory; 2. Experimental foundations of quantum theory; 3. Waves and particles; 4. Schrödinger picture, Heisenberg picture and probabilistic aspects; 5. Integrating the equations of motion; 6. Elementary applications: 1-dimensional problems; 7. Elementary applications: multidimensional problems; 8. Coherent states and related formalism; 9. Introduction to spin; 10. Symmetries in quantum mechanics; 11. Approximation methods; 12. Modern pictures of quantum mechanics; 13. Formulations of quantum mechanics and their physical implications; 14. Exam problems; Glossary of geometric concepts; References; Index.
Gamification of Quantum Mechanics Teaching
Ole Eggers Bjælde; Mads Kock Pedersen; Jacob Sherson
2015-06-26
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
Gamification of Quantum Mechanics Teaching
Bjælde, Ole Eggers; Sherson, Jacob
2015-01-01
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
NASA Astrophysics Data System (ADS)
Jones, Robert
2011-03-01
I do not agree with mind-body dualism. Today the consensus view is that thought and mind is a combination of processes like memory, generalization, comparison, deduction, organization, induction, classification, feature detection, analogy, etc. performed by computational machinery. (R. Jones, Trans. of the Kansas Acad. Sci., vol. 109, # 3/4, 2006 and www.robert-w-jones.com, philosopher, theory of thought) But I believe that quantum mechanics is a more plausible dualist theory of reality. The quantum mechanical wave function is nonphysical, it exists in a 3N space (for an N body system) not in (x,y,z,t) 4-space, and does not possess physical properties. But real physical things like energy (which do exist in our 4-space world) influence the wave function and the wave function, in its turn, influences real physical things, like where a particle can be found in 4-space. The coupling between the spirit-like wave function and things found in the real (4-space) world (like energy) is via mathematical equations like the Schrodinger equation and Born normalization.
Equivalence between Quantum Mechanics and PT Symmetric Quantum Mechanics
David Girardelli; Eduardo M. Zavanin; Marcelo M. Guzzo
2015-02-24
In this paper we develop a discussion about PT Symmetric Quantum Mechanics, working with basics elements of this theory. In a simple case of two body system, we developed the Quantum Brachistochrone problem. Comparing the results obtained through the PT Symmetric Quantum Mechanics with that ones obtained using the standard formalism, we conclude that this new approach is not able to reveal any new effect.
Quantum Leap Quantum Mechanics' Killer App
Bigelow, Stephen
Quantum Leap Quantum Mechanics' Killer App Q&A with Craig Hawker Director of the Materials Research in the nation Thomson Reuters ranked Materials research at UCSB as second in the world in terms of research. Q&A with Craig Hawker LEAP The Materials Research Laboratory is the only Wes
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics. PMID:23509390
Tensorial description of quantum mechanics
J. Clemente-Gallardo; G. Marmo
2013-02-01
Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a covariant formulation of quantum mechanics under the full diffeomorphism group.
Invariance in adelic quantum mechanics
Branko Dragovich
2006-12-07
Adelic quantum mechanics is form invariant under an interchange of real and p-adic number fields as well as rings of p-adic integers. We also show that in adelic quantum mechanics Feynman's path integrals for quadratic actions with rational coefficients are invariant under changes of their entries within nonzero rational numbers.
Thompson, M.A.; Glendening, E.D.; Feller, D.; Kendall, R.
1995-08-01
Synthetic macrocycles have drawn much experimental and theoretical interest since Pederson first synthesized the crown-ether 18-crown-6 (18c6) in 1967. Crown-ethers show a remarkable range of specificity for a wide variety of cations that depends, in part, on the size of the ether, the type of donor atoms (e.g. oxygen, nitrogen, sulfur), and the polarity of the solvent. Crown-ethers and related macrocycles are of particular interest to research efforts in chemical separations applied to environmental remediation. For example, at the Hanford nuclear facility {sup 9O}Sr{sup 2+} and {sup 137}Cs{sup +} are two major generators of heat which complicate the disposal of nuclear waste. One example of the use of crown-ethers for radionuclide separation is the Strontium Extraction (SREX) process which uses di-t-butylcyclohexano-18-crown-6 for recovering {sup 9O}Sr{sup 2+} from acidic solution. A more thorough understanding of fundamental interactions of cation/crown-ether solution chemistry may provide the basis for rational design of new ligands useful in the separation of these and other radionuclides from radionuclide-containing waste streams at hazardous waste storage facilities. There is also a growing interest in the use of crown-ethers, cryptands, and other ligands for use in chemical sensors. Specifically, fluoroionophores, which consisting of a fluorophore (e.g. dye-molecule) linked to an ionophore (e.g. crown-ether), exhibit measurable changes in the photophysical properties of the fluorophore upon ion binding by the ionophore. Fluoroionophores would be useful for monitoring ground-water aquifers and industrial effluent streams for low-levels of hazardous radionuclides and other toxic metals.
Cisneros, G A; Tholander, S Na-Im; Parisel, O; Darden, T A; Elking, D; Perera, L; Piquemal, J-P
2008-01-01
We present a simple damping scheme for point-charge electrostatics that could be used directly in classical force fields. The approach acts at the charge (or monopole) level only and allows the inclusion of short-range electrostatic penetration effects at a very low cost. Results are compared with density functional theory Coulomb intermolecular interaction energies and with several other methods such as distributed multipoles, damped distributed multipoles, and transferable Hermite-Gaussian densities. Realistic trends in the interactions are observed for atom-centered Mertz-Kollman corrected point-charge distributions. The approach allows increasing the selectivity of parameters in the case of metal complexes. In addition, two QM/MM calculations are presented where the damping function is employed to include the MM atoms located at the QM/MM boundary. The first calculation corresponds to the gas-phase proton transfer of aspartic acid through water and the second is the first step of the reaction catalyzed by the 4-oxalocrotonate tautomerase (4OT) enzyme. First, improved agreement is observed when using the damping approach compared with the conventional excluded charge method or when including all charges in the calculation. Second, in the case of 4OT, the damped charge approach is in agreement with previous calculations, whereas including all charges gives a significantly higher energy barrier. In both cases, no reparameterization of the van der Waals part of the force field was performed. PMID:19606279
Quantum Mechanics 1 for graduate students
Course 606 Quantum Mechanics 1 for graduate students Fall 2010 Instructor Valery Pokrovsky 1 electromagnetic field. Gauge invariance. Landau levels. 7. Semiclassical approximation. 8. Quantum mechanics. Scattering. The main textbook is E. Merzbacher, Quantum Mechanics, third edition, Wiley. Additional
Quantum Mechanics as Classical Physics
Charles Sebens
2015-04-02
Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.
Decoherence in quantum mechanics and quantum cosmology
NASA Technical Reports Server (NTRS)
Hartle, James B.
1992-01-01
A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.
Phase Space Quantum Mechanics - Direct
S. Nasiri; Y. Sobouti; F. Taati
2006-05-15
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of non commuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.
Phase space quantum mechanics - Direct
Nasiri, S.; Sobouti, Y.; Taati, F. [Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of) and Department of Physics, Zanjan University, Zanjan (Iran); Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of); Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of) and Department of Physics, University of Kurdistan, D-78457 Sanadaj (Iran)
2006-09-15
Conventional approach to quantum mechanics in phase space (q,p), is to take the operator based quantum mechanics of Schroedinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.
Scattering Relativity in Quantum Mechanics
Richard Shurtleff
2011-08-09
Transforming from one reference frame to another yields an equivalent physical description. If quantum fields are transformed one way and quantum states transformed a different way then the physics changes. We show how to use the resulting changed physical description to obtain the equations of motion of charged, massive particles in electromagnetic and gravitational fields. The derivation is based entirely on special relativity and quantum mechanics.
Quantum mechanics from classical statistics
Wetterich, C. [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)], E-mail: c.wetterich@thphys.uni-heidelberg.de
2010-04-15
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.
Progress in Supersymmetric Quantum Mechanics
2003-01-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General dedicated to the subject of Supersymmetric Quantum Mechanics as featured in the International Conference in Supersymmetric Quantum Mechanics (PSQM03), 15--19 July 2003, University of Valladolid, Spain (http:\\/\\/metodos.fam.cie.uva.es\\/~susy_qm_03\\/). Participants at that meeting, as well as other researchers working in this area or in
Bush, John W. M.
Some two centuries before the quantum revolution, Newton (1) suggested that corpuscles of light generate waves in an aethereal medium like skipping stones generate waves in water, with their motion then being affected by ...
Chem 793 Quantum Mechanics I Chemistry 793
Chem 793 Quantum Mechanics I Chemistry 793 Quantum Mechanics I Fall 2000 Course outline 1 formulation. · Constants of the motion. 2. Probability in classical and quantum mechanics · Probability University #12;Chem 793 Quantum Mechanics I 7. Separable problems in 2D and 3D · Direct product functions
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics, 2009 #12;Quantum Mechanics: Measurement and Uncertainty Thursday, May 7, 2009 #12;Puzzle: The Stern it. Quantum mechanics understanding: the particle exists in a state without definite position
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics) New Particles anti-particles (combining special relativity and quantum mechanics pions (mediator/momentum/mass discrepancy must fit inside the quantum mechanical uncertainty p, E E2 - p2 c2 = 0 Thursday, May 7, 2009 #12
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Strings and the Strong Force Thursday, May 7, 2009 #12;Review of Quantum Mechanics In general, particles Planck's constant determines the scale where quantum mechanical effects become important Thursday, May 7
What quantum computers may tell us about quantum mechanics
Monroe, Christopher
17 What quantum computers may tell us about quantum mechanics Christopher R. Monroe University of Michigan, Ann Arbor Quantum mechanics occupies a unique position in the history of science. It has sur successes of quantum mechanics, its foundations are often questioned, owing to the glaring difficulties
Quantum Mechanics and Determinism
Gerard't Hooft
2001-01-01
It is shown how to map the quantum states of a system of free scalar\\u000aparticles one-to-one onto the states of a completely deterministic model. It is\\u000aa classical field theory with a large (global) gauge group. The mapping is now\\u000aalso applied to free Maxwell fields. Lorentz invariance is demonstrated.
NSDL National Science Digital Library
Galvez, Enrique
This web site, authored by Enrique Galvez and Charles Holbrow of Colgate University, outlines a project to develop undergraduate physics labs that investigate quantum interference and entanglement with photons. The labs are designed for simplicity and low cost. A description of the lab set up, background information, and an article on the project are provided.
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics with constant velocity with respect to each other (These are inertial reference frames) Newton's Laws (mechanics
Quantum Mechanics (QM) Measurement Package
NSDL National Science Digital Library
Belloni, Mario
This set of tutorial worksheets, based on the OSP Quantum Mechanics Simulations, help students explore the effects of position, momentum, and energy measurements on quantum state wavepackets. The probabilistic change in the wavefunction upon measurements and the time propagation of the states are illustrated. Similar worksheets are available for measurements of single and superpositions of energy eigenstates. The worksheets can be run online or downloaded as a pdf (attached).
PT quantum mechanics - Recent results
Bender, Carl M. [Physics Department, Washington University, St. Louis, MO 63130 (United States)
2012-09-26
Most quantum physicists believe that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under matrix transposition and complex conjugation) to be sure that the energy eigenvalues are real and that time evolution is unitary. However, the non-Dirac-hermitian Hamiltonian H p{sup 2}+ix{sup 3} has a real positive discrete spectrum and generates unitary time evolution and defines a fully consistent and physical quantum theory. Evidently, Dirac Hermiticity is too restrictive. While H = p{sup 2}+ix{sup 3} is not Dirac Hermitian, it is PT symmetric (invariant under combined space reflection P and time reversal T). Another PT-symmetric Hamiltonian whose energy levels are real, positive and discrete is H = p{sup 2}-x{sup 4}, which contains an upside-down potential. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics and quantum field theory are extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past two years some of these properties have been verified in laboratory experiments. Here, we first discuss PT-symmetric Hamiltonians at a simple intuitive level and explain why the energy levels of such Hamiltonians may be real, positive, and discrete. Second, we describe a recent experiment in which the PT phase transition was observed. Third, we briefly mention that PT-symmetric theories can be useful at a fundamental level. While the double-scaling limit of an O(N)-symmetric g{phi}{sup 4} quantum field theory appears to be inconsistent because the critical value of g is negative, this limit is in fact not inconsistent because the critical theory is PT symmetric.
Quantum Mechanics: Sum Over Paths
NSDL National Science Digital Library
Taylor, Edwin F.
Created by Edwin F. Taylor a former professor at the Department of Physics at the Massachusetts Institute of Technology, this material describes methods of presenting quantum mechanics using the path-integral formulation. Included are links to a paper and presentation outlining the method, software to simulate the path integrals, and student workbook materials. This course has been used for introducing quantum physics to high school teachers.
ccsd00002942, ON SUPERSYMMETRIC QUANTUM MECHANICS
ccsdÂ00002942, version 1 Â 25 Sep 2004 ON SUPERSYMMETRIC QUANTUM MECHANICS M.R. KIBLER Institut de Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl supersymmetric Quantum Mechanics corresponds to k = 2. A connection between fractional supersymmetric Quantum
Histories Approach to Quantum Mechanics
Tulsi Dass
2005-01-27
These lecture notes cover the important developments in histories approach to quantum mechanics with overall content and emphasis somewhat different from other reviews and books on the subject.The idea of Houtappel, Van Dam and Wigner of employing objects based on primitive concepts of physical theories is discussed in some detail and the fact that histories are such objects is emphasized. Application of histories formalism to the problem of understanding the quasiclassical domain is treated in some detail. Other topics discussed include generalized histories-based quantum mechanics and its application to the quantum mechanics of space-time,generalization of the notion of time sequences employing partial semigroups,quasitemporal structures, history projection operator (HPO) formalism, the algebraic scheme of Isham and Linden, an axiomatic scheme for quasitemporal histories-based theories and symmetries and conservation laws in histories-based theories.
Wüthrich, Christian
THE OBJECTIVE INDEFINITENESS INTERPRETATION OF QUANTUM MECHANICS: Partition logic, logical information theory, and quantum mechanics David Ellerman University of California at Riverside www ago that quantum mechanics was not compatible with Boolean logic, then the natural thing to do would
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
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.
Kowalevski top in quantum mechanics
Matsuyama, A., E-mail: spamatu@ipc.shizuoka.ac.jp
2013-09-15
The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra. -- Highlights: •Quantum spectra of the Kowalevski top are calculated. •Semiclassical quantization is carried out by the EBK formulation. •Quantum states are labeled by the semiclassical integer quantum numbers. •Multiplicity of the classical torus makes the spectra nearly degenerate. •Symmetries, quantum numbers and near-degenerate spectra are closely related.
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Mechanical Particle Physics General Relativistic Quantum Gravity increasing speed decreasing size increasing Extra Dimensions Strings and the Strong Force Thursday, June 4, 2009 #12;The Higgs Mechanism Summary
Remarks on osmosis, quantum mechanics, and gravity
Robert Carroll
2011-04-03
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
Remarks on osmosis, quantum mechanics, and gravity
Carroll, Robert
2011-01-01
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
The quantum field theory interpretation of quantum mechanics
Alberto C. de la Torre
2015-03-02
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
Quantum tunneling process and Zambrini's Euclidean quantum mechanics
Mari Jibu; Kunio Yasue
1992-01-01
By adopting Zambrini's new Euclidean quantum mechanics, a theoretical procedure to describe the ill-defined problem of quantum tunneling processes studied recently in quantum cosmology is proposed. It is shown that the tunneling process from the vacuum state to a semi-classical state can be analyzed a priori in consrast with the conventional Copenhagen interpretation of quantum mechanics.
Quantum tunneling process and Zambrini's Euclidean quantum mechanics
NASA Astrophysics Data System (ADS)
Jibu, Mari; Yasue, Kunio
1992-11-01
By adopting Zambrini's new Euclidean quantum mechanics, a theoretical procedure to describe the ill-defined problem of quantum tunneling processes studied recently in quantum cosmology is proposed. It is shown that the tunneling process from the vacuum state to a semi-classical state can be analyzed a priori in consrast with the conventional Copenhagen interpretation of quantum mechanics.
Quantum mechanics and brain uncertainty.
Macgregor, Ronald J
2006-09-01
This paper argues that molecular governing structures (such as receptors, gating molecules, or ionic channels) which operate pervasively in the brain, often with small number particle systems (as, for example, at the surfaces of membranes, synaptic clefts, or macromolecules), may plausibly be vehicles for the transmutation of quantum mechanical fluctuations to normal-level neural signaling. PMID:17125159
Quantum Mechanics and Leggett's Inequalities
NASA Astrophysics Data System (ADS)
Socolovsky, M.
2009-12-01
We show that when the proper description of the behaviour of individual photons or spin {{1}over{2}} particles in a spherically symmetric entangled pair is done through the use of the density matrix, the Leggett’s inequality is not violated by quantum mechanics.
Time, Quantum Mechanics, and Probability
Simon Saunders
2001-11-07
A "geometric" intepretation of probability is proposed, modelled on the treatment of tense in 4-dimensional spacetime. It is applied to Everett's approach to quantum mechanics, as formulated in terms of consistent histories. Standard objections to Everett's approach, based on the difficulties of interpreting probability in its terms, are considered in detail, but found to be wanting.
Delay Time in Quaternionic Quantum Mechanics
Stefano De Leo; Gisele Ducati
2012-04-11
In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex quantum mechanics.
Star Products for Relativistic Quantum Mechanics
P. Henselder
2007-05-24
The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.
Quantum Mechanics Revisited Jean Claude Dutailly
Boyer, Edmond
Quantum Mechanics Revisited Jean Claude Dutailly Paris (France) August 20, 2014 Abstract The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general a new theoretical foundation. ii) The quantum mechanics (QM) which is presented in all the books
Quantum Mechanics for Mathematicians: Introduction and Overview
Woit, Peter
Quantum Mechanics for Mathematicians: Introduction and Overview Peter Woit Department Richard Feynman goes "I think it is safe to say that no one understands quantum mechanics."[1 was contrasting quantum mechanics with the theory of general relativity, a supposedly equally hard to understand
On a realistic interpretation of quantum mechanics
Neumaier, Arnold
On a realistic interpretation of quantum mechanics Arnold Neumaier Institut fur Mathematik respecting the indeter- ministic nature of quantum mechanics, allows to speak of de#12;nite values for all], there are at least two levels of inter- preting quantum mechanics: the statistical interpretation in the narrower
First Day Handout Phys 430: Quantum Mechanics
Nickrent, Daniel L.
First Day Handout Phys 430: Quantum Mechanics (Dated: 18 August 2014) Meeting times: MWF 1:00-1:50 Room: Neckers 410 Text: "Introduction to Quantum Mechanics," 2nd Edition, by D. Griffiths. Instructor Interpretation (e) The Uncertainty Principle (f) Dirac Notation 4. Chapter 4: Quantum Mechanics in Three
On the interpretation of quantum mechanics
V. A. Fock
1957-01-01
After a brief discussion of the reasons for the complete failure of a deterministic interpretation of quantum mechanics (§ 1)Niels Bohr's ideas on quantum mechanics are exposed. The importance of Bohr's idea on the necessity of combining the quantum-mechanical description of atomic objects with a classical description of the instruments is stressed (§ 2).It is pointed out, however, that the
Visualizing quantum mechanics in phase space
Heiko Bauke; Noya Ruth Itzhak
2011-01-11
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner function formalism resembles the mathematical language of classical mechanics of non-interacting particles. Thus, it allows a more direct comparison between classical and quantum dynamical features.
