Nunthaboot, Nadtanet; Pianwanit, Somsak; Parasuk, Vudhichai; Ebalunode, Jerry O.; Briggs, James M.; Kokpol, Sirirat
2007-01-01
Human immunodeficiency virus (HIV)-1 integrase (IN) is an attractive target for development of acquired immunodeficiency syndrome chemotherapy. In this study, conventional and coupled quantum mechanical and molecular mechanical (QM/MM) molecular dynamics (MD) simulations of HIV-1 IN complexed with 5CITEP (IN-5CITEP) were carried out. In addition to differences in the bound position of 5CITEP, significant differences at the two levels of theory were observed in the metal coordination geometry and the areas involving residues 116–119 and 140–166. In the conventional MD simulation, the coordination of Mg2+ was found to be a near-perfect octahedral geometry whereas a distorted octahedral complex was observed in QM/MM. All of the above reasons lead to a different pattern of protein-ligand salt link formation that was not observed in the classical MD simulation. Furthermore to provide a theoretical understanding of inhibition mechanisms of 5CITEP and its derivative (DKA), hybrid QM/MM MD simulations of the two complexes (IN-5CITEP and IN-DKA) have been performed. The results reveal that areas involving residues 60–68, 116–119, and 140–149 were substantially different among the two systems. The two systems show similar pattern of metal coordination geometry, i.e., a distorted octahedron. In IN-DKA, both OD1 and OD2 of Asp-64 coordinate the Mg2+ in a monodentate fashion whereas only OD1 is chelated to the metal as observed in IN-5CITEP. The high potency of DKA as compared to 5CITEP is supported by a strong salt link formed between its carboxylate moiety and the ammonium group of Lys-159. Detailed comparisons between HIV-1 IN complexed with DKA and with 5CITEP provide information about ligand structure effects on protein-ligand interactions in particular with the Lys-159. This is useful for the design of new selective HIV-1 IN inhibitors. PMID:17693479
Giese, Timothy J; York, Darrin M
2016-06-14
A new approach for performing Particle Mesh Ewald in ab initio quantum mechanical/molecular mechanical (QM/MM) simulations with extended atomic orbital basis sets is presented. The new approach, the Ambient-Potential Composite Ewald (CEw) method, does not perform the QM/MM interaction with Mulliken charges nor electrostatically fit charges. Instead the nuclei and electron density interact directly with the MM environment, but in a manner that avoids the use of dense Fourier transform grids. By performing the electrostatics with the underlying QM density, the CEw method avoids self-consistent field instabilities that have been encountered with simple charge mapping procedures. Potential of mean force (PMF) profiles of the p-nitrophenyl phosphate dissociation reaction in explicit solvent are computed from PBE0/6-31G* QM/MM molecular dynamics simulations with various electrostatic protocols. The CEw profiles are shown to be stable with respect to real-space Ewald cutoff, whereas the PMFs computed from truncated and switched electrostatics produce artifacts. PBE0/6-311G**, AM1/d-PhoT, and DFTB2 QM/MM simulations are performed to generate two-dimensional PMF profiles of the phosphoryl transesterification reactions with ethoxide and phenoxide leaving groups. The semiempirical models incorrectly produce a concerted ethoxide mechanism, whereas PBE0 correctly produces a stepwise mechanism. The ab initio reaction barriers agree more closely to experiment than the semiempirical models. The failure of Mulliken-charge QM/MM-Ewald is analyzed. PMID:27171914
Moreira, Cátia; Ramos, Maria J; Fernandes, Pedro Alexandrino
2016-06-27
This paper is devoted to the understanding of the reaction mechanism of mycobacterium tuberculosis glutamine synthetase (mtGS) with atomic detail, using computational quantum mechanics/molecular mechanics (QM/MM) methods at the ONIOM M06-D3/6-311++G(2d,2p):ff99SB//B3LYP/6-31G(d):ff99SB level of theory. The complete reaction undergoes a three-step mechanism: the spontaneous transfer of phosphate from ATP to glutamate upon ammonium binding (ammonium quickly loses a proton to Asp54), the attack of ammonia on phosphorylated glutamate (yielding protonated glutamine), and the deprotonation of glutamine by the leaving phosphate. This exothermic reaction has an activation free energy of 21.5 kcal mol(-1) , which is consistent with that described for Escherichia coli glutamine synthetase (15-17 kcal mol(-1) ). The participating active site residues have been identified and their role and energy contributions clarified. This study provides an insightful atomic description of the biosynthetic reaction that takes place in this enzyme, opening doors for more accurate studies for developing new anti-tuberculosis therapies. PMID:27225077
Schiffmann, Christoph; Sebastiani, Daniel
2011-05-10
We present an algorithmic extension of a numerical optimization scheme for analytic capping potentials for use in mixed quantum-classical (quantum mechanical/molecular mechanical, QM/MM) ab initio calculations. Our goal is to minimize bond-cleavage-induced perturbations in the electronic structure, measured by means of a suitable penalty functional. The optimization algorithm-a variant of the artificial bee colony (ABC) algorithm, which relies on swarm intelligence-couples deterministic (downhill gradient) and stochastic elements to avoid local minimum trapping. The ABC algorithm outperforms the conventional downhill gradient approach, if the penalty hypersurface exhibits wiggles that prevent a straight minimization pathway. We characterize the optimized capping potentials by computing NMR chemical shifts. This approach will increase the accuracy of QM/MM calculations of complex biomolecules. PMID:26610125
McGrath, Matthew J; Kuo, I-F Will; Hayashi, Shigehiko; Takada, Shoji
2013-06-19