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Particle Interaction Summary quantum mechanics and special relativity together imply the existence of anti-particles forces are mediated
129 Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
129 Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion
221B Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion
221B Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We, similarly to the Newton's equation of motion in mechanics. The initial condtions to solve the Newton
Quantum Mechanics: Structures, Axioms and Paradoxes
Aerts, Diederik
Quantum Mechanics: Structures, Axioms and Paradoxes Diederik Aerts Center Leo Apostel, Brussels present an analysis of quantum mechanics and its problems and para- doxes taking into account the results a genuine incomplete- ness of standard quantum mechanics, however not an incompleteness that means
A Criterion for Holism in Quantum Mechanics
Seevinck, Michiel
A Criterion for Holism in Quantum Mechanics M.P Seevinck E-mail: M.P.Seevinck@phys.uu.nl Utrecht University, The Netherlands, August 2003. 1 #12; Motivation · The question whether or not quantum mechanics is it that makes quantum mechanics a holistic theory (if so), and other physical theories not (if so). · I propose
Entanglement and Disentanglement in Relativistic Quantum Mechanics
Stanford, Kyle
Entanglement and Disentanglement in Relativistic Quantum Mechanics Jeffrey A. Barrett August 16, 2014 Abstract A satisfactory formulation of relativistic quantum mechanics re- quires that one be able in relativistic quantum mechanics must ultimately depend on the details of one's strategy for addressing
QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT
Stanford, Kyle
QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT Abstract. The quantum measurement problem has led mechanics, a strong variety of mind-body dualism provides a natural criterion for when collapses occur, and in a no-collapse formulation of quantum mechanics, a strong variety of dualism provides a way to account
Probability in modal interpretations of quantum mechanics
Seevinck, Michiel
Probability in modal interpretations of quantum mechanics Dennis Dieks Institute for the History interpretations have the ambition to construe quantum mechanics as an ob- jective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix
Improving student understanding of quantum mechanics
NASA Astrophysics Data System (ADS)
Singh, Chandralekha
2015-04-01
Learning quantum mechanics is challenging for many students. We are investigating the difficulties that upper-level students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) and tools for peer-instruction. Many of the QuILTs employ computer simulations to help students visualize and develop better intuition about quantum phenomena. We will discuss the common students' difficulties and research-based tools we are developing to bridge the gap between quantitative and conceptual aspects of quantum mechanics and help students develop a solid grasp of quantum concepts. Support from the National Science Foundation is gratefully acknowledged.
Nielsen, Steven O.
The Postulates of Quantum Mechanics (from Quantum Mechanics by Claude Cohen-Tannoudji, Bernard Diu, and Franck Lalo¨e) Introduction The postulates of quantum mechanics are the theory. Their physical content to the following questions: (i) How is the state of a quantum mechanical system at a given time described
Paradoxical Reflection in Quantum Mechanics
Pedro L. Garrido; Sheldon Goldstein; Jani Lukkarinen; Roderich Tumulka
2011-05-03
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This phenomenon is suggested by non-normalizable solutions to the time-independent Schroedinger equation, and we present evidence, numerical and mathematical, that it is also indeed predicted by the time-dependent Schroedinger equation. Furthermore, this paradoxical reflection effect suggests, and we confirm mathematically, that a quantum particle can be trapped for a long time (though not forever) in a region surrounded by downward potential steps, that is, on a plateau.
Quantum mechanics and the psyche
NASA Astrophysics Data System (ADS)
Galli Carminati, G.; Martin, F.
2008-07-01
In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.
The Transactional Interpretation of Quantum Mechanics and Quantum Nonlocality
John G. Cramer
2015-02-28
Quantum nonlocality is discussed as an aspect of the quantum formalism that is seriously in need of interpretation. The Transactional Interpretation of quantum mechanics, which describes quantum processes as transactional "handshakes" between retarded $\\psi$ waves and advanced $\\psi*$ waves, is discussed. Examples of the use of the Transactional Interpretation in resolving quantum paradoxes and in understanding the counter-intuitive aspects of the formalism, particularly quantum nonlocality, are provided.
The Mechanism of Quantum Computation
NASA Astrophysics Data System (ADS)
Castagnoli, Giuseppe
2008-08-01
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine whose coordinates are submitted to a nonfunctional relation representing all the problem constraints; moving an input part, reversibly and nondeterministically produces a solution through a many body interaction. The machine can be considered the many body generalization of another perfect machine, the bouncing ball model of reversible computation. The mathematical description of the machine’s motion, as it is, is applicable to quantum problem solving, an extension of the quantum algorithms that comprises the physical representation of the interdependence between the problem and the solution. The configuration space of the classical machine is replaced by the phase space of the quantum machine. The relation between the coordinates of the machine parts now applies to the populations of the reduced density operators of the parts of the computer register throughout state vector reduction. Thus, reduction produces the solution of the problem under a nonfunctional relation representing the problem-solution interdependence. At the light of this finding, the quantum speed up turns out to be “precognition” of the solution, namely the reduction of the initial ignorance of the solution due to backdating, to before running the algorithm, a part of the state vector reduction on the solution (a time-symmetric part in the case of unstructured problems); as such, it is bounded by state vector reduction through an entropic inequality. The computation mechanism under discussion might also explain the wholeness appearing in the introspective analysis of perception.
Supersymmetric Quantum Mechanics with Reflections
S. Post; L. Vinet; A. Zhedanov
2011-08-09
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wave functions of extended Scarf I potentials with different parameters are presented.
Complementarity in Categorical Quantum Mechanics
NASA Astrophysics Data System (ADS)
Heunen, Chris
2012-07-01
We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a `point-free' definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.
Effective equations for the quantum pendulum from momentous quantum mechanics
Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)
2012-08-24
In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Exploration of similarities between classical wave mechanics and quantum mechanics
Kim Fook Lee
2002-01-01
This dissertation explores classical analogs of one particle wave mechanics and multiparticle quantum entanglement by using classical wave optics. We develop classical measurement techniques to simulate one particle wave mechanics and quantum entanglement for up to four particles. Classical simulation of multi-particle entanglement is useful for quantum information processing (QIP) because much of the QIP does not require collapse and
Quantum mechanical light harvesting mechanisms in photosynthesis
NASA Astrophysics Data System (ADS)
Scholes, Gregory
2012-02-01
More than 10 million billion photons of light strike a leaf each second. Incredibly, almost every red-coloured photon is captured by chlorophyll pigments and initiates steps to plant growth. Last year we reported that marine algae use quantum mechanics in order to optimize photosynthesis [1], a process essential to its survival. These and other insights from the natural world promise to revolutionize our ability to harness the power of the sun. In a recent review [2] we described the principles learned from studies of various natural antenna complexes and suggested how to utilize that knowledge to shape future technologies. We forecast the need to develop ways to direct and regulate excitation energy flow using molecular organizations that facilitate feedback and control--not easy given that the energy is only stored for a billionth of a second. In this presentation I will describe new results that explain the observation and meaning of quantum-coherent energy transfer. [4pt] [1] Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer, and Gregory D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature 463, 644-648 (2010).[0pt] [2] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro and Rienk van Grondelle, ``Lessons from nature about solar light harvesting'' Nature Chem. 3, 763-774 (2011).
Levitated Quantum Nano-Magneto-Mechanical Systems
Mauro Cirio; Jason Twamley; Gavin K. Brennen; Gerard J. Milburn
2011-01-01
Quantum nanomechanical sysems have attracted much attention as they provide new macroscopic platforms for the study of quantum mechanics but may also have applications in ultra-sensitive sensing, high precision measurements and in quantum computing. In this work we study the control and cooling of a quantum nanomechanical system which is magnetically levitated via the Meissner effect. Supercurrents in nano-sized superconducting
Quantum mechanical effects from deformation theory
Much, A. [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)
2014-02-15
We consider deformations of quantum mechanical operators by using the novel construction tool of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a role. Furthermore, a quantum plane can be defined by using the deformation techniques. This in turn gives an experimentally verifiable effect.
Teaching Quantum Mechanics on an Introductory Level.
ERIC Educational Resources Information Center
Muller, Rainer; Wiesner, Hartmut
2002-01-01
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
Quantum Mechanical Observers and Time Reparametrization Symmetry
Eiji Konishi
2012-12-20
We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their non-unitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.
Quantum Mechanical Observers and Time Reparametrization Symmetry
NASA Astrophysics Data System (ADS)
Konishi, Eiji
2012-07-01
We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their nonunitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.
Orthodox Quantum Mechanics Free from Paradoxes
Rodrigo Medina
2005-08-02
A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The classical paradoxes of quantum mechanics are analyzed and their origin is found to be the fictitious properties that are usually attributed to quantum-mechanical states. The hypothesis that any mixed state can always be considered as an incoherent superposition of pure states is found to contradict quantum mechanics. A solution of EPR paradox is proposed. It is shown that entanglement of quantum states is compatible with realism and locality of events, but implies non-local encoding of information.
Quantum Mechanics Joachim Burgdorfer and Stefan Rotter
Rotter, Stefan
1 1 Quantum Mechanics Joachim BurgdÂ¨orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution 29 1.8.3 Resonances 30 1.9 Semiclassical Mechanics 31 1.9.1 The WKB Approximation 31 1.9.2 The EBK
BOOK REVIEWS: Quantum Mechanics: Fundamentals
NASA Astrophysics Data System (ADS)
Whitaker, A.
2004-02-01
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried’s well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantum mechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell’s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried’s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried’s book. Gottfried had devoted a chapter of his book to these matters, titled ‘The Measurement Process and the Statistical Interpretation of Quantum Mechanics’. Gottfried considered the von Neumann or Dirac ‘collapse of state-vector’ (or ‘reduction postulate’ or ‘projection postulate’) was unsatisfactory, as he argued that it led inevitably to the requirement to include ‘consciousness’ in the theory. He replaced this by a more mathematically and conceptually sophisticated treatment in which, following measurement, the density matrix of the correlated measured and measuring systems, rho, is replaced by hat rho, in which the interference terms from rho have been removed. rho represents a pure state, and hat rho a mixture, but Gottfried argued that they are ‘indistinguishable’, and that we may make our replacement, ‘safe in the knowledge that the error will never be found’. Now our combined state is represented as a mixture, it is intuitive, Gottfried argued, to interpret it in a probabilistic way, |cm|2 being the probability of obtaining the mth measurement result. Bell liked Gottfried’s treatment little more than the cruder ‘collapse’ idea of von Neumann, and when, shortly before Bell’s death, his polemical article ‘Against measurement’ was published in the August 1990 issue of Physics World (pages 33-40), his targets included, not only Landau and Lifshitz’s classic Quantum Mechanics, pilloried for its advocacy of old-fashioned collapse, and a paper by van Kampen in Physica, but also Gottfried’s approach. Bell regarded his replacement of rho by hat rho as a ‘butchering’ of the density matrix, and considered, in any case, that even the butchered density matrix should represent co-existence of different terms, not a set of probabilities. Gottfried has replied to Bell ( Physics World, October 1991, pages 34-40; Nature 405, 533-36 (2000)). He has also become a major commentator on Bell’s work, for example editing the section on quantum foundations in the World Scientific edition of Bell’s collected works. Thus it is exceedingly interesting to disco
Treating time travel quantum mechanically
NASA Astrophysics Data System (ADS)
Allen, John-Mark A.
2014-10-01
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilizing the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their nonlinearity and time-travel paradoxes. In particular, the "equivalent circuit model"—which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory—is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of alternate theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features—such as time-travel paradoxes, the ability to distinguish nonorthogonal states with certainty, and the ability to clone or delete arbitrary pure states—that are present with D-CTCs and P-CTCs. The problems with nonlinear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
Treating Time Travel Quantum Mechanically
John-Mark A. Allen
2014-10-10
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their non-linearity and time travel paradoxes. In particular, the "equivalent circuit model"---which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory---is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of new theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features---such as time travel paradoxes, the ability to distinguish non-orthogonal states with certainty, and the ability to clone or delete arbitrary pure states---that are present with D-CTCs and P-CTCs. The problems with non-linear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
The Linguistic Interpretation of Quantum Mechanics
Ishikawa, Shiro
2012-01-01
About twenty years ago, we proposed the mathematical formulation of Heisenberg's uncertainty principle, and further, we concluded that Heisenberg's uncertainty principle and EPR-paradox are not contradictory. This is true, however we now think that we should have argued about it under a certain firm interpretation of quantum mechanics. Recently we proposed the linguistic quantum interpretation (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy). In fact, we can consider that traditional philosophies have progressed toward quantum philosophy. In this paper, we first review the linguistic quantum interpretation, and further, clarify the relation between EPR-paradox and Heisenberg's uncertainty...
Errors and paradoxes in quantum mechanics
D. Rohrlich
2007-08-28
Errors and paradoxes in quantum mechanics, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear
Fun with supersymmetric quantum mechanics
Freedman, B.; Cooper, F.
1984-04-01
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup ..cap alpha../ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index ..delta.. which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if ..delta.. is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate ..delta.. for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references.
The Konigsberg Interpretation Of Quantum Mechanics?
Horner, Jack K.
THE KÖNIGSBERG INTERPRETATION OF QUANTUM MECHANICS? Jack K. Horner It is surely a truism that the science and philos ophy of an age influence one another; and this century has been no exception: the rise of quantum theory in particular... against this criterion to show that the rejoinder must, if cogent, assume B. 1. The EPR argument. The object of the EPR argu ment Ts to show that the quantum theory fails to describe "completely" certain quantum-mechanical events. Provided...
A mathematical theory for deterministic quantum mechanics
Gerard't Hooft
2007-01-01
Classical, i.e. deterministic theories underlying quantum mechanics are considered, and it is shown how an apparent quantum mechanical Hamiltonian can be defined in such theories, being the operator that generates evolution in time. It includes various types of interactions. An explanation must be found for the fact that, in the real world, this Hamiltonian is bounded from below. The mechanism
Quantum Mechanics Dung-Hai Lee
Murayama, Hitoshi
Quantum Mechanics Dung-Hai Lee Summer 2000 #12;Contents 1 A brief reminder of linear Algebra 3 1 mechanics as Feynman path inte- grals in imaginary time . . . . . . . . . . . . . . . . . . . 47 3.14 From classical to quantum mechanics . . . . . . . . . . . 47 3.14.1 Route I
A Criterion for Holism in Quantum Mechanics
Seevinck, Michiel
A Criterion for Holism in Quantum Mechanics M.P Seevinck Utrecht University, The Netherlands, June 2003. 1 #12; Motivation · The question whether or not quantum mechanics (QM) gives rise to some mechanics a holistic theory (if so), and other physical theories not (if so). · I propose an operational
A Criterion for Holism in Quantum Mechanics
Seevinck, Michiel
A Criterion for Holism in Quantum Mechanics # M.P Seevinck # # Utrecht University, The Netherlands, June 2003. # 1 #12; # Motivation # . The question whether or not quantum mechanics (QM) gives rise mechanics a holistic theory (if so), and other physical theories not (if so). . I propose an operational
Chaos in Bohmian quantum mechanics
NASA Astrophysics Data System (ADS)
Efthymiopoulos, C.; Contopoulos, G.
2006-02-01
This paper presents a number of numerical investigations of orbits in the de Broglie-Bohm version of quantum mechanics. We first clarify how the notion of chaos should be implemented in the case of Bohmian orbits. Then, we investigate the Bohmian orbits in three different characteristic quantum systems: (a) superposition of three stationary states in the Hamiltonian of two uncoupled harmonic oscillators with incommensurable frequencies, (b) wave packets in a Hénon-Heiles-type Hamiltonian and (c) a modified two-slit experiment. In these examples, we identify regular or chaotic orbits and also orbits exhibiting a temporarily regular and then chaotic behaviour. Then, we focus on a numerical investigation of the Bohm-Vigier (Bohm and Vigier 1954 Phys. Rev. 26 208) theory, that an arbitrary initial particle distribution P should asymptotically tend to |?|2, by considering the role of chaotic mixing in causing irregularity of Madelung's flow, a necessary condition for P to tend to |?|2. We find that the degree of chaos of a particular system correlates with the speed of convergence of P to |?|2. In the case of wave-packet dynamics, our numerical data show that the time of convergence scales exponentially with the inverse of the effective perturbation from the harmonic oscillator Hamiltonian. The latter result can be viewed as a quantum analogue of Nekhoroshev's (Nekhoroshev 1977 Russ. Math. Surveys 32 1) theorem of exponential stability in classical nonlinear Hamiltonian dynamics.
Quantum mechanics as a complete physical theory
D. A. Slavnov
2002-11-10
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that allow constructing a renewed mathematical scheme of quantum mechanics. This scheme involves the standard mathematical formalism of quantum mechanics. Simultaneously, it contains a mathematical object that adequately describes a single experiment. We give an example of the application of the proposed scheme.
Principles of a 2nd Quantum Mechanics
Mioara Mugur-Schächter
2014-10-23
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this representation as a reference-and-imbedding-structure, the foundations of an intelligible reconstruction of the Hilbert-Dirac formulation of Quantum Mechanics is developed. Inside this reconstruction the measurement problem as well as the other major problems raised by the quantum mechanical formalism, dissolve.
Bohmian particle trajectories contradict quantum mechanics
Michael Zirpel
2009-03-23
The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to avoid contradictions with quantum mechanics. There are correlations between particle positions at different times which cannot be reproduced with real particle trajectories. A simple rearrangement of an experimental test of the Bell-CHSH inequality demonstrates this.
Quantum Mechanics and Closed Timelike Curves
Florin Moldoveanu
2007-04-23
General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal region of space-time are investigated. If the correspondence principle is true, then all generalizations of quantum mechanics on acausal manifolds are not renormalizable. Therefore quantum mechanics can only be defined on global hyperbolic manifolds and all general relativity solutions exhibiting time travel are unphysical.
Emergent Quantum Mechanics and Emergent Symmetries
Gerard't Hooft; Gerard t
2007-01-01
Quantum mechanics is ‘emergent’ if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such theories allow for a natural explanation of the existence of gauge equivalence classes (gauge orbits), including the equivalence classes
Kindergarten Quantum Mechanics: Lecture Notes
NASA Astrophysics Data System (ADS)
Coecke, Bob
2006-01-01
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in [3, 4]) which subsumes my Logic of Entanglement [11]. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes [12, 13]. In a last section we provide some pointers to the body of technical literature on the subject.
Thermodynamic integration from classical to quantum mechanics
Habershon, Scott [Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS (United Kingdom); Manolopoulos, David E. [Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ (United Kingdom)
2011-12-14
We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.
Tests of CPT and Quantum Mechanics: experiment
NASA Astrophysics Data System (ADS)
Ambrosino, F.; Antonelli, A.; Antonelli, M.; Bacci, C.; Barva, M.; Beltrame, P.; Bencivenni, G.; Bertolucci, S.; Bini, C.; Bloise, C.; Bocchetta, S.; Bocci, V.; Bossi, F.; Bowring, D.; Branchini, P.; Bulychjov, S. A.; Caloi, R.; Campana, P.; Capon, G.; Capussela, T.; Carboni, G.; Ceradini, F.; Cervelli, F.; Chi, S.; Chiefari, G.; Ciambrone, P.; Conetti, S.; De Lucia, E.; De Santis, A.; De Simone, P.; De Zorzi, G.; Dell'Agnello, S.; Denig, A.; Di Domenico, A.; Di Donato, C.; Di Falco, S.; Di Micco, B.; Doria, A.; Dreucci, M.; Farilla, A.; Felici, G.; Ferrari, A.; Ferrer, M. L.; Finocchiaro, G.; Fiore, S.; Forti, C.; Franzini, P.; Gatti, C.; Gauzzi, P.; Giovannella, S.; Gorini, E.; Graziani, E.; Incagli, M.; Kluge, W.; Kulikov, V.; Lacava, F.; Lanfranchi, G.; Lee-Franzini, J.; Leone, D.; Martemianov, M.; Martini, M.; Massarotti, P.; Matsyuk, M.; Mei, W.; Meola, S.; Messi, R.; Miscetti, S.; Moulson, M.; Müller, S.; Murtas, F.; Napolitano, M.; Nguyen, F.; Palutan, M.; Pasqualucci, E.; Passalacqua, L.; Passeri, A.; Patera, V.; Perfetto, F.; Pontecorvo, L.; Primavera, M.; Santangelo, P.; Santovetti, E.; Saracino, G.; Schamberger, R. D.; Sciascia, B.; Sciubba, A.; Scuri, F.; Sfiligoi, I.; Sibidanov, A.; Spadaro, T.; Spiriti, E.; Tabidze, M.; Testa, M.; Tortora, L.; Valente, P.; Valeriani, B.; Venanzoni, G.; Veneziano, S.; Ventura, A.; Ventura, S.; Versaci, R.; Villella, I.; Xu, G.; KLOE Collaboration
2007-05-01
Neutral kaons provide one of the systems most sensitive to quantum mechanics and CPT violation. Models predicting quantum mechanics violation, also related to CPT violation, have been tested at the CPLEAR and KLOE experiments. In this report results of CPLEAR obtained by studying the time evolution of single and two entangled kaons are reviewed. New or improved limits on decoherence and CPT violation parameters have been obtained by KLOE studying the quantum interference in the channel ??KK?????. No deviations from the expectations of quantum mechanics and CPT symmetry have been observed.
Experimental status of quaternionic quantum mechanics
S. P. Brumby; G. C. Joshi
1996-01-01
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic effects in
Quantum mechanics on a real Hilbert space
Jan Myrheim
1999-01-01
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics, keeping the same set of physical states, but admitting more general observables. The standard time reversal operator involves complex conjugation, in
On the quantum mechanics of supermembranes
Bernard de Wit; J. Hoppe; H. Nicolai
1988-01-01
We study the quantum-mechanical properties of a supermembrane and examine the nature of its ground state. A supersymmetric gauge theory of area-preserving transformations provides a convenient framework for this study. The supermembrane can be viewed as a limiting case of a class of models in supersymmetric quantum mechanics. Its mass does not depend on the zero modes and vanishes only
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Friday, June 19, 2009 #12;String Theory Origins We introduced string theory as a possible solution to our
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification that is naturally solved by string theory Strings vibrating in a variety of ways give rise to particles of different
Quaternionic Formulation of Supersymmetric Quantum Mechanics
Seema Rawat; O. P. S. Negi
2007-03-18
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with the results of quantum mechanics.