Kinesin is a molecular motor that hydrolyzes adenosine triphosphate (ATP) and moves along microtubules against load. While motility and atomic structures have been well-characterized for various members of the kinesin family, not much is known about ATP hydrolysis inside the active site. Here, we study ATP hydrolysis mechanisms in the kinesin-5 protein Eg5 by using combined quantum mechanics/molecular mechanics metadynamics simulations. Approximately 200 atoms at the catalytic site are treated by a dispersion-corrected density functional and, in total, 13 metadynamics simulations are performed with their cumulative time reaching ~0.7 ns. Using the converged runs, we compute free energy surfaces and obtain a few hydrolysis pathways. The pathway with the lowest free energy barrier involves a two-water chain and is initiated by the Pγ-Oβ dissociation concerted with approach of the lytic water to PγO3-. This immediately induces a proton transfer from the lytic water to another water, which then gives a proton to the conserved Glu270. Later, the proton is transferred back from Glu270 to HPO(4)2- via another hydrogen-bonded chain. We find that the reaction is favorable when the salt bridge between Glu270 in switch II and Arg234 in switch I is transiently broken, which facilitates the ability of Glu270 to accept a proton. When ATP is placed in the ADP-bound conformation of Eg5, the ATP-Mg moiety is surrounded by many water molecules and Thr107 blocks the water chain, which together make the hydrolysis reaction less favorable. The observed two-water chain mechanisms are rather similar to those suggested in two other motors, myosin and F1-ATPase, raising the possibility of a common mechanism. PMID:23751065
The Role of Gln61 in HRas GTP Hydrolysis: A Quantum Mechanics/Molecular Mechanics Study
Martín-García, Fernando; Mendieta-Moreno, Jesús Ignacio; López-Viñas, Eduardo; Gómez-Puertas, Paulino; Mendieta, Jesús
2012-01-01
Activation of the water molecule involved in GTP hydrolysis within the HRas⋅RasGAP system is analyzed using a tailored approach based on hybrid quantum mechanics/molecular mechanics (QM/MM) simulation. A new path emerges: transfer of a proton from the attacking water molecule to a second water molecule, then a different proton is transferred from this second water molecule to the GTP. Gln61 will stabilize the transient OH− and H3O+ molecules thus generated. This newly proposed mechanism was generated by using, for the first time to our knowledge, the entire HRas-RasGAP protein complex in a QM/MM simulation context. It also offers a rational explanation for previous experimental results regarding the decrease of GTPase rate found in the HRas Q61A mutant and the increase exhibited by the HRas Q61E mutant. PMID:22225809
Rosta, Edina; Nowotny, Marcin; Yang, Wei; Hummer, Gerhard
2011-06-15
We use quantum mechanics/molecular mechanics simulations to study the cleavage of the ribonucleic acid (RNA) backbone catalyzed by ribonuclease H. This protein is a prototypical member of a large family of enzymes that use two-metal catalysis to process nucleic acids. By combining Hamiltonian replica exchange with a finite-temperature string method, we calculate the free energy surface underlying the RNA-cleavage reaction and characterize its mechanism. We find that the reaction proceeds in two steps. In a first step, catalyzed primarily by magnesium ion A and its ligands, a water molecule attacks the scissile phosphate. Consistent with thiol-substitution experiments, a water proton is transferred to the downstream phosphate group. The transient phosphorane formed as a result of this nucleophilic attack decays by breaking the bond between the phosphate and the ribose oxygen. In the resulting intermediate, the dissociated but unprotonated leaving group forms an alkoxide coordinated to magnesium ion B. In a second step, the reaction is completed by protonation of the leaving group, with a neutral Asp132 as a likely proton donor. The overall reaction barrier of ∼15 kcal mol(-1), encountered in the first step, together with the cost of protonating Asp132, is consistent with the slow measured rate of ∼1-100/min. The two-step mechanism is also consistent with the bell-shaped pH dependence of the reaction rate. The nonmonotonic relative motion of the magnesium ions along the reaction pathway agrees with X-ray crystal structures. Proton-transfer reactions and changes in the metal ion coordination emerge as central factors in the RNA-cleavage reaction. PMID:21539371
A density-based adaptive quantum mechanical/molecular mechanical method.
Waller, Mark P; Kumbhar, Sadhana; Yang, Jack
2014-10-20
We present a density-based adaptive quantum mechanical/molecular mechanical (DBA-QM/MM) method, whereby molecules can switch layers from the QM to the MM region and vice versa. The adaptive partitioning of the molecular system ensures that the layer assignment can change during the optimization procedure, that is, on the fly. The switch from a QM molecule to a MM molecule is determined if there is an absence of noncovalent interactions to any atom of the QM core region. The presence/absence of noncovalent interactions is determined by analysis of the reduced density gradient. Therefore, the location of the QM/MM boundary is based on physical arguments, and this neatly removes some empiricism inherent in previous adaptive QM/MM partitioning schemes. The DBA-QM/MM method is validated by using a water-in-water setup and an explicitly solvated L-alanyl-L-alanine dipeptide. PMID:24954803
Quantum mechanical/molecular mechanical (QM/MM) docking: an evaluation for known test systems
NASA Astrophysics Data System (ADS)
Beierlein, Frank; Lanig, Harald; Schürer, Gudrun; Horn, Anselm H. C.; Clark, Timothy
A combined quantum mechanical/molecular mechanical (QM/MM) docking approach for the investigation of protein-inhibitor complexes is presented. Starting points for QM/MM optimizations are generated with AutoDock. The subsequent semiempirical AM1 QM/MM optimization of the complex obtained by the docking procedure gives a more detailed description of the binding mode and the electronic properties of the ligand. As we use a flexible protein environment in the QM/MM optimizations, we are able to simulate limited structural changes of the enzyme upon binding a ligand, even within a simple geometry optimization. The method was validated using a set of structurally known protein-inhibitor complexes, whose crystallographic data were taken from the Protein Data Bank. In addition to protein structures taken directly from complexes with the inhibitors, structures of uncomplexed HIV-1-protease and thrombin were also used successfully for QM/MM docking experiments. By comparing the resulting structures with those obtained using protein structures from protein-inhibitor complexes, we find that the method is able to simulate the effect of the induced fit when a simple optimization is adequate to reproduce the protein movement. Describing the ligand quantum mechanically gives a detailed view of its electronic properties, for example its polarization within the active site of the enzyme. This study suggests strongly that a QM/MM molecular dynamics approach will be able to simulate the induced fit in general cases.
Computing pKa Values with a Mixing Hamiltonian Quantum Mechanical/Molecular Mechanical Approach.