Quantum mechanics in complex systems
NASA Astrophysics Data System (ADS)
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown. These nodes are spaced far enough from each other to minimized the electronic repulsion of the electrons, while still providing adequate enough attraction so as to bind the excess elections into orbitals. We have found that even with relativistic considerations these species are stably bound within the field. It was also found that performing the dimensional scaling calculations for systems within the confines of laser fields to be a much simpler and more cost-effective method than the supporting D=3 SCF method. The dimensional scaling method is general and can be extended to include relativistic corrections to describe the stability of simple molecular systems in super-intense laser fields. Chapter 3, we delineate the model, and aspects therein, of inelastic electron tunneling and map this model to the protein environment. G protein-coupled receptors (GPCRs) constitute a large family of receptors that sense molecules outside of a cell and activate signal transduction pathways inside the cell. Modeling how an agonist activates such a receptor is important for understanding a wide variety of physiological processes and it is of tremendous value for pharmacology and drug design. Inelastic electron tunneling spectroscopy (IETS) has been proposed as the mechanism by which olfactory GPCRs are activated by an encapsulated agonist. In this note we apply this notion to GPCRs within the mammalian nervous system using ab initio quantum chemical modeling. We found that non-endogenous agonists of the serotonin receptor share a singular IET spectral aspect both amongst each other and with the serotonin molecule: a peak that scales in intensity with the known agonist activities. We propose an experiential validation of this model by utilizing lysergic acid dimethylamide (DAM-57), an ergot derivative, and its isotopologues in which hydrogen atoms are replaced by deuterium. If validated our theory may provide new avenues for guided drug design and better in silico prediction of efficacies. Our final chapter, explores methods which may be explored to assist in the early instructio
An entropic picture of emergent quantum mechanics
D. Acosta; P. Fernandez de Cordoba; J. M. Isidro; J. L. G. Santander
2011-09-20
Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on space. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant h from Boltzmann's constant k.
Quantum Mechanical Models Of The Fermi Shuttle
Sternberg, James [University of Tennessee, Department of Physics and Astronomy, Knoxville TN 37996 (United States)
2011-06-01
The Fermi shuttle is a mechanism in which high energy electrons are produced in an atomic collision by multiple collisions with a target and a projectile atom. It is normally explained purely classically in terms of the electron's orbits prescribed in the collision. Common calculations to predict the Fermi shuttle use semi-classical methods, but these methods still rely on classical orbits. In reality such collisions belong to the realm of quantum mechanics, however. In this paper we discuss several purely quantum mechanical calculations which can produce the Fermi shuttle. Being quantum mechanical in nature, these calculations produce these features by wave interference, rather than by classical orbits.
Polymer Quantum Mechanics and its Continuum Limit
Alejandro Corichi; Tatjana Vukasinac; Jose A. Zapata
2007-08-22
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle and a simple cosmological model.
Superconformal Quantum Mechanics from M2-branes
Tadashi Okazaki
2015-03-12
We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a number of exotic and enlightening properties which do not occur in higher dimensional field theories. We see that superfield and superspace formalism is available for $\\mathcal{N}\\le 8$ superconformal mechanical models. We then discuss the M2-branes with a focus on the world-volume descriptions of the multiple M2-branes which are superconformal three-dimensional Chern-Simons matter theories. Finally we argue that the two topics are connected in M-theoretical construction by considering the multiple M2-branes wrapped around a compact Riemann surface and study the emerging IR quantum mechanics. We establish that the resulting quantum mechanics realizes a set of novel $\\mathcal{N}\\ge 8$ superconformal quantum mechanical models which have not been reached so far. Also we discuss possible applications of the superconformal quantum mechanics to mathematical physics.
NON-COMMUTATIVE SPHERES AND NUMERICAL QUANTUM MECHANICS
Arveson, William
NON-COMMUTATIVE SPHERES AND NUMERICAL QUANTUM MECHANICS basic issues that arise when one attempts to mo* *del quantum mechanical systems on a computer, quantum mechanics. Contributed to the proceedings of a NATO conference on operator algebras, ma
OPTI 570A-Quantum Mechanics Course Description
Arizona, University of
OPTI 570A- Quantum Mechanics Course Description: This is a one-semester course designed to provide students with a solid understanding of quantum mechanics formalism, techniques, and important example physics, quantum optics, relativistic quantum mechanics and other advanced quantum mechanics topics
Dorit Aharonov; Umesh Vazirani
2012-06-16
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regime by extending the usual scientific paradigm to include {\\it interactive experiments}.
Aalok Pandya
2008-09-08
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.
Causal structure in categorical quantum mechanics
NASA Astrophysics Data System (ADS)
Lal, Raymond Ashwin
Categorical quantum mechanics is a way of formalising the structural features of quantum theory using category theory. It uses compound systems as the primitive notion, which is formalised by using symmetric monoidal categories. This leads to an elegant formalism for describing quantum protocols such as quantum teleportation. In particular, categorical quantum mechanics provides a graphical calculus that exposes the information flow of such protocols in an intuitive way. However, the graphical calculus also reveals surprising features of these protocols; for example, in the quantum teleportation protocol, information appears to flow `backwards-in-time'. This leads to question of how causal structure can be described within categorical quantum mechanics, and how this might lead to insight regarding the structural compatibility between quantum theory and relativity. This thesis is concerned with the project of formalising causal structure in categorical quantum mechanics. We begin by studying an abstract view of Bell-type experiments, as described by `no-signalling boxes', and we show that under time-reversal no-signalling boxes generically become signalling. This conflicts with the underlying symmetry of relativistic causal structure. This leads us to consider the framework of categorical quantum mechanics from the perspective of relativistic causal structure. We derive the properties that a symmetric monoidal category must satisfy in order to describe systems in such a background causal structure. We use these properties to define a new type of category, and this provides a formal framework for describing protocols in spacetime. We explore this new structure, showing how it leads to an understanding of the counter-intuitive information flow of protocols in categorical quantum mechanics. We then find that the formal properties of our new structure are naturally related to axioms for reconstructing quantum theory, and we show how a reconstruction scheme based on purification can be formalised using the structures of categorical quantum mechanics. Finally, we discuss the philosophical aspects of using category theory to describe fundamental physics. We consider a recent argument that category-theoretic formulations of physics, such as categorical quantum mechanics, can be used to support a variant of structural realism. We argue against this claim. The work of this thesis suggests instead that the philosophy of categorical quantum mechanics is subtler than either operationalism or realism.
Four-dimensional understanding of quantum mechanics
Jarek Duda
2009-10-14
In this paper I will try to convince that quantum mechanics does not have to lead to indeterminism, but is just a natural consequence of four-dimensional nature of our world - that for example particles shouldn't be imagined as 'moving points' in space, but as their trajectories in the spacetime like in optimizing action formulation of Lagrangian mechanics. There will be analyzed simplified model - Boltzmann distribution among trajectories occurs to give quantum mechanic like behavior - for example electron moving in proton's potential would make some concrete trajectory which average exactly to the probability distribution of the quantum mechanical ground state. We will use this model to build intuition about quantum mechanics and discuss its generalizations to get some effective approximation of physics. We will see that topological excitations of the simplest model obtained this way already creates known from physics particle structure, their decay modes and electromagnetic/gravitational interactions between them.
Is quantum field theory a generalization of quantum mechanics?
A. V. Stoyanovsky
2009-01-01
We construct a mathematical model analogous to quantum field theory, but without the notion of vacuum and without measurable physical quantities. This model is a direct mathematical generalization of scattering theory in quantum mechanics to path integrals with multidimensional trajectories (whose mathematical interpretation has been given in a previous paper). In this model the normal ordering of operators in the
Chem 7940 Quantum Mechanics II Spring 2010 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2010 Chemistry 7940 Quantum Mechanics II Spring 2010 Mechanics in Chemistry (Dover reprint). [8] D. J. Tannor, Introduction to Quantum Mechanics: a Time. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940 Quantum Mechanics II Spring 2013 Mechanics in Chemistry (Dover reprint). [6] P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
Visual Quantum Mechanics: Online Interactive Programs
NSDL National Science Digital Library
The Visual Quantum Mechanics project, from the Physics Education Group of Kansas State University's Department of Physics, develops innovative ways to "introduce quantum physics to high school and college students who do not have a background in modern physics or higher level math." Funded by the National Science Foundation, this resource for educators provides interactive computer visualizations and animations that introduce quantum mechanics. The interactive programs (which require Shockwave) include a spectroscopy lab suite, a probability illustrator, an energy band creator, quantum tunneling, a color creator (a Java version is also available), a wave function sketcher, a wave packet explorer, an energy diagram explorer, a diffraction suite, and a hydrogen spectroscopy program. These online demonstrations should prove to be excellent visual, hands-on teaching aids when introducing concepts involving quantum mechanics. Users can download Shockwave at the site.
Quantum Mechanical Search and Harmonic Perturbation
Jiang, J H R; Wu, C E; Chiou, Dah-Wei; Jiang, Jie-Hong R.; Wu, Cheng-En
2007-01-01
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some important technology advances, such as masers, lasers, nuclear magnetic resonance, etc., originated from it. Here we add quantum computation to this list with a theoretical demonstration. Based on harmonic perturbation, a quantum mechanical algorithm is devised to search the ground state of a given Hamiltonian. The intrinsic complexity of the algorithm is continuous and parametric in both time T and energy E. More precisely, the probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is optimal. As harmonic perturbation provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers.
Quantum Mechanical Search and Harmonic Perturbation
Jie-Hong R. Jiang; Dah-Wei Chiou; Cheng-En Wu
2007-09-14
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some important technology advances, such as masers, lasers, nuclear magnetic resonance, etc., originated from it. Here we add quantum computation to this list with a theoretical demonstration. Based on harmonic perturbation, a quantum mechanical algorithm is devised to search the ground state of a given Hamiltonian. The intrinsic complexity of the algorithm is continuous and parametric in both time T and energy E. More precisely, the probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is optimal. As harmonic perturbation provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers.
A Quantum Mechanical Travelling Salesman
Ravindra N. Rao
2011-08-23
A quantum simulation of a travelling salesman is described. A vector space for a graph is defined together with a sequence of operators which transform a special initial state into a superposition states representing Hamiltonian tours. The quantum amplitude for any tour is a function of the classical cost of travelling along the edges in that tour. Tours with the largest quantum amplitude may be different than those with the smallest classically-computed cost.
Playing Games with Quantum Mechanics
Simon J. D. Phoenix; Faisal Shah Khan
2012-02-22
We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence. We call such games playable. By focusing on the notion of playability for games we can more clearly see the distinction between classical and quantum games and tackle the thorny issue of what it means to quantize a game. The approach we take can more properly be thought of as gaming the quantum rather than quantizing a game and we find that in this perspective we can think of a complete quantum game, for a given set of preferences, as representing a single family of quantum games with many different playable versions. The versions of Quantum Prisoners Dilemma presented in the literature can therefore be thought of specific instances of the single family of Quantum Prisoner's Dilemma with respect to a particular measurement. The conditions for equilibrium are given for playable quantum games both in terms of expected outcomes and a geometric approach. We discuss how any quantum game can be simulated with a classical game played with classical coins as far as the strategy selections and expected outcomes are concerned.
Can Quantum Mechanics Heal Classical Singularities?
NASA Astrophysics Data System (ADS)
Helliwell, T. M.; Konkowski, D. A.
2008-09-01
We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. We show that a large subset of classically singular spacetimes is nevertheless nonsingular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint so the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities.
Quantum mechanics and the generalized uncertainty principle
NASA Astrophysics Data System (ADS)
Bang, Jang Young; Berger, Micheal S.
2006-12-01
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
Local quantum mechanics with finite Planck mass
M Kozlowski; J. Marciak -Kozlowska; M. pelc
2007-04-20
In this paper the motion of quantum particles with initial mass m is investigated. The quantum mechanics equation is formulated and solved. It is shown that the wave function contains the component which is depended on the gravitation fine structure constant
The Compton effect: Transition to quantum mechanics
R. H. Stuewer
2000-01-01
The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite
Quantum Mechanics and the Generalized Uncertainty Principle
Jang Young Bang; Micheal S. Berger
2006-11-30
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
Quantum Mechanics and Multiply Connected Spaces
B. G. Sidharth
2006-05-16
t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of the fact that Quantum Theory is actually a theory in multiply connected space while Classical Theory operates in simply connected space.
Student Difficulties in Learning Quantum Mechanics.
ERIC Educational Resources Information Center
Johnston, I. D.; Crawford, K.; Fletcher, P. R.
1998-01-01
Reports on a preliminary project that uses a phenomenographic approach to explore the ways in which a small number of fundamental ideas are conceptualized by students who are judged to have mastered quantum mechanics material. (DDR)
A quantum mechanical investigation of silsesquioxane cages
Earley, C.W. [Univ. of Missouri, Kansas City, MO (United States)
1994-09-01
A quantum mechanical investigation of molecular silsesquioxane cages determined that molecules containing (Si-O-){sub 3} rings were more unstable than those with larger rings. 49 refs., 2 figs., 4 tabs.
Scattering in conformally invariant quantum mechanics
Oksak, A.I.
1986-08-01
The S matrix conformally invariant quantum mechanics is determined by the multiple valuedness of the representation of the conformal group (i.e., by the operator that realizes conformal rotation through angle 2..pi..).
Beyond Quantum Mechanics and General Relativity
Andrea Gregori
2010-02-24
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
Quantum mechanical streamlines. I - Square potential barrier
NASA Technical Reports Server (NTRS)
Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.
1974-01-01
Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.
Remarks on Quantum Mechanics Norbert Dragon
Dragon, Norbert
Remarks on Quantum Mechanics Norbert Dragon #12;Intended as completion, repetition and comment once: //www.itp.uni-hannover.de/~dragon. I am grateful for feedback concerning errors, including type slips
Supersymmetric q-deformed quantum mechanics
Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
2012-06-27
A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.
Is quantum field theory a generalization of quantum mechanics?
A. V. Stoyanovsky
2009-09-10
We construct a mathematical model analogous to quantum field theory, but without the notion of vacuum and without measurable physical quantities. This model is a direct mathematical generalization of scattering theory in quantum mechanics to path integrals with multidimensional trajectories (whose mathematical interpretation has been given in a previous paper). In this model the normal ordering of operators in the Fock space is replaced by the Weyl-Moyal algebra. This model shows to be useful in proof of various results in quantum field theory: one first proves these results in the mathematical model and then "translates" them into the usual language of quantum field theory by more or less "ugly" procedures.
Aalok Pandya
2009-01-19
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of probability in Quantum Mechanics and its interpretations. We give yet another interpretation to the notion of Faraday lines and loops as the locus of probability flow. Also, the possibilities of visualization of spectra of area operators by means of classical geometric forms and conventional Quantum Mechanics are explored.
Experimental status of quaternionic quantum mechanics
Brumby, S P
1996-01-01
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic effects in correlated multi-particle systems. We set out how such experiments might distinguish between the several quaternionic models proposed in the literature.
Experimental status of quaternionic quantum mechanics
S. P. Brumby; G. C. Joshi
1996-10-08
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic effects in correlated multi-particle systems. We set out how such experiments might distinguish between the several quaternionic models proposed in the literature.
Epistemic cognition: issues in learning quantum mechanics
NASA Astrophysics Data System (ADS)
Oliver, Keith; Bao, Lei
2001-10-01
Epistemology is the branch of philosophy concerned with the nature and justification of knowledge. Epistemic cognition is thinking about the general methodologies and epistemological/philosophical views about learning. Quantum mechanics is the branch of physics that involves a fundamental uncertainty and that is being continuously developed and argued both theoretically and practically. We will illustrate the potential opportunity quantum mechanics presents us in discussing epistemic issues with our students and in exploring the nature of student epistemology.
Some mutant forms of quantum mechanics
NASA Astrophysics Data System (ADS)
Takeuchi, Tatsu; Chang, Lay Nam; Lewis, Zachary; Minic, Djordje
2012-12-01
We construct a 'mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative 'mutation' is also suggested.
Quantum mechanics in de Sitter space
Subir Ghosh; Salvatore Mignemi
2011-01-25
We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however of the order of the ratio between the length scale of the quantum mechanical system and the de Sitter radius, and therefore exceedingly small. Nevertheless, the existence of effects due to the large scale curvature of spacetime in atomic experiments has a theoretical relevance.
2T Physics and Quantum Mechanics
W. Chagas-Filho
2008-02-20
We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit described by the same Hamiltonian. One of these formulations is used as a basis for a complementation of the usual quantum mechanics when in the presence of gravity.
CLNS 96/1399 Peculiarities of Quantum Mechanics
CLNS 96/1399 Peculiarities of Quantum Mechanics: Origins and Meaning Yuri F. Orlov Floyd R. Newman, specifically quantum, features of quantum mechanics --- quan tum nonlocality, indeterminism, interference are quantum observables themselves and are represented in quantum mechanics by density matrices of pure states
Theoretical Chemistry I Quantum Mechanics 16 October 2008
Pfeifer, Holger
Theoretical Chemistry I Quantum Mechanics Axel Groß 16 October 2008 #12;#12;Preface Theoretical Chemistry 1 Quantum Mechanics Prof. Dr. Axel Groß Phone: 5022819 Room No.: O25/342 Email: axel of Quantum Mechanics 3. Quantum Dynamics 4. Angular Momentum 5. Approximation Methods 6. Symmetry in Quantum
On a New Form of Quantum Mechanics (II)
N. Gorobey; A. Lukyanenko; I. Lukyanenko
2009-12-16
The correspondence of a new form of quantum mechanics based on a quantum version of the action principle, which was proposed earlier [arXiv:0807.3508], with the ordinary quantum mechanics is established. New potentialities of the quantum action principle in the interpretation of quantum mechanics are considered.
Mechanical systems in the quantum regime
Menno Poot; Herre S. J. van der Zant
2011-10-12
Mechanical systems are ideal candidates for studying quantumbehavior of macroscopic objects. To this end, a mechanical resonator has to be cooled to its ground state and its position has to be measured with great accuracy. Currently, various routes to reach these goals are being explored. In this review, we discuss different techniques for sensitive position detection and we give an overview of the cooling techniques that are being employed. The latter include sideband cooling and active feedback cooling. The basic concepts that are important when measuring on mechanical systems with high accuracy and/or at very low temperatures, such as thermal and quantum noise, linear response theory, and backaction, are explained. From this, the quantum limit on linear position detection is obtained and the sensitivities that have been achieved in recent opto and nanoelectromechanical experiments are compared to this limit. The mechanical resonators that are used in the experiments range from meter-sized gravitational wave detectors to nanomechanical systems that can only be read out using mesoscopic devices such as single-electron transistors or superconducting quantum interference devices. A special class of nanomechanical systems are bottom-up fabricated carbon-based devices, which have very high frequencies and yet a large zero-point motion, making them ideal for reaching the quantum regime. The mechanics of some of the different mechanical systems at the nanoscale is studied. We conclude this review with an outlook of how state-of-the-art mechanical resonators can be improved to study quantum {\\it mechanics}.
Quantum Information Theory and the Foundations of Quantum Mechanics
Christopher Gordon Timpson
2004-12-08
This thesis is a contribution to the debate on the implications of quantum information theory for the foundations of quantum mechanics. In Part 1, the logical and conceptual status of various notions of information is assessed. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings `information' functions as an abstract noun, hence does not refer to a particular or substance (the worth of this point is illustrated in application to quantum teleportation). The claim that `Information is Physical' is assessed and argued to face a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. The reflections of Bruckner and Zeilinger (2001) and Deutsch and Hayden (2000) on the nature of information in quantum mechanics are critically assessed and some results presented on the characterization of entanglement in the Deutsch-Hayden formalism. Some philosophical aspects of quantum computation are discussed and general morals drawn concerning the nature of quantum information theory. In Part II, following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger's (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, Bub and Halvorson (2003) is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.
Testing foundations of quantum mechanics with photons
NASA Astrophysics Data System (ADS)
Shadbolt, Peter; Mathews, Jonathan C. F.; Laing, Anthony; O'Brien, Jeremy L.
2014-04-01
Quantum mechanics continues to predict effects at odds with a classical understanding of nature. Experiments with light at the single-photon level have historically been at the forefront of fundamental tests of quantum theory and the current developments in photonic technologies enable the exploration of new directions. Here we review recent photonic experiments to test two important themes in quantum mechanics: wave-particle duality, which is central to complementarity and delayed-choice experiments; and Bell nonlocality, where the latest theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different experiments.
Symplectic Topology and Geometric Quantum Mechanics
NASA Astrophysics Data System (ADS)
Sanborn, Barbara
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
Quantum mechanics: Passage through chaos
Daniel A. Steck
2009-01-01
A quantum system can undergo tunnelling even without a barrier to tunnel through. The latest experiments visualize this process in exquisite detail, completely reconstructing the state of the evolving system.
Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series
Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series: From Quantum Mechanics one component at a time. · Planck's constant determines the scale at which quantum mechanical effects could get rid of quantum mechanical effects The "wavelength" of particles given by h mv would all
Chem 7940 Quantum Mechanics II Spring 2011 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2011 Chemistry 7940 Quantum Mechanics II Spring 2011 in Chemistry (Dover reprint). [8] D. J. Tannor, Introduction to Quantum Mechanics: a Time-Dependent Perspective. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
Chem 7940 Quantum Mechanics II Spring 2012 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2012 Chemistry 7940 Quantum Mechanics II Spring 2012 Theory (Dover reprint). [6] G.C. Schatz and M.A. Ratner, Quantum Mechanics in Chemistry (Dover reprint. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
The Möbius Symmetry of Quantum Mechanics
Alon E. Faraggi; Marco Matone
2015-02-16
The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under $D$--dimensional M\\"obius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global M\\"obius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the M\\"obius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.
Probability in modal interpretations of quantum mechanics
Dennis Dieks
2007-03-02
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from introducing new structure by hand. In this paper we explain how this programme can be made concrete. In particular, we show that the Born probability rule, and sets of definite-valued observables to which the Born probabilities pertain, can be uniquely defined from the quantum state and Hilbert space structure. We discuss the status of probability in modal interpretations, and to this end we make a comparison with many-worlds alternatives. An overall point that we stress is that the modal ideas define a general framework and research programme rather than one definite and finished interpretation.
Statistical mechanics based on fractional classical and quantum mechanics
Korichi, Z.; Meftah, M. T., E-mail: mewalid@yahoo.com [Physics Department, LRPPS Laboratory, Ouargla University, Ouargla 30000 (Algeria)
2014-03-15
The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.
Quantum mechanics: last stop for reductionism
Gabriele Carcassi
2012-03-16
The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a complex vector space, used in quantum mechanics.
Foster, Mark P.
11 1 Introduction to quantum mechanics Quantum mechanics is the basic tool needed to describe, understand and devise NMR experiments. Fortunately for NMR spectroscopists, the quantum mechanics of nuclear mathematical concepts frequently encountered in quantum mechanics and NMR. 0DWKHPDWLFDO FRQFHSWV 1.1.1 Complex
Intrusion Detection with Quantum Mechanics: A Photonic Quantum Fence
Humble, Travis S [ORNL; Bennink, Ryan S [ORNL; Grice, Warren P [ORNL; Owens, Israel J [Los Alamos National Laboratory (LANL)
2008-01-01
We describe the use of quantum-mechanically entangled photons for sensing intrusions across a physical perimeter. Our approach to intrusion detection uses the no-cloning principle of quantum information science as protection against an intruder s ability to spoof a sensor receiver using a classical intercept-resend attack. We explore the bounds on detection using quantum detection and estimation theory, and we experimentally demonstrate the underlying principle of entanglement-based detection using the visibility derived from polarization-correlation measurements.
Operational measurements in quantum mechanics
NASA Astrophysics Data System (ADS)
Kocha?ski, Piotr; Wódkiewicz, Krzysztof
1997-10-01
The operational approach to quantum measurements is formulated in terms of a phase space propensity and the corresponding positive operator-valued measure. This general approach is illustrated by an operational measurement of the position and momentum of a particle, and by an operational Malus measurement of spin phases.
Quantum mechanism of Biological Search
Younghun Kwon
2006-05-09
We wish to suggest an algorithm for biological search including DNA search. Our argument supposes that biological search be performed by quantum search.If we assume this, we can naturally answer the following long lasting puzzles such that "Why does DNA use the helix structure?" and "How can the evolution in biological system occur?".
ERIC Educational Resources Information Center
Oss, Stefano; Rosi, Tommaso
2015-01-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many…
Levitated Quantum Nano-Magneto-Mechanical Systems
NASA Astrophysics Data System (ADS)
Cirio, Mauro; Twamley, Jason; Brennen, Gavin K.; Milburn, Gerard J.
2011-03-01
Quantum nanomechanical sysems have attracted much attention as they provide new macroscopic platforms for the study of quantum mechanics but may also have applications in ultra-sensitive sensing, high precision measurements and in quantum computing. In this work we study the control and cooling of a quantum nanomechanical system which is magnetically levitated via the Meissner effect. Supercurrents in nano-sized superconducting loops give rise to a motional restoring force (trap), when placed in an highly inhomogenous magnetic field and can yield complete trapping of all translational and rotational motions of the levitated nano-object with motional oscillation frequencies ? ~ 10 - 100 MHz. As the supercurrents experience little damping this system will possess unprecendented motional quality factors, with Qmotion ~109 -1013 , and motional superposition states may remain coherent for days. We describe how to execute sideband cooling through inductive coupling to a nearby flux qubit, cooling the mechanical motion close to the ground state.
Nonrelativistic Quantum Mechanics with Fundamental Environment
NASA Astrophysics Data System (ADS)
Gevorkyan, Ashot S.
2011-03-01
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ? R { ?}, where R 3 and R { ?} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.
Creation mechanism of quantum accelerator modes
NASA Astrophysics Data System (ADS)
Ahmadi, P.; Behinaein, G.; Ramareddy, V.; Summy, G. S.
2009-11-01
We investigate the creation mechanism of quantum accelerator modes which are attributed to the existence of the stability islands in an underlying pseudoclassical phase space of the quantum delta-kicked accelerator. Quantum accelerator modes can be created by exposing a Bose-Einstein condensate to a pulsed standing light wave. We show that constructive interference between momentum states populated by the pulsed light determines the stability island’s existence in the underlying pseudoclassical phase space. We generalize this interference model to incorporate higher-order accelerator modes, showing that they are generated if the rephasing occurs after multiple pulses. The model is extended to predict the momentum structure of the quantum accelerator modes close to higher-order quantum resonances. These predictions are in good agreement with our experimental observations.
Coherent states in noncommutative quantum mechanics
J Ben Geloun; F G Scholtz
2009-01-21
Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position uncertainty relation, obey a Poisson distribution and possess a flat geometry. Using the natural isometry between the quantum Hilbert space of Hilbert Schmidt operators and the tensor product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.
Coherent states in noncommutative quantum mechanics
Ben Geloun, J. [National Institute for Theoretical Physics, Private Bag X1, Matieland 7602 (South Africa); International Chair of Mathematical Physics and Applications (ICMPA-UNESCO Chair) 072 B.P. 50 Cotonou (Benin); Departement de Mathematiques et Informatique, Faculte des Sciences et Techniques, Universite Cheikh Anta Diop (Senegal); Scholtz, F. G. [National Institute for Theoretical Physics, Private Bag X1, Matieland 7602 (South Africa)
2009-04-15
Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position uncertainty relation, obey a Poisson distribution, and possess a flat geometry. Using the natural isometry between the quantum Hilbert space of Hilbert-Schmidt operators and the tensor product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.
Green's Functions and Their Applications to Quantum Mechanics
Morrow, James A.
Green's Functions and Their Applications to Quantum Mechanics Jeff Schueler June 2, 2011 Contents 1 Green's Functions in Quantum Mechanics and Many-body Theory 8 3.1 Time Independent Green's Fuctions, specifically in how they apply to quantum mechan- ics. I plan to introduce some of the fundamentals of quantum
CLNS 96/1443 Peculiarities of Quantum Mechanics
CLNS 96/1443 REVISED Peculiarities of Quantum Mechanics: Origins and Meaning 1 Yuri F. Orlov Floyd The most peculiar, specifically quantum, features of quantum mechanics --- quan tum nonlocality mechanics 1 This paper, to be presented to the Nordic Symposium on Basic Problems in Quantum Physics, June
Emergent Quantum Mechanics and Emergent Symmetries
Hooft, Gerard 't [Institute for Theoretical Physics Utrecht University and Spinoza Institute Postbox 80.195 3508 TD Utrecht (Netherlands)
2007-11-20
Quantum mechanics is 'emergent' if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such theories allow for a natural explanation of the existence of gauge equivalence classes (gauge orbits), including the equivalence classes generated by general coordinate transformations. Thus, local gauge symmetries and general coordinate invariance could be emergent symmetries, and this might lead to new alleys towards understanding the flatness problem of the Universe.
Optimal guidance law in quantum mechanics
Yang, Ciann-Dong, E-mail: cdyang@mail.ncku.edu.tw; Cheng, Lieh-Lieh, E-mail: leo8101@hotmail.com
2013-11-15
Following de Broglie’s idea of a pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by the Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle’s motion is just the wavefunction ?(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for ?(t,x), from which quantum operators emerge naturally. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function ?{sup ?}?. -- Highlights: •Treating quantum mechanics as a pursuit-evasion game. •Reveal an interesting analogy between guided flight motion and guided quantum motion. •Solve optimal quantum guidance problem by dynamic programming. •Gives a formal proof of de Broglie–Bohm’s idea of a pilot wave. •The optimal pilot wave is shown to be a wavefunction solved from Schrödinger equation.
Improving students' understanding of quantum mechanics
NASA Astrophysics Data System (ADS)
Singh, Chandralekha
2011-03-01
Learning quantum mechanics is especially challenging, in part due to the abstract nature of the subject. We have been conducting investigations of the difficulties that students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) as well as tools for peer-instruction. The goal of QuILTs and peer-instruction tools is to actively engage students in the learning process and to help them build links between the formalism and the conceptual aspects of quantum physics without compromising the technical content. They focus on helping students integrate qualitative and quantitative understanding, confront and resolve their misconceptions and difficulties, and discriminate between concepts that are often confused. In this talk, I will give examples from my research in physics education of how students' prior knowledge relevant for quantum mechanics can be assessed, and how learning tools can be designed to help students develop a robust knowledge structure and critical thinking skills. Supported by the National Science Foundation.
Quantum mechanics-based properties for 3D-QSAR.
El Kerdawy, Ahmed; Güssregen, Stefan; Matter, Hans; Hennemann, Matthias; Clark, Timothy
2013-06-24
We have used a set of four local properties based on semiempirical molecular orbital calculations (electron density (?), hydrogen bond donor field (HDF), hydrogen bond acceptor field (HAF), and molecular lipophilicity potential (MLP)) for 3D-QSAR studies to overcome the limitations of the current force field-based molecular interaction fields (MIFs). These properties can be calculated rapidly and are thus amenable to high-throughput industrial applications. Their statistical performance was compared with that of conventional 3D-QSAR approaches using nine data sets (angiotensin converting enzyme inhibitors (ACE), acetylcholinesterase inhibitors (AchE), benzodiazepine receptor ligands (BZR), cyclooxygenase-2 inhibitors (COX2), dihydrofolate reductase inhibitors (DHFR), glycogen phosphorylase b inhibitors (GPB), thermolysin inhibitors (THER), thrombin inhibitors (THR), and serine protease factor Xa inhibitors (fXa)). The 3D-QSAR models generated were tested thoroughly for robustness and predictive ability. The average performance of the quantum mechanical molecular interaction field (QM-MIF) models for the nine data sets is better than that of the conventional force field-based MIFs. In the individual data sets, the QM-MIF models always perform better than, or as well as, the conventional approaches. It is particularly encouraging that the relative performance of the QM-MIF models improves in the external validation. In addition, the models generated showed statistical stability with respect to model building procedure variations such as grid spacing size and grid orientation. QM-MIF contour maps reproduce the features important for ligand binding for the example data set (factor Xa inhibitors), demonstrating the intuitive chemical interpretability of QM-MIFs. PMID:23692495
Multichannel framework for singular quantum mechanics
Camblong, Horacio E., E-mail: camblong@usfca.edu [Department of Physics and Astronomy, University of San Francisco, San Francisco, CA 94117-1080 (United States); Epele, Luis N., E-mail: epele@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Fanchiotti, Huner, E-mail: huner@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina)] [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); García Canal, Carlos A., E-mail: garcia@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Ordóñez, Carlos R., E-mail: ordonez@uh.edu [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States)
2014-01-15
A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.
The statistical origins of quantum mechanics
U. Klein
2011-03-08
It is shown that Schroedinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle mechanics by replacing all observables by statistical averages. The second is a local conservation law of probability with a probability current which takes the form of a gradient. The third is a principle of maximal disorder as realized by the requirement of minimal Fisher information. The rule for calculating expectation values is obtained from a fourth postulate, the requirement of energy conservation in the mean. The fact that all these basic relations of quantum theory may be derived from premises which are statistical in character is interpreted as a strong argument in favor of the statistical interpretation of quantum mechanics. The structures of quantum theory and classical statistical theories are compared and some fundamental differences are identified.
Probability in the Many-Worlds Interpretation of Quantum Mechanics
Vaidman, Lev
of standard quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence
The Quantum Mechanics of Hyperion
Nathan Wiebe; L. E. Ballentine
2005-03-21
This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as hbar^{2/3} for chaotic states, and as hbar^2 for non-chaotic states, leading to negligible QC differences for a macroscopic object like Hyperion. The quantum probability distributions do not approach their classical limit smoothly, having an extremely fine oscillatory structure superimposed on the smooth classical background. For a macroscopic object, this oscillatory structure is too fine to be resolved by any realistic measurement. Either a small amount of smoothing (due to the finite resolution of the apparatus) or a very small amount of environmental decoherence is sufficient ensure the classical limit. Under decoherence, the QC differences in the probability distributions scale as (hbar^2/D)^{1/6}, where D is the momentum diffusion parameter. We conclude that decoherence is not essential to explain the classical behavior of macroscopic bodies.
Fractional quantum mechanics and Lévy path integrals
NASA Astrophysics Data System (ADS)
Laskin, Nikolai
2000-04-01
A new extension of a fractality concept in quantum physics has been developed. The path integrals over the Lévy paths are defined and fractional quantum and statistical mechanics have been developed via new fractional path integrals approach. A fractional generalization of the Schrödinger equation has been found. The new relation between the energy and the momentum of non-relativistic fractional quantum-mechanical particle has been established. We have derived a free particle quantum-mechanical kernel using Fox's H-function. The equation for the fractional plane wave function has been obtained. As a physical application of the developed fQM we have proposed a new fractional approach to the QCD problem of quarkonium. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in term of the Fox's H-function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics.
Quantum mechanics on a real Hilbert space
Jan Myrheim
1999-05-11
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics, keeping the same set of physical states, but admitting more general observables. The standard time reversal operator involves complex conjugation, in this sense it goes beyond the complex theory and may serve as an example to motivate the generalization. Another example is unconventional canonical quantization such that the harmonic oscillator of angular frequency $\\omega$ has any given finite or infinite set of discrete energy eigenvalues, limited below by $\\hbar\\omega/2$.
Quantum mechanics on a real Hilbert space
Myrheim, Jan
1999-01-01
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics, keeping the same set of physical states, but admitting more general observables. The standard time reversal operator involves complex conjugation, in this sense it goes beyond the complex theory and may serve as an example to motivate the generalization. Another example is unconventional canonical quantization such that the harmonic oscillator of angular frequency $\\omega$ has any given finite or infinite set of discrete energy eigenvalues, limited below by $\\hbar\\omega/2$.
Space and time from quantum mechanics
Chew, G.F.
1992-09-16
Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over collapse of the quantum-mechanical state vector when measurement is performed. Additionally, pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.
Space and time from quantum mechanics
NASA Astrophysics Data System (ADS)
Chew, G. F.
1992-09-01
Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over the collapse of the quantum-mechanical state vector when measurement is performed. Additionally, the pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as a coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.
Scattering Relativity in Quantum Mechanics
Richard Shurtleff
2015-07-06
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the particle field translated along one displacement, particle states are translated along a possibly different displacement. Arbitrary phase results. And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when field and states are translated. It is shown that a path of extreme phase obeys a semiclassical equation for force with derived terms that can describe electromagnetism and gravitation.
Quantum statistical mechanics, L-series, Anabelian Geometry
Marcolli, Matilde
Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Adem Lectures, Mexico City, January 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12 Mechanics, L-series and Anabelian Geometry, arXiv:1009.0736 Matilde Marcolli Quantum statistical mechanics
A new introductory quantum mechanics curriculum
NASA Astrophysics Data System (ADS)
Kohnle, Antje; Bozhinova, Inna; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth
2014-01-01
The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum-mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of the interpretive aspects of quantum mechanics and quantum information theory. This paper gives an overview of the resources available from the IOP website. The core text includes around 80 articles which are co-authored by leading experts, arranged in themes, and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is included in the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways, from being supplemental to existing courses to forming a complete programme.
Macroscopic Quantum Mechanics in a Classical Spacetime
Huan Yang; Haixing Miao; Da-Shin Lee; Bassam Helou; Yanbei Chen
2013-04-23
We apply the many-particle Schr\\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schr\\"odinger-Newton equation for their centers of mass, which are degrees of freedom that can be monitored and manipulated at the quantum mechanical levels by state-of-the-art optoemchanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, we found that its quantum uncertainty evolves in a different frequency from its classical eigenfrequency --- with a difference that depends on the internal structure of the object, and can be observable using current technology. For several objects, the Schr\\"odinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet they do not allow quantum uncertainty to be transferred from one object to another through gravity.
Quantum mechanics of time travel through post-selected teleportation
Maccone, Lorenzo
This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based ...
CPT and Quantum Mechanics Tests with Kaons
Jose Bernabeu; John Ellis; Nick E. Mavromatos; Dimitri V. Nanopoulos; Joannis Papavassiliou
2006-07-28
In this review we first discuss the theoretical motivations for possible CPT violation and deviations from ordinary quantum-mechanical behavior of field-theoretic systems in the context of an extended class of quantum-gravity models. Then we proceed to a description of precision tests of CPT symmetry using mainly neutral kaons. We emphasize the possibly unique role of neutral meson factories in providing specific tests of models where the quantum-mechanical CPT operator is not well-defined, leading to modifications of Einstein-Podolsky-Rosen particle correlators. Finally, we present tests of CPT, T, and CP using charged kaons, and in particular K_l4 decays, which are interesting due to the high statistics attainable in experiments.
A Euclidean formulation of relativistic quantum mechanics
Philip Kopp; Wayne Polyzou
2011-06-21
In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear operators on a Hilbert space, it has many of the advantages of quantum mechanics. One interesting feature of this approach is that matrix elements of operators in normalizable states on the physical Hilbert space can be calculated directly using the Euclidean Green functions without performing an analytic continuation. The formalism is summarized in this paper. We discuss the motivation, advantages and difficulties in using this formalism. We discuss how to compute bound states, scattering cross sections, and finite Poincare transformations without using analytic continuation. A toy model is used to demonstrate how matrix elements of exp(-beta H) in normalizable states can be used to construct-sharp momentum transition matrix elements.
Stainless steel optimization from quantum mechanical calculations
Levente Vitos; Pavel A. Korzhavyi; Börje Johansson
2003-01-01
Alloy steel design has always faced a central problem: designing for a specific property very rarely produces a simultaneous significant improvement in other properties. For instance, it is difficult to design a material that combines high values of two of the most important mechanical characteristics of metals, hardness and ductility. Here we use the most recent quantum theories of random
Euclidean formulation of relativistic quantum mechanics
W. N. Polyzou; Philip Kopp
2009-08-10
We discuss preliminary work on a formulation of relativistic quantum mechanics that uses reflection-positive Euclidean Green functions or their generating functionals as phenomenological input. We discuss the construction of a Poincare invariant S-matrix from matrix element of exp(- \\beta H).
Quantum mechanics with applications to quarkonium
C. Quigg; Jonathan L. Rosner
1979-01-01
Some methods of nonrelativistic quantum mechanics which are particularly useful for studying the variation of bound-state parameters with constituent mass and excitation energy are reviewed. These techniques rely upon elementary scaling arguments and on the semiclassical (WKB) approximation. They are of general interest, but are applied here to the study of bound systems of a heavy quark and antiquark. Properties
Physical Interpretations of Nilpotent Quantum Mechanics
Peter Rowlands
2010-01-01
Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization,
WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN
Rosner, Jonathan L.
WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN PHYS 342 Final Project March 10, 2011 Contents of Postselection 4 4. Impossible Spin Measurements 5 5. Hardy's Paradox 5 6. Controversy over Weak Measurement 8 7 of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to be 100." [1] The topic
Dissipation in Quantum Mechanics. The Harmonic Oscillator
I. R. Senitzky
1960-01-01
The need for a quantum-mechanical formalism for systems with dissipation which is applicable to the radiation field of a cavity is discussed. Two methods that have been used in this connection are described. The first, which starts with the classical Newtonian equation of motion for a damped oscillator and applies the conventional formal quantization techniques, leads to an exact solution;
Quantum Mechanics Studies of Cellobiose Conformations
Technology Transfer Automated Retrieval System (TEKTRAN)
Three regions of the Phi,Psi space of cellobiose were analyzed with quantum mechanics. A central region, in which most crystal structures are found, was covered by a 9 x 9 grid of 20° increments of Phi and Psi. Besides these 81 constrained minimizations, we studied two central sub-regions and two re...
Is Quantum Mechanics needed to explain consciousness ?
Knud Thomsen
2007-11-13
In this short comment to a recent contribution by E. Manousakis [1] it is argued that the reported agreement between the measured time evolution of conscious states during binocular rivalry and predictions derived from quantum mechanical formalisms does not require any direct effect of QM. The recursive consumption analysis process in the Ouroboros Model can yield the same behavior.
Quantum Mechanical Effects in Gravitational Collapse
Eric Greenwood
2010-01-12
In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schr\\"odinger formalism. The Functional Schr\\"odinger formalism allows us to investigate the time-dependent evolutions of the quantum mechanical effects, which is beyond the scope of the usual methods used to investigate the quantum mechanical corrections of gravitational collapse. Utilizing the time-dependent nature of the Functional Schr\\"odinger formalism, we study the quantization of a spherically symmetric domain wall from the view point of an asymptotic and infalling observer, in the absence of radiation. To build a more realistic picture, we then study the time-dependent nature of the induced radiation during the collapse using a semi-classical approach. Using the domain wall and the induced radiation, we then study the time-dependent evolution of the entropy of the domain wall. Finally we make some remarks about the possible inclusion of backreaction into the system.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-01
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. PMID:26124252
Comparison of Classical and Quantum Mechanical Uncertainties.
ERIC Educational Resources Information Center
Peslak, John, Jr.
1979-01-01
Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)
Morozov, Alexandre V.
Comparison of Quantum Mechanics and Molecular Mechanics Dimerization Energy Landscapes for Pairs, quantum mechanical calculations on small molecule models, and molecular mechanics potential decomposition find reasonable qualitative agreement between molecular mechanics and quantum chemistry calculations
Consistent interpretations of quantum mechanics
Omnes, R. (Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris XI, Batiment 211, 91405 Orsay CEDEX (France))
1992-04-01
Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counterexamples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.
The Compton effect: Transition to quantum mechanics
NASA Astrophysics Data System (ADS)
Stuewer, R. H.
2000-11-01
The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite Robert A. Millikan's confirmation of Einstein's equation of the photoelectric effect in 1915. I then follow in some detail the experimental and theoretical research program that Arthur Holly Compton pursued between 1916 and 1922 at the University of Minnesota, the Westinghouse Lamp Company, the Cavendish Laboratory, and Washington University that culminated in his discovery of the Compton effect. Surprisingly, Compton was not influenced directly by Einstein's light-quantum hypothesis, in contrast to Peter Debye and H.A. Kramers, who discovered the quantum theory of scattering independently. I close by discussing the most significant response to that discovery, the Bohr-Kramers-Slater theory of 1924, its experimental refutation, and its influence on the emerging new quantum mechanics.
Time and the foundations of quantum mechanics
NASA Astrophysics Data System (ADS)
Pashby, Thomas
Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of `time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on re ection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.
BERNSTEIN PROCESSES, EUCLIDEAN QUANTUM MECHANICS AND INTEREST RATE MODELS
Lescot, Paul
works with J.-C. Zambrini, of the link between euclidean quantum mechanics, Bernstein processes = as a new parameter. In Zambrini's Euclidean Quantum Mechanics (see e.g. [1]), this equation splits into : 2
ABOUT A HUNDRED YEARS HAVE PASSED since quantum mechanics was first developed. Quantum
Bier, Martin
of Physical Law, noted: "I think I can safely say that nobody under- stands quantum mechanics."1 record in physics before he devoted himself at a later age Quantum Consciousness and Other Spooky MythsABOUT A HUNDRED YEARS HAVE PASSED since quantum mechanics was first developed. Quantum mechanics
Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics
Zambrini, Jean-Claude
Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics S. Albeverio, a new rigorous, but not probabilistic, Lagrangian version of nonrelativistic quantum mechanics is given in SchrÃ¶dinger's Euclidean quantum mechanics."1 There, a proba- bilistic i.e., "Euclidean" generalization
Modality, Potentiality and Contradiction in Quantum Mechanics
Christian de Ronde
2015-02-17
In [11], Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum mechanics (QM) attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause [1, 2, 3] have raised several arguments against this approach and claimed that, taking into account the square of opposition, quantum superpositions are better understood in terms of contrariety propositions rather than contradictory propositions. In [17] we defended the Paraconsistent Approach to Quantum Superpositions (PAQS) and provided arguments in favor of its development. In the present paper we attempt to analyze the meanings of modality, potentiality and contradiction in QM, and provide further arguments of why the PAQS is better suited, than the Contrariety Approach to Quantum Superpositions (CAQS) proposed by Arenhart and Krause, to face the interpretational questions that quantum technology is forcing us to consider.
A Signal Processing Model of Quantum Mechanics
Chris Thron; Johnny Watts
2012-05-08
This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing the amplitude and phase information of a modulated carrier wave. Particle transmission events are modeled as the outcome of a process of signal accumulation that occurs in an extra (non-spacetime) dimension. Besides giving a natural interpretation of the wavefunction and the Born rule, the model accommodates the collapse of the wave packet and other quantum paradoxes such as EPR and the Ahanorov-Bohm effect. The model also gives a new perspective on the 'relational' nature of quantum mechanics: that is, whether the wave function of a physical system is "real" or simply reflects the observer's partial knowledge of the system. We simulate the model for a 2-slit experiment, and indicate possible deviations of the model's predictions from conventional quantum mechanics. We also indicate how the theory may be extended to a field theory.
Web-based Quantum Mechanics II Course
NSDL National Science Digital Library
Breinig, Marianne
This web site, authored by Marianne Breinig, is an entire web-based Quantum Mechanics II Course based at the University of Tennessee. It has instructional materials, in-class tutorials, simulations, links to other quantum resources, a discussion forum, homework assignments, and solutions. A schedule and syllabus are also included for easier implementation into a curriculum. Most of the tools on the website require a browser of Internet Explorer 4 or higher to function. This is a nice set of resources for students or instructors interested in physics.
Quantum mechanical coherence, resonance, and mind
Stapp, H.P.
1995-03-26
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Quantum Mechanical Scattering in Nanoscale Systems
NASA Astrophysics Data System (ADS)
Gianfrancesco, A. G.; Ilyashenko, A.; Boucher, C. R.; Ram-Mohan, L. R.
2012-02-01
We investigate quantum scattering using the finite element method. Unlike textbook treatments employing asymptotic boundary conditions (BCs), we use modified BCs, which permits computation close to the near-field region and reduces the Cauchy BCs to Dirichlet BCs, greatly simplifying the analysis. Scattering from any finite quantum mechanical potential can be modeled, including scattering in a finite waveguide geometry and in the open domain. Being numerical, our analysis goes beyond the Born Approximation, and the finite element approach allows us to transcend geometric constraints. Results of the formulation will be presented with several case studies, including spin dependent scattering, demonstrating the high accuracy and flexibility attained in this approach.
Quantum-mechanical phase locking in weak-link arrays
Widom, A. (Physics Department, Northeastern University, Boston, Massachusetts 02115 (United States)); Vittoria, C. (Department of Electrical Engineering, Northeastern University, Boston, Massachusetts 02115 (United States))
1991-12-01
Quantum-mechanical descriptions of arrays of Josephson weak links often invoke electric-field-energy storage in the weak-link capacitors. However, such quantum-electrodynamic mechanism is by no means a requirement for the notion of macroscopic quantum-mechanical wave functions for the array as a whole. These statements are illustrated for the phenomena of quantum-mechanical phase locking'' in one- and two-dimensional arrays in electromagnetic fields.
Deformation Quantization: From Quantum Mechanics to Quantum Field Theory
P. Tillman
2006-10-31
The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to quantum field theory. Also, we discuss some of the conceptual advantages of DQ and how DQ may be related to algebraic quantum field theory. Additionally, our previous results are summarized which includes the construction of the Fedosov star-product on dS/AdS. One of the goals of these results was to verify that DQ gave the same results as previous analyses of these spaces. Another was to verify that the formal series used in the conventional treatment converged by obtaining exact and nonperturbative results for these spaces.
Progress in Euclidean relativistic few-body quantum mechanics
Polyzou, Wayne
Progress in Euclidean relativistic few-body quantum mechanics Wayne Polyzou The University of Iowa Iowa City, IA 52242 October 9, 2012 Abstract We discuss recent progress in the Euclidean formulation of relativistic few-body quantum mechanics. 1 Introduction Euclidean relativistic quantum mechanics is a formalism
Harvard University Physics 143b: Quantum Mechanics II
Harvard University Physics 143b: Quantum Mechanics II Instructor : Subir Sachdev, Lyman 343@fas.harvard.edu This is the second half of an introductory course on quantum mechanics. The course will complete the text book: the photon 5. Relativistic quantum mechanics: the Dirac equation 6. Einstein-Podolsky-Rosen "paradox", Bell
Harvard University Physics 143b: Quantum Mechanics II
Harvard University Physics 143b: Quantum Mechanics II Instructor : Subir Sachdev, Lyman 343@physics.harvard.edu This is the second half of an introductory course on quantum mechanics. The course will complete the text book: the photon 5. Relativistic quantum mechanics: the Dirac equation 6. Scattering theory. 7. Einstein
Outline of Quantum Mechanics William G. Faris 1
Ueltschi, Daniel
Contents Outline of Quantum Mechanics William G. Faris 1 Inequalities for SchrÂ¨odinger Operators is the goal of the present lecture notes. They include an excellent introduction to quantum mechanics been de- veloped over the years for, and because of, quantum mechanics. These are the subject of two
The syllabus of the Course 624 Quantum Mechanics 2
The syllabus of the Course 624 Quantum Mechanics 2 Spring 2009. Instructor V.L. Pokrovsky. 1. Many-body quantum mechanics. Second quantization. Spin and statistics. Bose- Einstein condensation. 6's phase. Landau-Zener theory. Principal textbook: E. Merzbacher, Quantum Mechanics, 3-d edition, Wiley
Quantum statistical mechanics, L-series, Anabelian Geometry
Marcolli, Matilde
Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Colloquium, Harvard University, March 24, 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12 as partition functions of physical systems Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian
Quantum statistical mechanics, L-series, Anabelian Geometry
Marcolli, Matilde
Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Beijing, August 2013 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;joint work with Gunther Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;Number fields: finite
Predicting crystal structure by merging data mining with quantum mechanics
Ceder, Gerbrand
ARTICLES Predicting crystal structure by merging data mining with quantum mechanics CHRISTOPHER C@mit.edu Published online: 9 July 2006; doi:10.1038/nmat1691 Modern methods of quantum mechanics have proved with quantum mechanics if an algorithm to direct the search through the large space of possible structures
MSE 157: Quantum Mechanics of Nanoscale Materials Course Information
MSE 157: Quantum Mechanics of Nanoscale Materials Course Information Basic info Prof. Aaron there. Textbook The textbook for this course is Introduction to Quantum Mechanics by David Griffiths. We interest. Other recommended books for outside reading: Applied Quantum Mechanics by David Levi Applied
Quantum Mechanics as a Science -Religion Bridge By Stanley Klein
Klein, Stanley
Quantum Mechanics as a Science - Religion Bridge By Stanley Klein (May 1, 2002) Stanley Klein and for fitting contact lenses. Klein's interest in quantum mechanics and brain research has led him to explore of more than 20 years, DUALITY, summarizes his theme that the duality of quantum mechanics provides
The Objective Inde...niteness Interpretation of Quantum Mechanics
Wüthrich, Christian
The Objective Inde...niteness Interpretation of Quantum Mechanics David Ellerman University of California at Riverside Draft (not for quotation) May 28, 2013 Abstract Quantum mechanics (QM models indef- inite elements that become more de...nite as distinctions are made. If quantum mechanics
Truong, Thanh N.
a combined quantum mechanical/molecular mechanics QM/MM potential confirms the accuracy and usefulness half century, quantum chemistry has made significant progress in prediction properties of gas-phase pro is to construct an approximate solventsolute interaction potential either using classical molecular mechanics
Measurement and Fundamental Processes in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Jaeger, Gregg
2015-07-01
In the standard mathematical formulation of quantum mechanics, measurement is an additional, exceptional fundamental process rather than an often complex, but ordinary process which happens also to serve a particular epistemic function: during a measurement of one of its properties which is not already determined by a preceding measurement, a measured system, even if closed, is taken to change its state discontinuously rather than continuously as is usual. Many, including Bell, have been concerned about the fundamental role thus given to measurement in the foundation of the theory. Others, including the early Bohr and Schwinger, have suggested that quantum mechanics naturally incorporates the unavoidable uncontrollable disturbance of physical state that accompanies any local measurement without the need for an exceptional fundamental process or a special measurement theory. Disturbance is unanalyzable for Bohr, but for Schwinger it is due to physical interactions' being borne by fundamental particles having discrete properties and behavior which is beyond physical control. Here, Schwinger's approach is distinguished from more well known treatments of measurement, with the conclusion that, unlike most, it does not suffer under Bell's critique of quantum measurement. Finally, Schwinger's critique of measurement theory is explicated as a call for a deeper investigation of measurement processes that requires the use of a theory of quantum fields.
Does quantum mechanics require non-locality?
Ghenadie N. Mardari
2014-10-29
Non-commutative properties of single quanta must violate the limit of Bell's theorem, but not the boundary of Tsirelson's theorem. This is a consequence of three basic principles: superposition (every quantum is in many states at the same time), correspondence (only the net state of interference is real), and uncertainty (conjugate variables have inversely proportional spectra). The two conditions have only been verified with entangled pairs of quanta. It is not possible to perform incompatible measurements on the same entity. Hence, the principles of quantum mechanics cannot be verified directly. At least one of them could be wrong. Though, as shown by EPR, this can only be true if non-locality is at work. In light of the latest developments in quantum theory, even that assumption is insufficient. Non-local effects are either unable to cross Bell's limit, or forced to violate Tsirelson's bound. New layers of hidden variables are required to maintain belief in action-at-a-distance, but the three principles cannot be rejected in any case. Therefore, quantum mechanics is immune to this challenge. The hypothesis of non-locality is superfluous.
The preparation of states in quantum mechanics
Juerg Froehlich; Baptiste Schubnel
2014-09-28
The important problem of how to prepare a quantum mechanical system, $S$, in a specific initial state of interest - e.g., for the purposes of some experiment - is addressed. Three distinct methods of state preparation are described. One of these methods has the attractive feature that it enables one to prepare $S$ in a preassigned initial state with certainty; i.e., the probability of success in preparing $S$ in a given state is unity. This method relies on coupling $S$ to an open quantum-mechanical environment, $E$, in such a way that the dynamics of $S \\vee E$ pulls the state of $S$ towards an "attractor", which is the desired initial state of $S$. This method is analyzed in detail.
Quantum mechanics on phase space and teleportation
NASA Astrophysics Data System (ADS)
Messamah, Juba; Schroeck, Franklin E.; Hachemane, Mahmoud; Smida, Abdallah; Hamici, Amel H.
2015-03-01
The formalism of quantum mechanics on phase space is used to describe the standard protocol of quantum teleportation with continuous variables in order to partially investigate the interplay between this formalism and quantum information. Instead of the Wigner quasi-probability distributions used in the standard protocol, we use positive definite true probability densities which account for unsharp measurements through a proper wave function representing a non-ideal quantum measuring device. This is based on a result of Schroeck and may be taken on any relativistic or nonrelativistic phase space. The obtained formula is similar to a known formula in quantum optics, but contains the effect of the measuring device. It has been applied in three cases. In the first case, the two measuring devices, corresponding to the two entangled parts shared by Alice and Bob, are not entangled and described by two identical Gaussian wave functions with respect to the Heisenberg group. They lead to a probability density identical to the function which is analyzed and compared with the Wigner formalism. A new expression of the teleportation fidelity for a coherent state in terms of the quadrature variances is obtained. In the second case, these two measuring devices are entangled in a two-mode squeezed vacuum state. In the third case, two Gaussian states are combined in an entangled squeezed state. The overall observation is that the state of the measuring devices shared by Alice and Bob influences the fidelity of teleportation through their unsharpness and entanglement.
Applications of computational quantum mechanics
NASA Astrophysics Data System (ADS)
Temel, Burcin
This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts with novel properties. Doping a metal oxide may alter its intrinsic properties drastically. A catalytically non-active material can be activated by doping. In this study, we showed that pure zirconia (ZrO2) has almost no activity in methanol coupling reaction, whereas when it is doped with aluminum, the doped catalyst produces dimethyl ether (DME), which is valuable as an alternative future energy source.
Principle of Least Action in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Kobe, Donald H.
2004-10-01
We show that Hamilton's Principle of Least (or Extremum) Action for a complex scalar field to give the Schroedinger equation is equivalent to a commonly used time-dependent variational principle used in quantum mechanics with a Lagrangian density involving the wave function and the Hamiltonian operator. The method is applied to a many-boson system to derive a time-dependent Gross-Pitaevski equation.
Grounding quantum probability in psychological mechanism.
Love, Bradley C
2013-06-01
Pothos & Busemeyer (P&B) provide a compelling case that quantum probability (QP) theory is a better match to human judgment than is classical probability (CP) theory. However, any theory (QP, CP, or other) phrased solely at the computational level runs the risk of being underconstrained. One suggestion is to ground QP accounts in mechanism, to leverage a wide range of process-level data. PMID:23673043
Physical Interpretations of Nilpotent Quantum Mechanics
Rowlands, Peter
2010-01-01
Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization, and related issues.
Quantum Mechanics and Motion: A Modern Perspective
Gerald E. Marsh
2009-12-27
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum, yields a world-line. If a force acts on the particle, its probability distribution is accordingly modified. This must also be true for macroscopic objects, although now the description is far more complicated by the structure of matter and associated surface physics.
Chiral quantum mechanics (CQM) for antihydrogen systems
G. Van Hooydonk
2005-12-03
A first deception of QM on antiH already appears in one-center integrals for two-center systems (G. Van Hooydonk, physics/0511115). In reality, full QM is a theory for chiral systems but the QM establishment was wrong footed with a permutation of reference frames. With chiral quantum mechanics (CQM), the theoretical ban on natural antiH must be lifted as soon as possible.
Modern Quantum Mechanics Experiments for Undergraduates
NSDL National Science Digital Library
Beck, Mark
Authored by Mark Beck of Whitman College's Department of Physics, this site provides information about simplified quantum mechanics experiments such as the Grangier experiment and single photon interference. Included are a general description, an overview, course materials, experiments, external links and notes. Each experiment or lesson provides instructions and other need information such as images, charts or graphs. This series of resources could be used to enhance or create curricula in the field.
Collocation method for fractional quantum mechanics
Amore, Paolo; Hofmann, Christoph P.; Saenz, Ricardo A. [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diagonal 113 y 64 S/N, Sucursal 4, Casilla de correo 16, 1900 La Plata (Argentina)
2010-12-15
We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schroedinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed.
No Labeling Quantum Mechanics of Indiscernible Particles
NASA Astrophysics Data System (ADS)
Domenech, G.; Holik, F.; Kniznik, L.; Krause, D.
2010-12-01
Our aim in this paper is to show an example of the formalism we have developed to avoid the label-tensor-product-vector-space-formalism of quantum mechanics when dealing with indistinguishable quanta. States in this new vector space, that we call the Q-space, refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the unobservability of permutations, a goal of quasi-set theory.
Superconformal multi-black hole quantum mechanics
Jeremy Michelson; Andrew Strominger
1999-01-01
The quantum mechanics of N slowly-moving charged BPS black holes in five-dimensional Script N = 1 supergravity is considered. The moduli space metric of the N black holes is derived and shown to admit 4 supersymmetries. A near-horizon limit is found in which the dynamics of widely separated black holes decouples from that of strongly-interacting, near-coincident black holes. This decoupling
Physical Interpretations of Nilpotent Quantum Mechanics
Peter Rowlands
2010-04-09
Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization, and related issues.