Liu, Yang; Fan, Xiaoli; Jin, Yingdi; Hu, Xiangqian; Hu, Hao
2013-09-10
Accurate computation of the pKa value of a compound in solution is important but challenging. Here, a new mixing quantum mechanical/molecular mechanical (QM/MM) Hamiltonian method is developed to simulate the free-energy change associated with the protonation/deprotonation processes in solution. The mixing Hamiltonian method is designed for efficient quantum mechanical free-energy simulations by alchemically varying the nuclear potential, i.e., the nuclear charge of the transforming nucleus. In pKa calculation, the charge on the proton is varied in fraction between 0 and 1, corresponding to the fully deprotonated and protonated states, respectively. Inspired by the mixing potential QM/MM free energy simulation method developed previously [H. Hu and W. T. Yang, J. Chem. Phys. 2005, 123, 041102], this method succeeds many advantages of a large class of λ-coupled free-energy simulation methods and the linear combination of atomic potential approach. Theory and technique details of this method, along with the calculation results of the pKa of methanol and methanethiol molecules in aqueous solution, are reported. The results show satisfactory agreement with the experimental data. PMID:26592414
Altun, Ahmet; Yokoyama, Shozo; Morokuma, Keiji
2008-01-01
The protein environments surrounding the retinal tune electronic absorption maximum from 350 to 630 nm. Hybrid quantum mechanical/molecular mechanical (QM/MM) methods can be used in calculating excitation energies of retinal in its native protein environments and in studying the molecular basis of spectral tuning. We hereby review recent QM/MM results on the phototransduction of bovine rhodopsin, bacteriorhodopsin, sensory rhodopsin II, nonretinal photoactive yellow protein and their mutants. PMID:18331400
Ab Initio Quantum Mechanical/Molecular Mechanical Studies of Histone Modifying Enzymes
NASA Astrophysics Data System (ADS)
Zhang, Yingkai
Histone proteins that form the nucleosome core are subject to a variety of post-translational transformations. These histone modifications make up the histone code which extends the information in the genetic code and is emerging as an essential mechanism to regulate gene expression. In spite of a current flurry of significant advances in experimental studies, there has been little theoretical understanding regarding how enzymes generate or remove these modifications. Very recently, we have made excellent progresses in investigating two such important histone-modifying enzyme families: zinc-dependent histone deacetylases (HDACs) and histone lysine methyltransferases (HKMTs). Our studies on a histonedeacetylase- like protein HDLP suggested a novel catalytic mechanism. The simulations on HKMT SET7/9 have characterized the histone lysine methylation reaction and elucidated the origin of enzyme catalysis. Our computational approaches centered on the pseudobond ab initio quantum mechanical/molecular mechanical (QM/MM) method, which allows for accurate modeling of the chemistry at the reaction active site while properly including the effects of the protein environment
Quantum mechanics/molecular mechanics study of oxygen binding in hemocyanin.
Saito, Toru; Thiel, Walter
2014-05-15
We report a combined quantum mechanics/molecular mechanics (QM/MM) study on the mechanism of reversible dioxygen binding in the active site of hemocyanin (Hc). The QM region is treated by broken-symmetry density functional theory (DFT) with spin projection corrections. The X-ray structures of deoxygenated (deoxyHc) and oxygenated (oxyHc) hemocyanin are well reproduced by QM/MM geometry optimizations. The computed relative energies strongly depend on the chosen density functional. They are consistent with the available thermodynamic data for oxygen binding in hemocyanin and in synthetic model complexes when the BH&HLYP hybrid functional with 50% Hartree-Fock exchange is used. According to the QM(BH&HLYP)/MM results, the reaction proceeds stepwise with two sequential electron transfer (ET) processes in the triplet state followed by an intersystem crossing to the singlet product. The first ET step leads to a nonbridged superoxo CuB(II)-O2(•-) intermediate via a low-barrier transition state. The second ET step is even more facile and yields a side-on oxyHc complex with the characteristic Cu2O2 butterfly core, accompanied by triplet-singlet intersystem crossing. The computed barriers are very small so that the two ET processes are expected to very rapid and nearly simultaneous. PMID:24762083
Gherman, Benjamin F.; Lippard, Stephen J.; Friesner, Richard A.
2005-01-26
The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. Using broken-symmetry unrestricted density functional theory quantum mechanical (QM) methods in concert with mixed quantum mechanics/molecular mechanics (QM/MM) methods, the hydroxylation of methane and substituted methanes by intermediate Q in methane monooxygenase hydroxylase (MMOH) has been quantitatively modeled. This protocol allows the protein environment to be included throughout the calculations and its effects (electrostatic, van der Waals, strain) upon the reaction to be accurately evaluated. With the current results, recent kinetic data for CH₃X (X ) H, CH₃, OH, CN, NO₂) substrate hydroxylation in MMOH (Ambundo, E. A.; Friesner, R. A.; Lippard, S. J. J. Am. Chem. Soc. 2002, 124, 8770-8771) can be rationalized. Results for methane, which provide a quantitative test of the protocol, including a substantial kinetic isotope effect (KIE), are in reasonable agreement with experiment. Specific features of the interaction of each of the substrates with MMO are illuminated by the QM/MM modeling, and the resulting effects upon substrate binding are quantitatively incorporated into the calculations. The results as a whole point to the success of the QM/MM methodology and enhance our understanding of MMOH catalytic chemistry. We also identify systematic errors in the evaluation of the free energy of binding of the Michaelis complexes of the substrates, which most likely arise from inadequate sampling and/or the use of harmonic approximations to evaluate the entropy of the complex. More sophisticated sampling methods will be required to achieve greater accuracy in this aspect of the calculation.
2012-01-01
Soluble epoxide hydrolase (sEH) is an enzyme involved in drug metabolism that catalyzes the hydrolysis of epoxides to form their corresponding diols. sEH has a broad substrate range and shows high regio- and enantioselectivity for nucleophilic ring opening by Asp333. Epoxide hydrolases therefore have potential synthetic applications. We have used combined quantum mechanics/molecular mechanics (QM/MM) umbrella sampling molecular dynamics (MD) simulations (at the AM1/CHARMM22 level) and high-level ab initio (SCS-MP2) QM/MM calculations to analyze the reactions, and determinants of selectivity, for two substrates: trans-stilbene oxide (t-SO) and trans-diphenylpropene oxide (t-DPPO). The calculated free energy barriers from the QM/MM (AM1/CHARMM22) umbrella sampling MD simulations show a lower barrier for phenyl attack in t-DPPO, compared with that for benzylic attack, in agreement with experiment. Activation barriers in agreement with experimental rate constants are obtained only with the highest level of QM theory (SCS-MP2) used. Our results show that the selectivity of the ring-opening reaction is influenced by several factors, including proximity to the nucleophile, electronic stabilization of the transition state, and hydrogen bonding to two active site tyrosine residues. The protonation state of His523 during nucleophilic attack has also been investigated, and our results show that the protonated form is most consistent with experimental findings. The work presented here illustrates how determinants of selectivity can be identified from QM/MM simulations. These insights may also provide useful information for the design of novel catalysts for use in the synthesis of enantiopure compounds. PMID:22280021
A quantum-mechanics molecular-mechanics scheme for extended systems
NASA Astrophysics Data System (ADS)
Hunt, Diego; Sanchez, Veronica M.; Scherlis, Damián A.