Relativistic non-Hermitian quantum mechanics
NASA Astrophysics Data System (ADS)
Jones-Smith, Katherine; Mathur, Harsh
2014-06-01
We develop relativistic wave equations in the framework of the new non-Hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT-symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that, in particular, the mass matrix be Hermitian also allows for models that have no counterpart in conventional quantum mechanics. For example it is well known that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here, we show that the same quartet of Weyl spinors, when coupled by a non-Hermitian but PT-symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is nonzero. The PT-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a noninteracting theory it violates P and T individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions and are shown to maintain many of the canonical structures from Hermitian field theory, but with new and interesting possibilities permitted by the non-Hermiticity parameter m2.
Quantum mechanics and low energy nucleon dynamics
Renat Kh. Gainutdinov; Aigul A. Mutygullina
2004-08-25
We discuss the problem of consistency of quantum mechanics as applied to low energy nucleon dynamics with the symmetries of QCD. It is shown that the dynamics consistent with these symmetries is not governed by the Schrodinger equation. We present a new way to formulate the effective theory of nuclear forces as an inevitable consequence of the basic principles of quantum mechanics and the symmetries of strong interactions. We show that being formulated in this way the effective theory of nuclear forces can be put on the same firm theoretical grounds as the quantum mechanics of atomic phenomena. In this case the effective theory allows one to describe with a given accuracy not only two-nucleon scattering, but also the evolution of nucleon systems, and places the constraints on the off-shell behavior of the two-nucleon interaction. In this way we predict the off-shell behavior of the S wave two-nucleon T-matrix at very low energies when the pionless theory is applicable. Further extensions and applications of this approach are discussed.
The cosmic origin of quantum mechanics
Ding-Yu Chung
2001-02-18
In this paper, the base of quantum mechanics is the spontaneous tendency for a microscopic object to fractionalize instantly into quasistates and condense instantly quasistates. This quasistate is equivalent to the eigenfunction. An object with the fractionalization-condensation is equivalent to the unitary wavefunction. Nonlocal operation is explicitly required to maintain communication among all quasistates regardless of distance during the fractionalization process. Interference effect is explicitly required for the condensation of quasistates. The collapse of the fractionalization-condensation is explicitly required when the fractionalization-condensation is disrupted. The cosmic origin of quantum mechanics is derived from the cyclic fractionalization-condensation in the cyclic universe, consisting of the unobservable cosmic vacuum and the observable universe. The cyclic fractionalization-condensation allows quasistates to appear cyclically rather than simultaneously. The cosmic vacuum involves the gradual cyclic fractionalization-condensation between the high energy eleven dimensional and low energy four dimensional spacetime. The observable universe involves the drastic cyclic fractionalization-condensation consisting of the cosmic instant fractionalization (the big bang) into various dimensional particles and the expansion-contraction by mostly cosmic radiation and gravity. The cosmic instant fractionalization leads to the microscopic instant fractionalization-condensation (the standard quantum mechanics) that allows all quasistates from an object to appear simultaneously.
Bhomian Mechanics vs. Standard Quantum Mechanics: a Difference in Experimental Predictions
Artur Szczepanski
2010-02-08
Standard Quantum Mechanics (QM) predicts an anti-intuitive fenomenon here referred to as "quantum autoscattering", which is excluded by Bhomian Mechanics. The scheme of a gedanken experiment testing the QM prediction is briefly discussed.
Unstable trajectories and the quantum mechanical uncertainty
Moser, Hans R. [Physics Institute, University of Zuerich, Winterthurerstrasse 190, CH-8057 Zuerich (Switzerland)], E-mail: moser@physik.uzh.ch
2008-08-15
There is still an ongoing discussion about various seemingly contradictory aspects of classical particle motion and its quantum mechanical counterpart. One of the best accepted viewpoints that intend to bridge the gap is the so-called Copenhagen Interpretation. A major issue there is to regard wave functions as probability amplitudes (usually for the position of a particle). However, the literature also reports on approaches that claim a trajectory for any quantum mechanical particle, Bohmian mechanics probably being the most prominent one among these ideas. We introduce a way to calculate trajectories as well, but our crucial ingredient is their well controlled local (thus also momentaneous) degree of instability. By construction, at every moment their unpredictability, i.e., their local separation rates of neighboring trajectories, is governed by the local value of the given modulus square of a wave function. We present extensive numerical simulations of the H and He atom, and for some velocity-related quantities, namely angular momentum and total energy, we inspect their agreement with the values appearing in wave mechanics. Further, we interpret the archetypal double slit interference experiment in the spirit of our findings. We also discuss many-particle problems far beyond He, which guides us to a variety of possible applications.
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Akhmedov, Evgeny Kh.; Kopp, Joachim; ,
2010-01-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Quantum mechanics with coordinate dependent noncommutativity
Kupriyanov, V. G. [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)] [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)
2013-11-15
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
An approach to nonstandard quantum mechanics
Andreas Raab
2006-12-27
We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to non-relativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the M{\\o}ller wave operators and the S-Matrix.
Euclidean formulation of relativistic quantum mechanics W. N. Polyzou1
Polyzou, Wayne
Euclidean formulation of relativistic quantum mechanics W. N. Polyzou1 and Philip Kopp1 1 of relativistic quantum mechanics that uses reflection-positive Euclidean Green functions or generating functionals as phenomenological input. This work is motivated by the Euclidean axioms of quantum field theory
QUANTUM MECHANICS IN SNYDER SPACE Mark K. Transtrum
Hart, Gus
QUANTUM MECHANICS IN SNYDER SPACE by Mark K. Transtrum Submitted to Brigham Young University and two dimensions. I discuss the relation between Snyder space and noncommutative quantum mechanics Huele, Advisor Date Eric Hintz, Research Coordinator Date Scott Sommerfeldt, Chair #12;ABSTRACT QUANTUM
Quantum Mechanics Joachim Burgd orfer and Stefan Rotter
Rotter, Stefan
1 1 Quantum Mechanics Joachim BurgdË? orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution 29 1.8.3 Resonances 30 1.9 Semiclassical Mechanics 31 1.9.1 The WKB Approximation 31 1.9.2 The EBK
Burton, Geoffrey R.
Quantum Information Theory Quantum mechanics makes probabilistic predictions about experiments algebra and probability. Previous experience with quantum mechanics is helpful, but not required. Instead lead to the development of a theory of quantum information that generalises previous notions
Adaptive Perturbation Theory I: Quantum Mechanics
Weinstein, Marvin; /SLAC
2005-10-19
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be treatable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, H, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. This paper introduces the method in the context of the pure anharmonic oscillator and then goes on to apply it to the case of tunneling between both symmetric and asymmetric minima. It concludes with an introduction to the extension of these methods to the discussion of a quantum field theory. A more complete discussion of this issue will be given in the second paper in this series, and it will show how to use the method of adaptive perturbation theory to non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.
Statistical Quantum Mechanics of Many Universes
Gamboa-Rios, J
2003-01-01
The quantum statistical mechanics of generally covariant systems --particles, strings and membranes-- on noncommutative field spaces is studied. We discuss how to introduce non-local communication among different systems via noncommutativity. This idea is applied to cosmology where we argue that due to the breaking of relativistic invariance one can consider a privileged reference system where many universes interact as a quantum gas in a reservoir. If roughly speaking, we approximate the universes as tensionless membranes, then, the interaction among universes provided by noncommutativity is harmonic. The oscillation frequency for each universe is proportional to $B/M$, where $B$ is the noncommutativity parameter --that we identify as the primordial magnetic field, {\\it i.e.} $\\sim 10^{-16} {GeV}^2$- and $M$ is the mass of the universe ($\\sim 10^{77} {GeV}$) and, therefore each universe have the pulsation frequency $\\omega \\sim 10^{-68} s^{-1}$.
Nielsen, Steven O.
FIG. 1: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. FIG. 2: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. 1 #12;FIG. 3: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect
5.74 Introductory Quantum Mechanics II, Spring 2003
Tokmakoff, Andrei
Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...
5.74 Introductory Quantum Mechanics II, Spring 2007
Tokmakoff, Andrei
Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...
5.74 Introductory Quantum Mechanics II, Spring 2005
Tokmakoff, Andrei
Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...
Lecture Script: Introduction to Computational Quantum Mechanics
Roman Schmied
2015-06-05
This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013 and in the Spring semester of 2015. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding analytical as well as numerical solutions and their visualization. Most of these calculations are too complicated to be done by hand. Even relatively simple problems, such as two interacting particles in a one-dimensional trap, do not have analytic solutions and require the use of computers for their solution and visualization. More complex problems scale exponentially with the number of degrees of freedom, and make the use of large computer simulations unavoidable. The course is taught using the Mathematica programming language; however, the concepts presented are readily translated to any other programming language.
The Smith chart and quantum mechanics
Rosner, J.L. (Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637 (United States))
1993-04-01
The Schroedinger equation and the equation describing the behavior of voltage on a transmission line are both linear second-order equations, which may be solved by convenient matrix methods. By drawing analogies between these two problems, it is shown that a method used for antenna impedance matching based on the Smith chart corresponds in quantum mechanics to a simple conformal transformation of the logarithmic derivative of the wave function. One thereby can arrive at an elementary derivation of the Wentzel--Kramers--Brillouin quantization condition.
Position-dependent noncommutativity in quantum mechanics
M. Gomes; V. G. Kupriyanov
2009-06-15
The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinates [x^{i},x^{j}]=\\omega^{ij}(x), and construct the complete algebra of commutation relations, including the operators of momenta. The constructed algebra is a deformation of a standard Heisenberg algebra and obey the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativety.
Hidden geometric character of relativistic quantum mechanics
Almeida, Jose B. [Physics Department, Universidade do Minho, 4710-057 Braga (Portugal)
2007-01-15
Geometry can be an unsuspected source of equations with physical relevance, as everybody is aware since Einstein formulated the general theory of relativity. However, efforts to extend a similar type of reasoning to other areas of physics, namely, electrodynamics, quantum mechanics, and particle physics, usually had very limited success; particularly in quantum mechanics the standard formalism is such that any possible relation to geometry is impossible to detect; other authors have previously trod the geometric path to quantum mechanics, some of that work being referred to in the text. In this presentation we will follow an alternate route to show that quantum mechanics has indeed a strong geometric character. The paper makes use of geometric algebra, also known as Clifford algebra, in five-dimensional space-time. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from such choice and their consistency with experimental results. Given a metric space of any dimension, one can define monogenic functions, the natural extension of analytic functions to higher dimensions; such functions have null vector derivative and have previously been shown by other authors to play a decisive role in lower dimensional spaces. All monogenic functions have null Laplacian by consequence; in a hyperbolic space this fact leads inevitably to a wave equation with planelike solutions. This is also true for five-dimensional space-time and we will explore those solutions, establishing a parallel with the solutions of the free particle Dirac equation. For this purpose we will invoke the isomorphism between the complex algebra of 4x4 matrices, also known as Dirac's matrices. There is one problem with this isomorphism, because the solutions to Dirac's equation are usually known as spinors (column matrices) that do not belong to the 4x4 matrix algebra and as such are excluded from the isomorphism. We will show that a solution in terms of Dirac spinors is equivalent to a plane wave solution. Just as one finds in the standard formulation, monogenic functions can be naturally split into positive/negative energy together with left/right ones. This split is provided by geometric projectors and we will show that there is a second set of projectors providing an alternate fourfold split. The possible implications of this alternate split are not yet fully understood and are presently the subject of profound research.
Wigner Measures in Noncommutative Quantum Mechanics
C. Bastos; N. C. Dias; J. N. Prata
2009-07-25
We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner measure, for a Gaussian to be a noncommutative Wigner measure, and derive certain properties of the marginal distributions which are not shared by ordinary Wigner measures. Moreover, we derive the Robertson-Schr\\"odinger uncertainty principle. Finally, we show explicitly how the set of noncommutative Wigner measures relates to the sets of Liouville and (commutative) Wigner measures.
Euclidean Quantum Mechanics and Universal Nonlinear Filtering
Bhashyam Balaji
2008-09-25
An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr\\"odinger equation.
Improved lattice actions for supersymmetric quantum mechanics
Sebastian Schierenberg; Falk Bruckmann
2012-10-19
We analyze the Euclidean version of supersymmetric quantum mechanics on the lattice by means of a numerical path integral. We consider two different lattice derivatives and improve the actions containing them with respect to supersymmetry by systematically adding interaction terms with non-zero extent. To quantize this improvement, we measure boson and fermion masses and Ward identities for the naive as well as the improved models. The masses are degenerate in all models, but the magnitude of the Ward identities decreases significantly for both derivative operators using the improved actions. This is a clear sign that the breaking of supersymmetry due to lattice artifacts is reduced.
BiHermitian supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Zucchini, Roberto
2007-04-01
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kähler manifolds recently developed by Gualtieri in [33]. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li in [9].
The Ithaca Interpretation of Quantum Mechanics
Mermin, N David
1996-01-01
I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and I discuss two simple theorems. One, as far as I know, is new; the other was only noted a few years ago. Both have important implications for such a sensible interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)
The Ithaca Interpretation of Quantum Mechanics
N. David Mermin
1996-09-17
I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and I discuss two simple theorems. One, as far as I know, is new; the other was only noted a few years ago. Both have important implications for such a sensible interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)
A note on the Landauer principle in quantum statistical mechanics
Boyer, Edmond
A note on the Landauer principle in quantum statistical mechanics Vojkan Jaksi´c1 and Claude results concerning the derivation of the Landauer bound from the first principles of statistical mechanics and proof of the Landauer principle in the context of quantum statistical mechanics has led to a number
Quantum Mechanical Transport in Submicron Electronic Devices.
NASA Astrophysics Data System (ADS)
Bagwell, Philip Frederick
Electronic devices with characteristic dimensions of the order of 100 nm or less exhibit many novel quantum transport phenomena at low temperatures when the phase -breaking length becomes comparable to the device size. This thesis describes electron transport mechanisms and the resulting current-voltage relationships in quasi-one-dimensional wires, superlattices, and resonant tunneling devices. An intuitive 'convolution method' is developed to describe the energy averaging due to a finite bias voltage, finite temperature, disorder, and the influence of emitter dimensionality on these currents. We emphasize the dominant effect of evanescent or 'cutoff' electron waveguide modes in determining the shape of the electrical conductance versus Fermi energy in a confined geometry such as a quantum wire. Finally, we study experimentally the magnetoconductance of a novel Si 'grating gate' field effect transistor where the current path can be varied electrostatically in a single device from many narrow wires in parallel, to a modulated periodic potential, to a two-dimensional electron gas. Electron weak-localization, the classical Drude magnetoconductance, and the quantum Hall effect are modified by the periodic potential. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).
A quantum protective mechanism in photosynthesis
Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk
2015-01-01
Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life. PMID:25732807
A quantum protective mechanism in photosynthesis.
Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk
2015-01-01
Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life. PMID:25732807
Noncommutative quantum mechanics as a gauge theory
Bemfica, F. S.; Girotti, H. O. [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 - Porto Alegre, RS (Brazil)
2009-06-15
The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second-class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system into an Abelian gauge theory exhibiting only first class constraints. The appropriateness of the BFT embedding, as implemented in this work, is verified by showing that there exists a one to one mapping linking the second-class model with the gauge invariant sector of the gauge theory. As is known, the functional quantization of a gauge theory calls for the elimination of its gauge freedom. Then, we have at our disposal an infinite set of alternative descriptions for noncommutative quantum mechanics, one for each gauge. We study the relevant features of this infinite set of correspondences. The functional quantization of the gauge theory is explicitly performed for two gauges and the results compared with that corresponding to the second-class system. Within the operator framework the gauge theory is quantized by using Dirac's method.
Quantum Mechanical Study of Nanoscale MOSFET
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan
2001-01-01
The steady state characteristics of MOSFETS that are of practical Interest are the drive current, off-current, dope of drain current versus drain voltage, and threshold voltage. In this section, we show that quantum mechanical simulations yield significantly different results from drift-diffusion based methods. These differences arise because of the following quantum mechanical features: (I) polysilicon gate depletion in a manner opposite to the classical case (II) dependence of the resonant levels in the channel on the gate voltage, (III) tunneling of charge across the gate oxide and from source to drain, (IV) quasi-ballistic flow of electrons. Conclusions dI/dV versus V does not increase in a manner commensurate with the increase in number of subbands. - The increase in dI/dV with bias is much smaller then the increase in the number of subbands - a consequence of bragg reflection. Our calculations show an increase in transmission with length of contact, as seen in experiments. It is desirable for molecular electronics applications to have a small contact area, yet large coupling. In this case, the circumferential dependence of the nanotube wave function dictates: - Transmission in armchair tubes saturates around unity - Transmission in zigzag tubes saturates at two.
A Foundation Theory of Quantum Mechanics
Richard A Mould
2006-07-10
The nRules are empirical regularities that were discovered in macroscopic situations where the outcome is known. When they are projected theoretically into the microscopic domain they predict a novel ontology including the frequent collapse of an atomic wave function, thereby defining an nRule based foundation theory. Future experiments can potentially discriminate between this and other foundation theories of (non-relativistic) quantum mechanics. Important features of the nRules are: (1) they introduce probability through probability current rather than the Born rule, (2) they are valid independent of size (micro or macroscopic), (3) they apply to individual trials, not just to ensembles of trials. (4) they allow all observers to be continuously included in the system without ambiguity, (5) they account for the collapse of the wave function without introducing new or using old physical constants, and (6) in dense environments they provide a high frequency of stochastic localizations of quantum mechanical objects. Key words: measurement, stochastic choice, state reduction.
The formal path integral and quantum mechanics
Johnson-Freyd, Theo [Department of Mathematics, University of California - Berkeley, 970 Evans Hall, Berkeley, California 94720 (United States)
2010-11-15
Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.
A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation
Lomonaco, S J
2000-01-01
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief ...
A ROSETTA STONE FOR QUANTUM MECHANICS WITH AN INTRODUCTION TO QUANTUM COMPUTATION VERSION 1.5
SAMUEL J. LOMONACO
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
A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation
Samuel J. Lomonaco; jr
2000-01-01
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American
Tulsi Dass
2006-12-29
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.
Information security and quantum mechanics: Security of quantum protocols
Patrick Oscar Boykin
2002-01-01
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
Information Security and Quantum Mechanics:Security of Quantum Protocols
P. Oscar Boykin
2002-01-01
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
Minnesota, University of
A Combined Quantum Mechanical and Molecular Mechanical Study of the Reaction Mechanism and r-Amino Acidity in Alanine Racemase Dan Thomas Major and Jiali Gao* Contribution from the Department of Chemistry Received August 31, 2006; E-mail: gao@chem.umn.edu Abstract: Combined quantum mechanical
Fundamental phenomena of quantum mechanics explored with neutron interferometers
J. Klepp; S. Sponar; Y. Hasegawa
2014-07-11
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.
Symmetry as a foundational concept in Quantum Mechanics
Ziaeepour, Houri
2015-01-01
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.
Supersymmetric quantum mechanics and Painlevé equations
Bermudez, David; Fernández C, David J. [Departamento de Física, Cinvestav, A.P. 14-740, 07000 México D.F. (Mexico)
2014-01-08
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.
Quantum mechanics without an equation of motion
Alhaidari, A. D. [Saudi Center for Theoretical Physics, Jeddah 21438 (Saudi Arabia)
2011-06-15
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.
Quantum mechanical calculations to chemical accuracy
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.
1991-01-01
The accuracy of current molecular-structure calculations is illustrated with examples of quantum mechanical solutions for chemical problems. Two approaches are considered: (1) the coupled-cluster singles and doubles (CCSD) with a perturbational estimate of the contribution of connected triple excitations, or CCDS(T); and (2) the multireference configuration-interaction (MRCI) approach to the correlation problem. The MRCI approach gains greater applicability by means of size-extensive modifications such as the averaged-coupled pair functional approach. The examples of solutions to chemical problems include those for C-H bond energies, the vibrational frequencies of O3, identifying the ground state of Al2 and Si2, and the Lewis-Rayleigh afterglow and the Hermann IR system of N2. Accurate molecular-wave functions can be derived from a combination of basis-set saturation studies and full configuration-interaction calculations.
Supersymmetric quantum mechanics and Painlevé equations
NASA Astrophysics Data System (ADS)
Bermudez, David; Fernández C., David J.
2014-01-01
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.
A Causal Net Approach to Relativistic Quantum Mechanics
R. D. Bateson
2012-05-13
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.