2016-08-01
We introduce and discuss a hybrid quantum-mechanics molecular-mechanics (QM-MM) approach for Car–Parrinello DFT simulations with pseudopotentials and planewaves basis, designed for the treatment of periodic systems. In this implementation the MM atoms are considered as additional QM ions having fractional charges of either sign, which provides conceptual and computational simplicity by exploiting the machinery already existing in planewave codes to deal with electrostatics in periodic boundary conditions. With this strategy, both the QM and MM regions are contained in the same supercell, which determines the periodicity for the whole system. Thus, while this method is not meant to compete with non-periodic QM-MM schemes able to handle extremely large but finite MM regions, it is shown that for periodic systems of a few hundred atoms, our approach provides substantial savings in computational times by treating classically a fraction of the particles. The performance and accuracy of the method is assessed through the study of energetic, structural, and dynamical aspects of the water dimer and of the aqueous bulk phase. Finally, the QM-MM scheme is applied to the computation of the vibrational spectra of water layers adsorbed at the TiO2 anatase (1 0 1) solid–liquid interface. This investigation suggests that the inclusion of a second monolayer of H2O molecules is sufficient to induce on the first adsorbed layer, a vibrational dynamics similar to that taking place in the presence of an aqueous environment. The present QM-MM scheme appears as a very interesting tool to efficiently perform molecular dynamics simulations of complex condensed matter systems, from solutions to nanoconfined fluids to different kind of interfaces.
A quantum-mechanics molecular-mechanics scheme for extended systems.
Hunt, Diego; Sanchez, Veronica M; Scherlis, Damián A
2016-08-24
We introduce and discuss a hybrid quantum-mechanics molecular-mechanics (QM-MM) approach for Car-Parrinello DFT simulations with pseudopotentials and planewaves basis, designed for the treatment of periodic systems. In this implementation the MM atoms are considered as additional QM ions having fractional charges of either sign, which provides conceptual and computational simplicity by exploiting the machinery already existing in planewave codes to deal with electrostatics in periodic boundary conditions. With this strategy, both the QM and MM regions are contained in the same supercell, which determines the periodicity for the whole system. Thus, while this method is not meant to compete with non-periodic QM-MM schemes able to handle extremely large but finite MM regions, it is shown that for periodic systems of a few hundred atoms, our approach provides substantial savings in computational times by treating classically a fraction of the particles. The performance and accuracy of the method is assessed through the study of energetic, structural, and dynamical aspects of the water dimer and of the aqueous bulk phase. Finally, the QM-MM scheme is applied to the computation of the vibrational spectra of water layers adsorbed at the TiO2 anatase (1 0 1) solid-liquid interface. This investigation suggests that the inclusion of a second monolayer of H2O molecules is sufficient to induce on the first adsorbed layer, a vibrational dynamics similar to that taking place in the presence of an aqueous environment. The present QM-MM scheme appears as a very interesting tool to efficiently perform molecular dynamics simulations of complex condensed matter systems, from solutions to nanoconfined fluids to different kind of interfaces. PMID:27352028
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.
Nauton, Lionel; Hélaine, Virgil; Théry, Vincent; Hecquet, Laurence
2016-04-12
We propose the first computational model for transketolase (TK), a thiamine diphosphate (ThDP)-dependent enzyme, using a quantum mechanical/molecular mechanical method on the basis of crystallographic TK structures from yeast and Escherichia coli, together with experimental kinetic data reported in the literature with wild-type and mutant TK. This model allowed us to define a new route for ThDP activation in the enzyme environment. We evidenced a strong interaction between ThDP and Glu418B of the TK active site, itself stabilized by Glu162A. The crucial point highlighted here is that deprotonation of ThDP C2 is not performed by ThDP N4' as reported in the literature, but by His481B, involving a HOH688A molecule bridge. Thus, ThDP N4' is converted from an amino form to an iminium form, ensuring the stabilization of the C2 carbanion or carbene. Finally, ThDP activation proceeds via an intermolecular process and not by an intramolecular one as reported in the literature. More generally, this proposed ThDP activation mechanism can be applied to some other ThDP-dependent enzymes and used to define the entire TK mechanism with donor and acceptor substrates more accurately. PMID:26998737
Valiev, Marat; Yang, Jie; Adams, Joseph; Taylor, Susan S.; Weare, John H.
2007-11-29
Protein kinases catalyze the transfer of the γ-phosphoryl group from ATP, a key regulatory process governing signalling pathways in eukaryotic cells. The structure of the active site in these enzymes is highly conserved implying common catalytic mechanism. In this work we investigate the reaction process in cAPK protein kinase (PKA) using a combined quantum mechanics and molecular mechanics approach. The novel computational features of our work include reaction pathway determination with nudged elastic band methodology and calculation of free energy profiles of the reaction process taking into account finite temperature fluctuations of the protein environment. We find that the transfer of the γ-phosphoryl group in the protein environment is an exothermic reaction with the reaction barrier of 15 kcal/mol.