Equivalence relations between deterministic and quantum mechanical systems
Gerard't Hooft
1988-01-01
Several quantum mechanical models are shown to be equivalent to certain deterministic systems because a basis can be found in terms of which the wave function does not “spread.” This suggests that apparently indeterministic behavior typical for a quantum mechanical world can be the result of locally deterministic laws of physics. We show how certain deterministic systems allow the construction
Euclidean Relativistic Quantum Mechanics W. N. Polyzou, 1
Polyzou, Wayne
Euclidean Relativistic Quantum Mechanics W. N. Polyzou, 1 Philip Kopp 1 1 Department of Physics of exactly Poincarâ??e invariant quantum mechanics where the input is model Euclidean Green functions not have a simple connection with the Lagrangian formulation of the field theory. The Euclidean Green
Euclidean Relativistic Quantum Mechanics W. N. Polyzou,1
Polyzou, Wayne
Euclidean Relativistic Quantum Mechanics W. N. Polyzou,1 Philip Kopp1 1 Department of Physics of exactly PoincarÂ´e invariant quantum mechanics where the input is model Euclidean Green functions not have a simple connection with the Lagrangian formulation of the field theory. The Euclidean Green
Predicting crystal structure by merging data mining with quantum mechanics
Christopher C. Fischer; Kevin J. Tibbetts; Dane Morgan; Gerbrand Ceder
2006-01-01
Modern methods of quantum mechanics have proved to be effective tools to understand and even predict materials properties. An essential element of the materials design process, relevant to both new materials and the optimization of existing ones, is knowing which crystal structures will form in an alloy system. Crystal structure can only be predicted effectively with quantum mechanics if an
Quaternionic quantum mechanics allows non-local boxes
Matthew McKague
2009-11-09
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.
Design and Validation of the Quantum Mechanics Conceptual Survey
ERIC Educational Resources Information Center
McKagan, S. B.; Perkins, K. K.; Wieman, C. E.
2010-01-01
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…
Unraveling quantum mechanical effects in water using isotopic fractionation
Berne, Bruce J.
Unraveling quantum mechanical effects in water using isotopic fractionation Thomas E. Marklanda that equilibrium fractionation ratios, an entirely quantum mechan- ical property, also provide a sensitive probe- predict the magnitude of isotope fractionation. Models that account for anharmonicity in this coordinate
Quantum Mechanics from Periodic Dynamics: the bosonic case
Dolce, Donatello [Johannes-Gutenberg Universitaet, D-55099 Mainz (Germany)
2010-05-04
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.
In Defense of a Heuristic Interpretation of Quantum Mechanics
ERIC Educational Resources Information Center
Healy, Eamonn F.
2010-01-01
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…
Categorization of Quantum Mechanics Problems by Professors and Students
ERIC Educational Resources Information Center
Lin, Shih-Yin; Singh, Chandralekha
2010-01-01
We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…
New Potentials for Old: The Darboux Transformation in Quantum Mechanics
ERIC Educational Resources Information Center
Williams, Brian Wesley; Celius, Tevye C.
2008-01-01
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…
Developing and Evaluating Animations for Teaching Quantum Mechanics Concepts
ERIC Educational Resources Information Center
Kohnle, Antje; Douglass, Margaret; Edwards, Tom J.; Gillies, Alastair D.; Hooley, Christopher A.; Sinclair, Bruce D.
2010-01-01
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…
Environment-Induced Decoherence in Noncommutative Quantum Mechanics
Joao Nuno Prata; Nuno Costa Dias
2006-12-02
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.
Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems
ERIC Educational Resources Information Center
Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih
2009-01-01
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…
Quantum mechanical retrocausation? Call for nonlocal causal models!
Antoine Suarez
1998-02-12
A new possible version of multisimultaneous causality is proposed, and real experiments allowing us to decide between this view and quantum mechanical retrocausation are further discussed. The interest of testing quantum mechanics against as many nonlocal causal models as possible is stressed.
Depicting qudit quantum mechanics and mutually unbiased qudit theories
André Ranchin
2014-12-30
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.
Hart, Gus
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
Extending quantum mechanics entails extending special relativity
S. Aravinda; R. Srikanth
2015-06-09
The complementarity of signaling and local randomness in the resources required to simulate singlet statistics is generalized here by relaxing the assumption of free will in the choice of measurement settings. The complementarity implies that under the assumption of full free will, simulation resources with reduced randomness will be signaling. It would appear at first sight that an ontological extension based on such a simulation protocol would contradict no-signaling and free will. We prove that this is not so, by constructing such an extension through the "oblivious embedding" of the protocol in a Newtonian spacetime. Relativistic or other intermediate spacetimes are ruled out as the locus of the embedding because they would permit the violation of no-signaling at the operational level by virtue of hidden influence inequalities. This implies that predictively superior extensions of quantum mechanics (QM) must be Lorentz non-covariant. However, the operational theory reproduced by the extensions will be compatible with no-signaling and Lorentz covariance. This clarifies why in principle there is no obstacle to the compatibility of extensions of QM such as Bohmian mechanics and GRW-type collapse theories with special relativity. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime of the extensions has Minkowskian causal structure.
Hammes-Schiffer, Sharon
Proton transfer in solution: Molecular dynamics with quantum transitions Sharon Hammes May 1994) We apply "molecular dynamics with quantum transitions" (MDQT), a surface-hopping method is an atom. We use full classical mechanical molecular dynamics for the heavy atom degrees of freedom
The Born Rule in Quantum and Classical Mechanics
Paul Brumer; Jiangbin Gong
2006-04-24
Considerable effort has been devoted to deriving the Born rule (e.g. that $|\\psi(x)|^2 dx$ is the probability of finding a system, described by $\\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert space formulation of {\\it classical} mechanics as well. These results provide new insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.
Cloning in nonlinear Hamiltonian quantum and hybrid mechanics
D. Arsenovic; N. Buric; D. B. Popovic; M. Radonjic; S. Prvanovic
2014-11-17
Possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is then demonstrated that the addition of the cloning machine, treated as a quantum or as a classical system, makes the cloning possible by nonlinear Hamiltonian evolution. However, a special type of quantum-classical theory, known as the mean-field Hamiltonian hybrid mechanics, does not admit cloning by natural evolution. The latter represents an example of a theory where it appears to be possible to communicate between two quantum systems at super-luminal speed, but at the same time it is impossible to clone quantum pure states.
Quantum Mechanics as a Classical Theory III: Epistemology
L. S. F. Olavo
1995-03-31
The two previous papers developed quantum mechanical formalism from classical mechanics and two additional postulates. In the first paper it was also shown that the uncertainty relations possess no ontological validity and only reflect the formalism's limitations. In this paper, a Realist Interpretation of quantum mechanics based on these results is elaborated and compared to the Copenhagen Interpretation. We demonstrate that von Neumann's proof of the impossibility of a hidden variable theory is not correct, independently of Bell's argumentation. A local hidden variable theory is found for non-relativistic quantum mechanics, which is nothing else than newtonian mechanics itself. We prove that Bell's theorem does not imply in a non-locality of quantum mechanics, and also demonstrate that Bohm's theory cannot be considered a true hidden variable theory.
The Physical Principles of Quantum Mechanics. A critical review
F. Strocchi
2012-01-04
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more physically motivated formulation is discussed. The existence of non commuting observables, which characterizes quantum mechanics with respect to classical mechanics, is related to operationally testable complementarity relations, rather than to uncertainty relations. The drawbacks of Dirac argument for canonical quantization are avoided by a more geometrical approach.
Calendar effects in quantum mechanics in view of interactive holography
NASA Astrophysics Data System (ADS)
Berkovich, Simon
2013-04-01
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 .
Teaching Quantum Mechanical Commutation Relations via an Optical Experiment
Billur, A Alper; Bursal, Murat
2015-01-01
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the operator formalisms are generally given theoretically and it is documented that these abstract formalisms are usually misunderstood by the students. Based on the idea that quantum mechanical phenomena can be investigated via geometric optical tools, this study aims to introduce an experiment, where the quantum mechanical commutation relations are represented in a concrete way to provide students an easy and permanent learning. The experimental tools are chosen to be easily accessible and economic. The experiment introduced in this paper can be done with students or used as a demonstrative experiment in laboratory based or theory based courses requiring quantum physics content; particularly in physics, physics education and science education programs.
Is Holographic Entropy and Gravity the result of Quantum Mechanics?
Joakim Munkhammar
2010-03-09
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.
A Link between Quantum Logic and Categorical Quantum Mechanics
NASA Astrophysics Data System (ADS)
Harding, John
2009-03-01
Abramsky and Coecke (Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, pp. 415-425, IEEE Comput. Soc., New York, 2004) have recently introduced an approach to finite dimensional quantum mechanics based on strongly compact closed categories with biproducts. In this note it is shown that the projections of any object A in such a category form an orthoalgebra Proj A. Sufficient conditions are given to ensure this orthoalgebra is an orthomodular poset. A notion of a preparation for such an object is given by Abramsky and Coecke, and it is shown that each preparation induces a finitely additive map from Proj A to the unit interval of the semiring of scalars for this category. The tensor product for the category is shown to induce an orthoalgebra bimorphism Proj A× Proj B? Proj ( A ? B) that shares some of the properties required of a tensor product of orthoalgebras. These results are established in a setting more general than that of strongly compact closed categories. Many are valid in dagger biproduct categories, others require also a symmetric monoidal tensor compatible with the dagger and biproducts. Examples are considered for several familiar strongly compact closed categories.
Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics
NASA Astrophysics Data System (ADS)
Ohzeki, Masayuki
2013-09-01
In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called quantum annealing. The most typical instance is quantum adiabatic computation based on the adiabatic theorem. The quantum adiabatic computation as discussed in the other chapter, unfortunately, has a crucial bottleneck for a part of the optimization problems. We here introduce several recent trials to overcome such a weakpoint by use of developments in statistical mechanics. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.
Are quantum-mechanical-like models possible, or necessary, outside quantum physics?
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2014-12-01
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.
Information Security and Quantum Mechanics: Security of Quantum Protocols
P. Oscar Boykin
2002-10-28
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.
Information Security and Quantum Mechanics: Security of Quantum Protocols
NASA Astrophysics Data System (ADS)
Boykin, P. Oscar
2002-10-01
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.
Information security and quantum mechanics: Security of quantum protocols
NASA Astrophysics Data System (ADS)
Boykin, Patrick Oscar
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.
NASA Astrophysics Data System (ADS)
Cataloglu, Erdat
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.
Stochastic Theory of Relativistic Quantum Mechanics
Maurice Godart
2014-12-03
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it also relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the classical trajectories of the particles are identical to the sample functions of a diffusion Markov process, whose conditional probability density is proposed as a substitute for the wave function. Along the way, we introduce ad hoc hypotheses for the sole reason that they facilitate and even make possible the further development of the theory. These and the so-called Nelson equations are used to determine the drift vectors and the diffusion tensor characteristic of such a process. It is then possible to write down the Fokker-Planck and Kolmogorov equations that can be used to determine the normal and conditional probability densities. This logical sequence of steps leads to the solution of specific problems and we apply it to the special case of the free particle.
A Process Algebra Approach to Quantum Mechanics
William H. Sulis
2014-09-07
The process approach to NRQM offers a fourth framework for the quantization of physical systems. Unlike the standard approaches (Schrodinger-Heisenberg, Feynman, Wigner-Gronewald-Moyal), the process approach is not merely equivalent to NRQM and is not merely a re-interpretation. The process approach provides a dynamical completion of NRQM. Standard NRQM arises as a asymptotic quotient by means of a set-valued process covering map, which links the process algebra to the usual space of wave functions and operators on Hilbert space. The process approach offers an emergentist, discrete, finite, quasi-non-local and quasi-non-contextual realist interpretation which appears to resolve many of the paradoxes and is free of divergences. Nevertheless, it retains the computational power of NRQM and possesses an emergent probability structure which agrees with NRQM in the asymptotic quotient. The paper describes the process algebra, the process covering map for single systems and the configuration process covering map for multiple systems. It demonstrates the link to NRQM through a toy model. Applications of the process algebra to various quantum mechanical situations - superpositions, two-slit experiments, entanglement, Schrodinger's cat - are presented along with an approach to the paradoxes and the issue of classicality.
Auxiliary nRules of Quantum Mechanics
Richard A Mould
2005-05-31
Standard quantum mechanics makes use of four auxiliary rules that allow the Schrodinger solutions to be related to laboratory experience, such as the Born rule that connects square modulus to probability. These rules (here called the sRules) lead to some unacceptable results. They do not allow the primary observer to be part of the system. They do not allow individual observations (as opposed to ensembles) to be part of the system. They make a fundamental distinction between microscopic and macroscopic things, and they are ambiguous in their description of secondary observers such as Schrodingers cat. The nRules are an alternative set of auxiliary rules that avoid the above difficulties. In this paper we look at a wide range of representative experiments showing that the nRules adequately relate the Schrodinger solutions to empirical experience. This suggests that the sRules should be abandoned in favor of the more satisfactory nRules, or a third auxiliary rule-set called the oRules. Keywords: brain states, consciousness, decoherence, epistemology, measurement, ontology, stochastic, state reduction, wave collapse.
Linking Quantum Mechanics to Freshman Physics
NASA Astrophysics Data System (ADS)
Vandegrift, Guy
1998-10-01
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.
Contribution to understanding the mathematical structure of quantum mechanics
NASA Astrophysics Data System (ADS)
Skála, L.; Kapsa, V.
2007-09-01
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, the Born rule, commutation and uncertainty relations, probability density current, momentum operator, and rules for including the scalar and vector potentials and antiparticles can be obtained from the probabilistic description of results of measurement of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, the Schrödinger equation, and the Dirac equation are obtained from the requirement of the relativistic invariance of the space-time Fisher information. The limit case of th e ?-like probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Manyparticle systems and the postulates of quantum mechanics are also discussed.
Goddard III, William A.
Mechanism of Selective Oxidation of Propene to Acrolein on Bismuth Molybdates from Quantum for understanding the fundamental chemical mechanisms underlying the selective oxidation of propene to acrolein to form acrolein, and acrolein desorption. The formation of -allyl intermediate is reversible
The Arrow of Time in Rigged Hilbert Space Quantum Mechanics
Robert C. Bishop
2005-06-22
Arno Bohm and Ilya Prigogine's Brussels-Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm's theory of scattering is given. Similarly, the Brussels-Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is initially discussed focusing on their semi-group operators and time arrows. Finally a possible realist interpretation of the rigged Hilbert space formulation of quantum mechanics is considered.
The actual content of quantum theoretical kinematics and mechanics
NASA Technical Reports Server (NTRS)
Heisenberg, W.
1983-01-01
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.
The structure of supersymmetry in ${\\cal PT}$ symmetric quantum mechanics
D. Bazeia; Ashok Das; L. Greenwood; L. Losano
2009-03-17
The structure of supersymmetry is analyzed systematically in ${\\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\\cal PT}$ symmetric quantum mechanical theories. We show that there is a richer structure present in these theories compared to the conventional theories associated with Hermitian Hamiltonians. We bring out various properties associated with these supersymmetric systems and generalize such quantum mechanical theories to higher dimensions as well as to the case of one dimensional shape invariant potentials.
Is String Interaction the Origin of Quantum Mechanics?
Itzhak Bars; Dmitry Rychkov
2014-09-23
String theory developed by demanding consistency with quantum mechanics. In this paper we wish to reverse the reasoning. We pretend 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 deriving rather than assuming the quantum commutation rules among the usual canonical quantum variables for all physical systems derivable from open string field theory. Morally we would apply such an argument to M-theory to cover all physics. If string or M-theory really underlies all physics, it seems that the door has been opened to an understanding of the origins of quantum mechanics.
Attempt at perfecting quantum mechanics based on interaction
Tian-Hai Zeng
2013-07-07
Many wave phenomena are related to interactions. When preparing a particle in a superposed state starting from an eigenstate, we must let it interact with an apparatus or environment. Considering neglected interactions, states of apparatus and Newtonic idea about measurement, we attempt to modify some concepts of quantum mechanics. Our modifications include wave-particle duality, the principle of superposition of states, the meaning of the Schrodinger equation, the postulate of quantum measurement, and the uncertainty relations, without changing past correct results. These may help us to understand some typical quantum phenomena with near classical and intuitive ideas, to mediate some contradictions logically, and then to go a step further toward perfecting quantum mechanics. We also review the argument between Einstien and Bohr about quantum mechanics, and conclude that the result is a draw.
Quantum Approach to Classical Statistical Mechanics
R. D. Somma; Cristian D. Batista; Gerardo Ortiz
2007-01-01
We present a new approach to study the thermodynamic properties of\\u000a$d$-dimensional classical systems by reducing the problem to the computation of\\u000aground state properties of a $d$-dimensional quantum model. This\\u000aclassical-to-quantum mapping allows us to deal with standard optimization\\u000amethods, such as simulated and quantum annealing, on an equal basis.\\u000aConsequently, we extend the quantum annealing method to simulate
QUANTUM MECHANICS When German physicist Max Planck became the
Haas, Stephan
QUANTUM MECHANICS When German physicist Max Planck became the father of quantum theory in 1900, he and recentlyofGermany'sMaxPlanckInstitute.Ateam of computational scientists led by Dr. Roscilde is using the Oak under your arm. Planck had a much more modest and immediate need
Entanglement, thermalisation and stationarity: The computational foundations of quantum mechanics
V. Guruprasad
2000-01-01
'Tis said, to know others is to be learned, to know oneself, wise - I demonstrate that it could be more fundamental than knowing the rest of nature, by applying classical computational principles and engineering hindsight to derive and explain quantum entanglement, state space formalism and the statistical nature of quantum mechanics. I show that an entangled photon pair is
OSP Quantum Mechanics: Single Measurments of Spin States Worksheet
NSDL National Science Digital Library
Belloni, Mario
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.
Single-photon detection mechanism in a quantum dot transistor
N. S. Beattie; B. E. Kardynal; A. J. Shields; I. Farrer; D. A. Ritchie; M. Pepper
2005-01-01
We study the transport mechanisms in a quantum dot MODFET by tuning the localization induced by charge stored on the quantum dots with light. The temperature dependence of the resistivity of a macroscopic sample reveals a hopping transport when the dots contain an excess of electrons. The resistance of a mesoscopic sample however, which is capable of detecting single photons,
Consistent histories and the interpretation of quantum mechanics
Robert B. Griffiths
1984-01-01
The usual formula for transition probabilities in nonrelativistic quantum mechanics is generalized to yield conditional probabilities for selected sequences of events at several different times, called “consistent histories,” through a criterion which ensures that, within limits which are explicitly defined within the formalism, classical rules for probabilities are satisfied. The interpretive scheme which results is applicable to closed (isolated) quantum
An introduction to the semiclassical limit of Euclidean quantum mechanics
Torbjörn Kolsrud; Jean-Claude Zambrini
1992-01-01
A new class of Gaussian (‘‘Bernstein’’) diffusion processes associated with semiclassical quantum dynamics is introduced and studied according to a new Euclidean strategy for the quantization of systems of particles in a potential (‘‘Euclidean quantum mechanics’’). All the measures known by other means, up to now, are included as particular cases of the present framework. It is shown that the
Quantum Mechanics Concept Assessment: Development and Validation Study
ERIC Educational Resources Information Center
Sadaghiani, Homeyra R.; Pollock, Steven J.
2015-01-01
As part of an ongoing investigation of students' learning in first semester upper-division quantum mechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum…
On a commutative ring structure in quantum mechanics
Shigeki Matsutani
2009-10-10
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.
Generating Function in Quantum Mechanics: An Application to Counting Problems
Li Han
2007-11-19
In this paper we present a generating function approach to two counting problems in elementary quantum mechanics. The first is to find the total ways of distributing identical particles among different states. The second is to find the degeneracies of energy levels in a quantum system with multiple degrees of freedom. Our approach provides an alternative to the methods in textbooks.
Why are probabilistic laws governing quantum mechanics and neurobiology?
Kröger, H
2004-01-01
We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.
Why are probabilistic laws governing quantum mechanics and neurobiology?
NASA Astrophysics Data System (ADS)
Kröger, Helmut
2005-08-01
We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.
Why are probabilistic laws governing quantum mechanics and neurobiology?
H. Kroger
2004-06-14
We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.
Particles, Waves, and the Interpretation of Quantum Mechanics
ERIC Educational Resources Information Center
Christoudouleas, N. D.
1975-01-01
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)
A Computational Model for Observation in Quantum Mechanics
Rozas, Guillermo Juan
1987-03-01
A computational model of observation in quantum mechanics is presented. The model provides a clean and simple computational paradigm which can be used to illustrate and possibly explain some of the unintuitive and ...
The Thermodynamic Arrow-of-time and Quantum Mechanics
Maccone, Lorenzo
I give an explanation of the thermodynamic arrow-of-time (namely entropy increases with time) within a quantum mechanical framework. This entails giving a solution to the Loschmidt paradox, i.e. showing how an irreversible ...