Qi, Yue; Lu, Jiarui; Lai, Wenzhen
2016-05-26
To elucidate the reaction mechanism of the ring cleavage of homogentisate by homogentisate dioxygenase, quantum mechanical/molecular mechanical (QM/MM) calculations were carried out by using two systems in different protonation states of the substrate C2 hydroxyl group. When the substrate C2 hydroxyl group is ionized (the ionized pathway), the superoxo attack on the substrate is the rate-limiting step in the catalytic cycle, with a barrier of 15.9 kcal/mol. Glu396 was found to play an important role in stabilizing the bridge species and its O-O cleavage product by donating a proton via a hydrogen-bonded water molecule. When the substrate C2 hydroxyl group is not ionized (the nonionized pathway), the O-O bond cleavage of the bridge species is the rate-limiting step, with a barrier of 15.3 kcal/mol. The QM/MM-optimized geometries for the dioxygen and alkylperoxo complexes using the nonionized model (for the C2 hydroxyl group) are in agreement with the experimental crystal structures, suggesting that the C2 hydroxyl group is more likely to be nonionized. PMID:27119315
Zhang, Xiaodong; Bruice, Thomas C.
2006-01-01
The mechanism of DNA cytosine-5-methylation catalyzed by the bacterial M.HhaI enzyme has been considered as a stepwise nucleophilic addition of Cys-81-S− to cytosine C6 followed by C5 nucleophilic replacement of the methyl of S-adenosyl-l-methionine to produce 5-methyl-6-Cys-81-S-5,6-dihydrocytosine. In this study, we show that the reaction is concerted from a series of energy calculations by using the quantum mechanical/molecular mechanical hybrid method. Deprotonation of 5-methyl-6-Cys-81-S-5,6-dihydrocytosine and expulsion of Cys-81-S− provides the product DNA 5-methylcytosine. A required base catalyst for this deprotonation is not available as a member of the active site structure. A water channel between the active site and bulk water allows entrance of solvent to the active site. Hydroxide at 10−7 mole fraction (pH = 7) is shown to be sufficient for the required catalysis. We also show that Glu-119-CO2H can divert the reaction by protonating cytosine N3 when Cys-81-S− attacks cytosine, to form the 6-Cys-81-S-3-hydrocytosine. The reactants and 6-Cys-81-S-3-hydrocytosine product are in rapid equilibrium, and this explains the observed hydrogen exchange of cytosine with solvent. PMID:16606828
Smith, Adam J. T.; Li, Ying; Houk, K. N.
2011-01-01
The mechanisms of enzyme-catalyzed phosphate transfer and hydrolysis reactions are of great interest due to their importance and abundance in biochemistry. The reaction may proceed in a stepwise fashion, with either a pentavalent phosphorane or a metaphosphate anion intermediate, or by a concerted SN2 mechanism. Despite much theoretical work focused on a few key enzymes, a consensus for the mechanism has not been reached, and examples of all three possibilities have been demonstrated. We have investigated the mechanism of human uridine-cytidine kinase 2 (UCK2, EC 2.7.1.48), which catalyzes the transfer of a phosphate group from ATP to the ribose 5′-hydroxyl of cytidine and uridine. UCK2 is normally expressed in human placenta, but is overexpressed in certain cancer cells, where it is responsible for activating a class of antitumor prodrugs. The UCK2 mechanism was investigated by generating a 2D potential energy surface as a function of the P–O bonds forming and breaking, with energies calculated using a quantum mechanics/molecular mechanics potential (B3LYP/6–31G(d):AMBER). The mechanism of phosphate transfer is shown to be concerted, and is accompanied by concerted proton transfer from the 5′-hydroxyl to a conserved active site aspartic acid that serves as a catalytic base. The calculated barrier for this reaction is 15.1 kcal/mol, in relatively good agreement with the experimental barrier of 17.5 kcal/mol. The interactions of the enzyme active site with the reactant, transition state, and product are examined for their implications on the design of anticancer prodrugs or positron emission tomography (PET) reporter probes for this enzyme. PMID:19532987
NASA Astrophysics Data System (ADS)
Zeng, Xiancheng; Hu, Hao; Hu, Xiangqian; Cohen, Aron J.; Yang, Weitao
2008-03-01
Electron transfer (ET) reactions are one of the most important processes in chemistry and biology. Because of the quantum nature of the processes and the complicated roles of the solvent, theoretical study of ET processes is challenging. To simulate ET processes at the electronic level, we have developed an efficient density functional theory (DFT) quantum mechanical (QM)/molecular mechanical (MM) approach that uses the fractional number of electrons as the order parameter to calculate the redox free energy of ET reactions in solution. We applied this method to study the ET reactions of the aqueous metal complexes Fe(H2O)62+/3+ and Ru(H2O)62+/3+. The calculated oxidation potentials, 5.82 eV for Fe(II/III) and 5.14 eV for Ru(II/III), agree well with the experimental data, 5.50 and 4.96 eV, for iron and ruthenium, respectively. Furthermore, we have constructed the diabatic free energy surfaces from histogram analysis based on the molecular dynamics trajectories. The resulting reorganization energy and the diabatic activation energy also show good agreement with experimental data. Our calculations show that using the fractional number of electrons (FNE) as the order parameter in the thermodynamic integration process leads to efficient sampling and validate the ab initio QM/MM approach in the calculation of redox free energies.
Thellamurege, Nandun M.; Si, Dejun; Cui, Fengchao; Li, Hui
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.
NASA Astrophysics Data System (ADS)
Liu, Haiyan; Lu, Zhenyu; Cisneros, G. Andrés; Yang, Weitao
2004-07-01
The determination of reaction paths for enzyme systems remains a great challenge for current computational methods. In this paper we present an efficient method for the determination of minimum energy reaction paths with the ab initio quantum mechanical/molecular mechanical approach. Our method is based on an adaptation of the path optimization procedure by Ayala and Schlegel for small molecules in gas phase, the iterative quantum mechanical/molecular mechanical (QM/MM) optimization method developed earlier in our laboratory and the introduction of a new metric defining the distance between different structures in the configuration space. In this method we represent the reaction path by a discrete set of structures. For each structure we partition the atoms into a core set that usually includes the QM subsystem and an environment set that usually includes the MM subsystem. These two sets are optimized iteratively: the core set is optimized to approximate the reaction path while the environment set is optimized to the corresponding energy minimum. In the optimization of the core set of atoms for the reaction path, we introduce a new metric to define the distances between the points on the reaction path, which excludes the soft degrees of freedom from the environment set and includes extra weights on coordinates describing chemical changes. Because the reaction path is represented by discrete structures and the optimization for each can be performed individually with very limited coupling, our method can be executed in a natural and efficient parallelization, with each processor handling one of the structures. We demonstrate the applicability and efficiency of our method by testing it on two systems previously studied by our group, triosephosphate isomerase and 4-oxalocrotonate tautomerase. In both cases the minimum energy paths for both enzymes agree with the previously reported paths.
2015-01-01
In combined quantum mechanical/molecular mechanical (QM/MM) free energy calculations, it is often advantageous to have a frozen geometry for the quantum mechanical (QM) region. For such multiple-environment single-system (MESS) cases, two schemes are proposed here for estimating the polarization energy: the first scheme, termed MESS-E, involves a Roothaan step extrapolation of the self-consistent field (SCF) energy; whereas the other scheme, termed MESS-H, employs a Newton–Raphson correction using an approximate inverse electronic Hessian of the QM region (which is constructed only once). Both schemes are extremely efficient, because the expensive Fock updates and SCF iterations in standard QM/MM calculations are completely avoided at each configuration. They produce reasonably accurate QM/MM polarization energies: MESS-E can predict the polarization energy within 0.25 kcal/mol in terms of the mean signed error for two of our test cases, solvated methanol and solvated β-alanine, using the M06-2X or ωB97X-D functionals; MESS-H can reproduce the polarization energy within 0.2 kcal/mol for these two cases and for the oxyluciferin–luciferase complex, if the approximate inverse electronic Hessians are constructed with sufficient accuracy. PMID:25321186
Lonsdale, Richard; Fort, Rachel M; Rydberg, Patrik; Harvey, Jeremy N; Mulholland, Adrian J
2016-06-20
The mechanism of cytochrome P450(CYP)-catalyzed hydroxylation of primary amines is currently unclear and is relevant to drug metabolism; previous small model calculations have suggested two possible mechanisms: direct N-oxidation and H-abstraction/rebound. We have modeled the N-hydroxylation of (R)-mexiletine in CYP1A2 with hybrid quantum mechanics/molecular mechanics (QM/MM) methods, providing a more detailed and realistic model. Multiple reaction barriers have been calculated at the QM(B3LYP-D)/MM(CHARMM27) level for the direct N-oxidation and H-abstraction/rebound mechanisms. Our calculated barriers indicate that the direct N-oxidation mechanism is preferred and proceeds via the doublet spin state of Compound I. Molecular dynamics simulations indicate that the presence of an ordered water molecule in the active site assists in the binding of mexiletine in the active site, but this is not a prerequisite for reaction via either mechanism. Several active site residues play a role in the binding of mexiletine in the active site, including Thr124 and Phe226. This work reveals key details of the N-hydroxylation of mexiletine and further demonstrates that mechanistic studies using QM/MM methods are useful for understanding drug metabolism. PMID:27064685
NASA Astrophysics Data System (ADS)
Zeng, Xiancheng; Hu, Hao; Hu, Xiangqian; Yang, Weitao
2009-04-01
A quantum mechanical/molecular mechanical minimum free energy path (QM/MM-MFEP) method was developed to calculate the redox free energies of large systems in solution with greatly enhanced efficiency for conformation sampling. The QM/MM-MFEP method describes the thermodynamics of a system on the potential of mean force surface of the solute degrees of freedom. The molecular dynamics (MD) sampling is only carried out with the QM subsystem fixed. It thus avoids "on-the-fly" QM calculations and thus overcomes the high computational cost in the direct QM/MM MD sampling. In the applications to two metal complexes in aqueous solution, the new QM/MM-MFEP method yielded redox free energies in good agreement with those calculated from the direct QM/MM MD method. Two larger biologically important redox molecules, lumichrome and riboflavin, were further investigated to demonstrate the efficiency of the method. The enhanced efficiency and uncompromised accuracy are especially significant for biochemical systems. The QM/MM-MFEP method thus provides an efficient approach to free energy simulation of complex electron transfer reactions.
Zeng Xiancheng; Hu Hao; Hu Xiangqian; Yang Weitao
2009-04-28
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.
NASA Astrophysics Data System (ADS)
De Visser, Sam; Quesne, Matthew; Ward, Richard
2013-12-01
Cysteine protease enzymes are important for human physiology and catalyze key protein degradation pathways. These enzymes react via a nucleophilic reaction mechanism that involves a cysteine residue and the proton of a proximal histidine. Particularly efficient inhibitors of these enzymes are nitrile-based, however, the details of the catalytic reaction mechanism currently are poorly understood. To gain further insight into the inhibition of these molecules, we have performed a combined density functional theory and quantum mechanics/molecular mechanics study on the reaction of a nitrile-based inhibitor with the enzyme active site amino acids. We show here that small perturbations to the inhibitor structure can have dramatic effects on the catalysis and inhibition processes. Thus, we investigated a range of inhibitor templates and show that specific structural changes reduce the inhibitory efficiency by several orders of magnitude. Moreover, as the reaction takes place on a polar surface, we find strong differences between the DFT and QM/MM calculated energetics. In particular, the DFT model led to dramatic distortions from the starting structure and the convergence to a structure that would not fit the enzyme active site. In the subsequent QM/MM study we investigated the use of mechanical versus electronic embedding on the kinetics, thermodynamics and geometries along the reaction mechanism. We find minor effects on the kinetics of the reaction but large geometric and thermodynamics differences as a result of inclusion of electronic embedding corrections. The work here highlights the importance of model choice in the investigation of this biochemical reaction mechanism.