Probabilistic Approach to Teaching the Principles of Quantum Mechanics
ERIC Educational Resources Information Center
Santos, Emilio
1976-01-01
Approaches the representation of quantum mechanics through Hilbert space postulates. Demonstrates that if the representation is to be accurate, an evolution operator of the form of a Hamiltonian must be used. (CP)
QUANTUM MECHANICAL CARRIER OF THE IMPRINTS OF GRAVITATION a
Gerlach, Ulrich
QUANTUM MECHANICAL CARRIER OF THE IMPRINTS OF GRAVITATION invariance of spacetime in the absence of gravitation* *. This car- rier consists of the phase Einstein actually started o* *n the path which led towards his formulation of gravitation (general
Bernstein processes, Euclidean Quantum Mechanics and Interest Rate Models
Lescot, Paul
2009-01-01
We give an exposition, following joint works with J.-C. Zambrini, of the link between Euclidean Quantum Mechanics, Bernstein processes and isovectors for the heat equation. A new application to Mathematical Finance is then discussed.
BERNSTEIN PROCESSES, EUCLIDEAN QUANTUM MECHANICS AND INTEREST RATE MODELS
an exposition, following joint works with J.-C. Zambrini, of the link between Euclidean Quantum Mechanics, and for m = 1: i t = - 2 2 2 q2 + V . We shall henceforth treat = as a new parameter. In Zambrini
BERNSTEIN PROCESSES, EUCLIDEAN QUANTUM MECHANICS AND INTEREST RATE MODELS
Paris-Sud XI, UniversitÃ© de
an exposition, following joint works with J.-C. Zambrini, of the link between euclidean quantum mechanics, and for m = 1: i t = - 2 2 2 q2 + V . We shall henceforth treat = as a new parameter. In Zambrini
Crossover from quantum mechanical tunneling to incoherent (Ohmic)
Freericks, Jim
Crossover from quantum mechanical tunneling to incoherent (Ohmic) transport in a strongly, Georgetown University, Ustron conference, 2004 #12;Tunnel junctions in electronics · Sandwich of metal-barrier- metal with current moving perpendicular to the planes · Nonlinear current-voltage characteristics
Interpretation of Quantum Mechanics. A view of our universe
Lindgren, Ingvar
of bright young scientists, Werner Heisenberg, Wolfgang Pauli and others (Fig. 2). THE COPENHAGEN the foundation of quantum mechanics at the Bohr Institute with Werner Heisenberg (middle) and Wolfgang Pauli
Mechanical nanomanipulation of single strain-induced semiconductor quantum dots
Ludwig-Maximilians-Universität, München
strain field in the GaInAs/GaAs quantum well. By scanning the tip with a shear force contact of the order extent, tailored by mechanically removing some of the stressor material using a tuning fork shear force
Born series and unitarity in noncommutative quantum mechanics
F. S. Bemfica; H. O. Girotti
2008-02-11
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.
A Low Temperature Expansion for Matrix Quantum Mechanics
Ying-Hsuan Lin; Shu-Heng Shao; Yifan Wang; Xi Yin
2013-04-08
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.
Removing redundancy in relativistic quantum mechanics
Peter Rowlands
2005-01-01
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.
"Mysticism" in Quantum Mechanics: The Forgotten Controversy
ERIC Educational Resources Information Center
Marin, Juan Miguel
2009-01-01
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…
Removing redundancy in relativistic quantum mechanics
Peter Rowlands
2005-07-27
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.
The auxiliary field method in quantum mechanics
Bernard Silvestre-Brac; Claude Semay; Fabien Buisseret
2012-06-20
The auxiliary field method is a new technique to obtain closed formulae for the solutions of eigenequations in quantum mechanics. The idea is to replace a Hamiltonian $H$ for which analytical solutions are not known by another one $\\tilde H$, including one or more auxiliary fields. For instance, a potential $V(r)$ not solvable is replaced by another one $P(r)$ more familiar, or a semirelativistic kinetic part is replaced by an equivalent nonrelativistic one. The approximation comes from the replacement of the auxiliary fields by pure real constants. The approximant solutions for $H$, eigenvalues and eigenfunctions, are then obtained by the solutions of $\\tilde H$ in which the auxiliary parameters are eliminated by an extremization procedure for the eigenenergies. If $H=T(\\bm p)+V(r)$ and if $P(r)$ is a power law, the approximate eigenvalues can be written $T(p_0)+V(r_0)$, where the mean impulsion $p_0$ is a function of the mean distance $r_0$ and where $r_0$ is determined by an equation which is linked to the generalized virial theorem. The general properties of the method are studied and the connections with the envelope theory presented. This method is first applied to nonrelativistic and semirelativistic two-body systems, with a great variety of potentials. Closed formulae are produced for energies, eigenstates, various observables and critical constants, with sometimes a very good accuracy. The method is then used to solve nonrelativistic and semirelativistic many-body systems with one-body and two-body interactions. For such cases, analytical solutions can only be obtained for systems of identical particles, but several systems of interest for atomic and hadronic physics are studied. General results concerning the many-body critical constants are presented, as well as duality relations existing between approximate and exact eigenvalues.
Multi-instantons in large N Matrix Quantum Mechanics
Marcos Marino; Pavel Putrov
2009-11-16
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.
Geometrical description of algebraic structures: Applications to Quantum Mechanics
José F. Cariñena; Alberto Ibort; Giuseppe Marmo; Giuseppe Morandi
2012-09-20
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to quantum mechanics. We will concentrate our attention into quantum theories and we will show how to use in a systematic way the transition from algebraic to geometrical structures to explore their geometry, mainly its Jordan-Lie structure.
Path integral in energy representation in quantum mechanics
P. Putrov
2007-08-30
In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it is much more better defined than the usual functional integral. We investigate this representation from various directions and compare such approach to quantum mechanics with the standard ones.
Intrinsically Quantum-Mechanical Gravity and the Cosmological Constant Problem
Philip D. Mannheim
2010-01-01
We propose that gravity be intrinsically quantum-mechanical, so that in the\\u000aabsence of quantum mechanics the geometry of the universe would be Minkowski.\\u000aWe show that in such a situation gravity does not require any independent\\u000aquantization of its own, with it being quantized simply by virtue of its being\\u000acoupled to the quantized matter fields that serve as its
$\\cN$-FOLD SUPERSYMMETRY IN QUANTUM MECHANICAL MATRIX MODELS
NASA Astrophysics Data System (ADS)
Tanaka, Toshiaki
2012-03-01
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.
On the geometry of the energy operator in quantum mechanics
Carlos Tejero Prieto; Raffaele Vitolo
2014-08-26
We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations the operator contains the scalar curvature as a multiplicative term. We show that such term can be canceled or added with an arbitrary constant factor, both in the mainstream Geometric Quantization and in the Covariant Quantum Mechanics, developed by Jadczyk and Modugno with several contributions from many authors.
Why space has three dimensions: A quantum mechanical explanation
NASA Astrophysics Data System (ADS)
Marcer, Peter; Schempp, Walter
2000-05-01
The theoretical physics of a quantum mechanical model of space, relativistic quantum holography, is described. It specifies three dimensions, such as is validated by the nature of our spatial experience, but where additionally, quantum non-locality, which Feynman described as the only mystery of quantum theory, is made manifest by means of observable phase relationships. For example, synchronicity between events, and other phenomena such as are described by the geometric/Berry phase, etc., which are outside the bounds of classical explanation. It can therefore be hypothesized: a) that we live in a entirely quantum mechanical world/universe and not a classical mechanical one (where quantum phenomena are confined to the microscopic scale) as is the current generally held scientific view, b) that three spatial dimensions are a fundamental consequence of quantum mechanics, c) that quantum holography is a natural candidate to explain quantum gravity, such that mass/inertia concerns not the eigenvalues of some operator, but rather the observable gauge invariant phases of a state vector, postulated to be that of the universe itself, as a whole, and d) that this model provides a natural explanation in terms of relativistic quantum signal processing of any each individual's perception and cognition will be of a three dimensional world, defined similarly in relation to each individual's quantum state vector, describing its mind/body and associated gauge invariant phases or mindset, which have observable consequences, such that mental processes and events can cause neural events and processes! These testable hypotheses, if validated, will have profound implications for our understanding, radically changing our scientific perspective on the world, as we enter the new millennium. .
Is quantum mechanics based on an invariance principle?
Leon Brenig
2007-04-27
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.
Bohmian Trajectories as the Foundation of Quantum Mechanics
Sheldon Goldstein; Roderich Tumulka; Nino Zanghi
2009-12-14
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.
Quantum mechanics, Bayes' theorem and the conjunction fallacy
R. Franco
2007-05-17
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.
Bohmian Mechanics with Complex Action: A New Trajectory-Based Formulation of Quantum Mechanics
Yair Goldfarb; Ilan Degani; David J. Tannor
2006-04-20
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.
Duality, Mechanical Wave Theory, New Quantum Operators and Nonlinear Equations in Quantum Theory
Yi-Fang Chang
2010-08-17
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.
Probability in the Many-Worlds Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Vaidman, Lev
It is argued that, although in the Many-Worlds Interpretation of quantum mechanics there is no "probability" for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence between an illegitimate question: "What is the probability of an outcome of a quantum measurement?" with a legitimate question: "What is the probability that `I' am in the world corresponding to that outcome?"; (b) A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and (c) Relativistic causality, which together with (b) explain the Born rule of standard quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing probability measure are discussed.
Contexts, Systems and Modalities: a new ontology for quantum mechanics
Alexia Auffèves; Philippe Grangier
2015-01-23
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose to modify the quantum ontology, by requiring that physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary.
Lee, Sang-Bong
1993-09-01
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.
OPERA data and The Equivalence Postulate of Quantum Mechanics
Alon E. Faraggi
2011-10-24
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.
Whether quantum mechanics can be almighty even in information science
Koji Nagata; Tadao Nakamura
2008-11-28
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.
Statistical Structures Underlying Quantum Mechanics and Social Science
NASA Astrophysics Data System (ADS)
Wright, Ron
2007-08-01
Common observations of the unpredictability of human behavior and the influence of one question on the answer to another suggest social science experiments are probabilistic and may be mutually incompatible with one another, characteristics attributed to quantum mechanics (as distinguished from classical mechanics). This paper examines this superficial similarity in depth using the Foulis-Randall Operational Statistics language. In contradistinction to physics, social science deals with complex, open systems for which the set of possible experiments is unknowable and outcome interference is a graded phenomenon resulting from the ways the human brain processes information. It is concluded that social science is, in some ways, “less classical” than quantum mechanics, but that generalized “quantum” structures may provide appropriate descriptions of social science experiments. Specific challenges to extending “quantum” structures to social science are identified.
The M\\"obius Symmetry of Quantum Mechanics
Faraggi, Alon E
2015-01-01
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.
A Practical Quantum Mechanism for the Public Goods Game
Kay-Yut Chen; Tad Hogg; Raymond Beausoleil
2003-01-06
Quantum generalizations of conventional games broaden the range of available strategies, which can help improve outcomes for the participants. With many players, such quantum games can involve entanglement among many states which is difficult to implement, especially if the states must be communicated over some distance. This paper describes a quantum mechanism for the economically significant $n$-player public goods game that requires only two-particle entanglement and is thus much easier to implement than more general quantum mechanisms. In spite of the large temptation to free ride on the efforts of others in this game, two-particle entanglement is sufficient to give near optimal expected payoff when players use a simple mixed strategy for which no player can benefit by making different choices. This mechanism can also address some heterogeneous preferences among the players.
Motional sideband asymmetry in a quantum electro-mechanical device
NASA Astrophysics Data System (ADS)
Weinstein, Aaron; Lei, Chan U.; Wollman, Emma; Suh, Junho; Metelmann, Anja; Clerk, Aash; Schwab, Keith
2015-03-01
Quantum electro-mechanical systems offer a unique opportunity to probe quantum noise properties in macroscopic devices, properties which ultimately stem from Heisenberg's uncertainty relations. A simple example of this is expected to occur in a microwave parametric transducer, where mechanical motion generates motional sidebands corresponding to the up and down frequency-conversion of microwave photons. Due to quantum vacuum noise, the rates of these processes are expected to be unequal. We measure this fundamental imbalance in a microwave transducer coupled to a radio-frequency mechanical mode, cooled near the ground state of motion. We also discuss the subtle origin of this imbalance: with linear detection of the output light field, the imbalance is most naturally attributed to the quantum fluctuations of the electromagnetic field.
Statistical Structures Underlying Quantum Mechanics and Social Science
Ron Wright
2003-07-30
Common observations of the unpredictability of human behavior and the influence of one question on the answer to another suggest social science experiments are probabilistic and may be mutually incompatible with one another, characteristics attributed to quantum mechanics (as distinguished from classical mechanics). This paper examines this superficial similarity in depth using the Foulis-Randall Operational Statistics language. In contradistinction to physics, social science deals with complex, open systems for which the set of possible experiments is unknowable and outcome interference is a graded phenomenon resulting from the ways the human brain processes information. It is concluded that social science is, in some ways, "less classical" than quantum mechanics, but that generalized "quantum" structures may provide appropriate descriptions of social science experiments. Specific challenges to extending "quantum" structures to social science are identified.
Quantum mechanical studies of complex ferroelectric perovskites
NASA Astrophysics Data System (ADS)
Ramer, Nicholas John
In many electronic device applications, there is a need to interconvert electrical energy and other types of energy. Ferroelectric materials, which possess a voltage-dependent polarization, can enable this energy conversion process. Because of the broad interest in ferroelectric materials for these devices, there is a critical research effort, both experimental and theoretical, to understand these materials and aid in the development of materials with improved properties. This thesis presents detailed quantum mechanical investigations of the behavior of a complex ferroelectric perovskite under applied stress. In particular, we have chosen to study the solid solution PbZr1-xTix O3 (PZT). Since the study of ferroelectricity involves understanding both its structural and electronic signatures in materials, it has necessitated the development of a novel theoretical technique which improves the accuracy of the pseudopotentials used in our density functional theory calculations as well as a new method for constructing three-dimensional atomistic responses to small amounts of external stress. To examine the material's behavior under larger amounts of stress, we have studied the behavior of a composition of PZT lying near a structural phase boundary. On either side of the phase boundary, the material is characterized by a different polarization direction and may easily be switched between phases by applying external stress. In addition to stress-induced phase transitions, most ferroelectric materials also have composition dependent phase boundaries. Since different compositions of PZT would require increased computational effort, we have formulated an improved virtual crystal approach that makes tractable the study of the entire composition range. Using this method, we have been able to show for the first time via first-principles calculations, a composition dependent phase transition in a ferroelectric material. This thesis has accomplished three important goals: new theoretical methodology has been developed to enable accurate modeling of complex materials; application of these methods has been demonstrated for the study of ferroelectric oxides; and these investigations have revealed new insights into the relationships between stress, chemical composition, and ferroelectricity in oxides. This set of accomplishments enables the future study of even more complex perovskites and other multi-component systems.
Deformation quantization: Quantum mechanics lives and works in phase space
NASA Astrophysics Data System (ADS)
Zachos, Cosmas K.
2014-09-01
Wigner's 1932 quasi-probability Distribution Function in phase-space, his first paper in English, is a special (Weyl) representation of the density matrix. It has been useful in describing quantum flows in semiclassical limits; quantum optics; nuclear and physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" puzzles; molecular Talbot-Lau interferometry; atomic measurements. It is further of great importance in signal processing (time-frequency analysis). Nevertheless, a remarkable aspect of its internal logic, pioneered by H. Groenewold and J. Moyal, has only blossomed in the last quarter-century: It furnishes a third, alternate, formulation of Quantum Mechanics, independent of the conventional Hilbert Space (the gold medal), or Path Integral (the silver medal) formulations, and perhaps more intuitive, since it shares language with classical mechanics: one need not choose sides between coordinate or momentum space variables, since it is formulated simultaneously in terms of position and momentum. This bronze medal formulation is logically complete and self-standing, and accommodates the uncertainty principle in an unexpected manner, so that it offers unique insights into the classical limit of quantum theory. The observables in this formulation are cnumber functions in phase space instead of operators, with the same interpretation as their classical counterparts, only now composed together in novel algebraic ways using star products. One might then envision an imaginary world in which this formulation of quantum mechanics had preceded the conventional Hilbert-space formulation, and its own techniques and methods had arisen independently, perhaps out of generalizations of classical mechanics and statistical mechanics. A sampling of such intriguing techniques and methods has already been published in C. K. Zachos, Int Jou Mod Phys A17 297-316 (2002), and T. L. Curtright, D. B. Fairlie, and C. K. Zachos, A Concise Treatise on Quantum Mechanics in Phase Space, (Imperial Press & World Scientific, 2014).
Foundations of a spacetime path formalism for relativistic quantum mechanics
Seidewitz, Ed [14000 Gulliver's Trail, Bowie, Maryland 20720 (United States)
2006-11-15
Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for relativistic quantum mechanics, based on the parametrized paths of particles in spacetime. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such a spacetime approach has proved particularly useful in the study of quantum gravity and cosmology. This paper shows how a spacetime path formalism can be considered to arise naturally from the fundamental principles of the Born probability rule, superposition, and Poincare invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches in the literature, relating, in particular, 'off-shell' theories to traditional on-shell quantum field theory. It reproduces the results of perturbative quantum field theory for free and interacting particles, but provides intriguing possibilities for a natural program for regularization and renormalization. Further, an important consequence of the formalism is that a clear probabilistic interpretation can be maintained throughout, with a natural reduction to nonrelativistic quantum mechanics.
Multiple-event probability in general-relativistic quantum mechanics
Frank Hellmann; Mauricio Mondragon; Alejandro Perez; Carlo Rovelli
2006-10-27
We discuss the definition of quantum probability in the context of "timeless" general--relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multi-event probability. In conventional quantum mechanics this can be obtained by means of the ``wave function collapse" algorithm. We first point out certain difficulties of some natural definitions of multi-event probability, including the conditional probability widely considered in the literature. We then observe that multi-event probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum classical boundary, one can always trade a sequence of non-commuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the "wave function collapse" algorithm can nevertheless be recovered. The discussion bears also on the nature of the quantum collapse.
Quantum micro-mechanics with ultracold atoms
Botter, Thierry; Gupta, Subhadeep; Ma, Zhao-Yuan; Moore, Kevin L; Murch, Kater W; Purdy, Tom P; Stamper-Kurn, Dan M
2008-01-01
In many experiments isolated atoms and ions have been inserted into high-finesse optical resonators for the study of fundamental quantum optics and quantum information. Here, we introduce another application of such a system, as the realization of cavity optomechanics where the collective motion of an atomic ensemble serves the role of a moveable optical element in an optical resonator. Compared with other optomechanical systems, such as those incorporating nanofabricated cantilevers or the large cavity mirrors of gravitational observatories, our cold-atom realization offers direct access to the quantum regime. We describe experimental investigations of optomechanical effects, such as the bistability of collective atomic motion and the first quantification of measurement backaction for a macroscopic object, and discuss future directions for this nascent field.
Fault Models for Quantum Mechanical Switching Networks
Jacob Biamonte; Jeff S. Allen; Marek A. Perkowski
2010-01-19
The difference between faults and errors is that, unlike faults, errors can be corrected using control codes. In classical test and verification one develops a test set separating a correct circuit from a circuit containing any considered fault. Classical faults are modelled at the logical level by fault models that act on classical states. The stuck fault model, thought of as a lead connected to a power rail or to a ground, is most typically considered. A classical test set complete for the stuck fault model propagates both binary basis states, 0 and 1, through all nodes in a network and is known to detect many physical faults. A classical test set complete for the stuck fault model allows all circuit nodes to be completely tested and verifies the function of many gates. It is natural to ask if one may adapt any of the known classical methods to test quantum circuits. Of course, classical fault models do not capture all the logical failures found in quantum circuits. The first obstacle faced when using methods from classical test is developing a set of realistic quantum-logical fault models. Developing fault models to abstract the test problem away from the device level motivated our study. Several results are established. First, we describe typical modes of failure present in the physical design of quantum circuits. From this we develop fault models for quantum binary circuits that enable testing at the logical level. The application of these fault models is shown by adapting the classical test set generation technique known as constructing a fault table to generate quantum test sets. A test set developed using this method is shown to detect each of the considered faults.
From principles of mechanics to quantum mechanics - a survey on fuzziness in scientific theories
Rudolf Seising
2008-01-01
In this paper we discuss the principles of two fundamental theories of physics: mechanics and quantum mechanics. First, we consider two philosophical positions of the German physicist Heinrich Hertz. He established one of the both in the introduction of his well known Principles of Mechanics. This view - Hertz's \\