2015-01-01
The hepatitis delta virus (HDV) ribozyme catalyzes a self-cleavage reaction using a combination of nucleobase and metal ion catalysis. Both divalent and monovalent ions can catalyze this reaction, although the rate is slower with monovalent ions alone. Herein, we use quantum mechanical/molecular mechanical (QM/MM) free energy simulations to investigate the mechanism of this ribozyme and to elucidate the roles of the catalytic metal ion. With Mg2+ at the catalytic site, the self-cleavage mechanism is observed to be concerted with a phosphorane-like transition state and a free energy barrier of ∼13 kcal/mol, consistent with free energy barrier values extrapolated from experimental studies. With Na+ at the catalytic site, the mechanism is observed to be sequential, passing through a phosphorane intermediate, with free energy barriers of 2–4 kcal/mol for both steps; moreover, proton transfer from the exocyclic amine of protonated C75 to the nonbridging oxygen of the scissile phosphate occurs to stabilize the phosphorane intermediate in the sequential mechanism. To explain the slower rate observed experimentally with monovalent ions, we hypothesize that the activation of the O2′ nucleophile by deprotonation and orientation is less favorable with Na+ ions than with Mg2+ ions. To explore this hypothesis, we experimentally measure the pKa of O2′ by kinetic and NMR methods and find it to be lower in the presence of divalent ions rather than only monovalent ions. The combined theoretical and experimental results indicate that the catalytic Mg2+ ion may play three key roles: assisting in the activation of the O2′ nucleophile, acidifying the general acid C75, and stabilizing the nonbridging oxygen to prevent proton transfer to it. PMID:24383543
Ganguly, Abir; Thaplyal, Pallavi; Rosta, Edina; Bevilacqua, Philip C; Hammes-Schiffer, Sharon
2014-01-29
The hepatitis delta virus (HDV) ribozyme catalyzes a self-cleavage reaction using a combination of nucleobase and metal ion catalysis. Both divalent and monovalent ions can catalyze this reaction, although the rate is slower with monovalent ions alone. Herein, we use quantum mechanical/molecular mechanical (QM/MM) free energy simulations to investigate the mechanism of this ribozyme and to elucidate the roles of the catalytic metal ion. With Mg(2+) at the catalytic site, the self-cleavage mechanism is observed to be concerted with a phosphorane-like transition state and a free energy barrier of ∼13 kcal/mol, consistent with free energy barrier values extrapolated from experimental studies. With Na(+) at the catalytic site, the mechanism is observed to be sequential, passing through a phosphorane intermediate, with free energy barriers of 2-4 kcal/mol for both steps; moreover, proton transfer from the exocyclic amine of protonated C75 to the nonbridging oxygen of the scissile phosphate occurs to stabilize the phosphorane intermediate in the sequential mechanism. To explain the slower rate observed experimentally with monovalent ions, we hypothesize that the activation of the O2' nucleophile by deprotonation and orientation is less favorable with Na(+) ions than with Mg(2+) ions. To explore this hypothesis, we experimentally measure the pKa of O2' by kinetic and NMR methods and find it to be lower in the presence of divalent ions rather than only monovalent ions. The combined theoretical and experimental results indicate that the catalytic Mg(2+) ion may play three key roles: assisting in the activation of the O2' nucleophile, acidifying the general acid C75, and stabilizing the nonbridging oxygen to prevent proton transfer to it. PMID:24383543
NASA Astrophysics Data System (ADS)
Dieterich, Johannes M.; Werner, Hans-Joachim; Mata, Ricardo A.; Metz, Sebastian; Thiel, Walter
2010-01-01
Energy and free energy barriers for acetaldehyde conversion in aldehyde oxidoreductase are determined for three reaction pathways using quantum mechanical/molecular mechanical (QM/MM) calculations on the solvated enzyme. Ab initio single-point QM/MM energies are obtained at the stationary points optimized at the DFT(B3LYP)/MM level. These ab initio calculations employ local correlation treatments [LMP2 and LCCSD(T0)] in combination with augmented triple- and quadruple-zeta basis sets, and the final coupled cluster results include MP2-based corrections for basis set incompleteness and for the domain approximation. Free energy perturbation (FEP) theory is used to generate free energy profiles at the DFT(B3LYP)/MM level for the most important reaction steps by sampling along the corresponding reaction paths using molecular dynamics. The ab initio and FEP QM/MM results are combined to derive improved estimates of the free energy barriers, which differ from the corresponding DFT(B3LYP)/MM energy barriers by about 3 kcal mol-1. The present results confirm the qualitative mechanistic conclusions from a previous DFT(B3LYP)/MM study. Most favorable is a three-step Lewis base catalyzed mechanism with an initial proton transfer from the cofactor to the Glu869 residue, a subsequent nucleophilic attack that yields a tetrahedral intermediate (IM2), and a final rate-limiting hydride transfer. The competing metal center activated pathway has the same final step but needs to overcome a higher barrier in the initial step on the route to IM2. The concerted mechanism has the highest free energy barrier and can be ruled out. While confirming the qualitative mechanistic scenario proposed previously on the basis of DFT(B3LYP)/MM energy profiles, the present ab initio and FEP QM/MM calculations provide corrections to the barriers that are important when aiming at high accuracy.
Caratzoulas, Stavros; Courtney, Timothy; Vlachos, Dionisios G.
2011-01-01
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 β-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 α-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 α- and β-glucose. PMID:24308866
Friesner, Richard A.; Baik, Mu-Hyun; Gherman, Benjamin F.; Guallar, Victor; Wirstam, Maria E.; Murphy, Robert B.; Lippard, Stephen J.
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.
Sgrignani, Jacopo; Grazioso, Giovanni; De Amici, Marco
2016-09-13
The fast and constant development of drug resistant bacteria represents a serious medical emergency. To overcome this problem, the development of drugs with new structures and modes of action is urgently needed. In this work, we investigated, at the atomistic level, the mechanisms of hydrolysis of Meropenem by OXA-23, a class D β-lactamase, combining unbiased classical molecular dynamics and umbrella sampling simulations with classical force field-based and quantum mechanics/molecular mechanics potentials. Our calculations provide a detailed structural and dynamic picture of the molecular steps leading to the formation of the Meropenem-OXA-23 covalent adduct, the subsequent hydrolysis, and the final release of the inactive antibiotic. In this mechanistic framework, the predicted activation energy is in good agreement with experimental kinetic measurements, validating the expected reaction path. PMID:27534275
Hybrid Quantum Mechanical/Molecular Mechanics Study of the SN2 Reaction of CH3Cl+OH- in Water
Yin, Hongyun; Wang, Dunyou; Valiev, Marat
2011-11-03
The SN2 mechanism for the reaction of CH3Cl + OH- in aqueous solution was investigated using combined quantum mechanical and molecular mechanics methodology. We analyzed structures of reactant, transition and product states along the reaction pathway. The free energy profile was calculated using the multi-layered representation with the DFT and CCSD(T) level of theory for the quantum-mechanical description of the reactive region. Our results show that the aqueous environment has a significant impact on the reaction process. We find that solvation energy contribution raises the reaction barrier by ~18.9 kcal/mol and the reaction free energy by ~24.5 kcal/mol. The presence of the solvent also induces perturbations in the electronic structure of the solute leading to an increase of 3.5 kcal/mol for the reaction barrier and a decrease of 5.6 kcal/mol for the reaction free energy respectively. Combining the results of two previous calculation results on CHCl3 + OH- and CH2Cl2 + OH- reactions in water, we demonstrate that increase in the chlorination of the methyl group (from CH3Cl to CHCl3) is accompanied by the decrease in the free energy reaction barrier, with the CH3Cl + OH- having the largest barrier among the three reactions.
Pang, Jiayun; Scrutton, Nigel S; Sutcliffe, Michael J
2014-09-01
A computational study was performed on the experimentally elusive cyclisation step in the cofactor pyridoxal 5'-phosphate (PLP)-dependent D-ornithine 4,5-aminomutase (OAM)-catalysed reaction. Calculations using both model systems and a combined quantum mechanics/molecular mechanics approach suggest that regulation of the cyclic radical intermediate is achieved through the synergy of the intrinsic catalytic power of cofactor PLP and the active site of the enzyme. The captodative effect of PLP is balanced by an enzyme active site that controls the deprotonation of both the pyridine nitrogen atom (N1) and the Schiff-base nitrogen atom (N2). Furthermore, electrostatic interactions between the terminal carboxylate and amino groups of the substrate and Arg297 and Glu81 impose substantial "strain" energy on the orientation of the cyclic intermediate to control its trajectory. In addition the "strain" energy, which appears to be sensitive to both the number of carbon atoms in the substrate/analogue and the position of the radical intermediates, may play a key role in controlling the transition of the enzyme from the closed to the open state. Our results provide new insights into several aspects of the radical mechanism in aminomutase catalysis and broaden our understanding of cofactor PLP-dependent reactions. PMID:25048616
Jongkon, Nathjanan; Chotpatiwetchkul, Warot; Gleeson, M Paul
2015-09-01
The isocitrate lyase (ICL) superfamily catalyzes the cleavage of the C(2)-C(3) bond of various α-hydroxy acid substrates. Members of the family are found in bacteria, fungi, and plants and include ICL itself, oxaloacetate hydrolase (OAH), 2-methylisocitrate lyase (MICL), and (2R,3S)-dimethylmalate lyase (DMML) among others. ICL and related targets have been the focus of recent studies to treat bacterial and fungal infections, including tuberculosis. The catalytic process by which this family achieves C(2)-C(3) bond breaking is still not clear. Extensive structural studies have been performed on this family, leading to a number of plausible proposals for the catalytic mechanism. In this paper, we have applied quantum mechanical/molecular mechanical (QM/MM) methods to the most recently reported family member, DMML, to assess whether any of the mechanistic proposals offers a clear energetic advantage over the others. Our results suggest that Arg161 is the general base in the reaction and Cys124 is the general acid, giving rise to a rate-determining barrier of approximately 10 kcal/mol. PMID:26224328
2015-01-01
The glmS ribozyme catalyzes a self-cleavage reaction at the phosphodiester bond between residues A-1 and G1. This reaction is thought to occur by an acid–base mechanism involving the glucosamine-6-phosphate cofactor and G40 residue. Herein quantum mechanical/molecular mechanical free energy simulations and pKa calculations, as well as experimental measurements of the rate constant for self-cleavage, are utilized to elucidate the mechanism, particularly the role of G40. Our calculations suggest that an external base deprotonates either G40(N1) or possibly A-1(O2′), which would be followed by proton transfer from G40(N1) to A-1(O2′). After this initial deprotonation, A-1(O2′) starts attacking the phosphate as a hydroxyl group, which is hydrogen-bonded to deprotonated G40, concurrent with G40(N1) moving closer to the hydroxyl group and directing the in-line attack. Proton transfer from A-1(O2′) to G40 is concomitant with attack of the scissile phosphate, followed by the remainder of the cleavage reaction. A mechanism in which an external base does not participate, but rather the proton transfers from A-1(O2′) to a nonbridging oxygen during nucleophilic attack, was also considered but deemed to be less likely due to its higher effective free energy barrier. The calculated rate constant for the favored mechanism is in agreement with the experimental rate constant measured at biological Mg2+ ion concentration. According to these calculations, catalysis is optimal when G40 has an elevated pKa rather than a pKa shifted toward neutrality, although a balance among the pKa’s of A-1, G40, and the nonbridging oxygen is essential. These results have general implications, as the hammerhead, hairpin, and twister ribozymes have guanines at a similar position as G40. PMID:25526516
Le, Quang Anh Tuan; Kim, Seonghoon; Chang, Rakwoo; Kim, Yong Hwan
2015-07-30
Serum paraoxonase 1 (PON1) is a versatile enzyme for the hydrolysis of various substrates (e.g., lactones, phosphotriesters) and for the formation of a promising chemical platform γ-valerolactone. Elucidation of the PON1-catalyzed lactonase reaction mechanism is very important for understanding the enzyme function and for engineering this enzyme for specific applications. Kinetic study and hybrid quantum mechanics/molecular mechanics (QM/MM) method were used to investigate the PON1-catalyzed lactonase reaction of γ-butyrolactone (GBL) and (R)-γ-valerolactone (GVL). The activation energies obtained from the QM/MM calculations were in good agreement with the experiments. Interestingly, the QM/MM energy barriers at MP2/3-21G(d,p) level for the lactonase of GVL and GBL were respectively 14.3-16.2 and 11.5-13.1 kcal/mol, consistent with the experimental values (15.57 and 14.73 kcal/mol derived from respective kcat values of 36.62 and 147.21 s(-1)). The QM/MM energy barriers at MP2/6-31G(d) and MP2/6-31G(d,p) levels were also in relatively good agreements with the experiments. Importantly, the difference in the QM/MM energy barriers at MP2 level with all investigated basis sets for the lactonase of GVL and GBL were in excellent agreement with the experiments (0.9-3.1 and 0.8 kcal/mol, respectively). A detailed mechanism for the PON1-catalyzed lactonase reaction was also proposed in this study. PMID:26146888
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 σ-and π-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
Ferenczy, György G
2013-04-01
Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods. PMID:23281055
NASA Astrophysics Data System (ADS)
Soriano, Alejandro; Silla, Estanislao; Tuñón, Iñaki
2002-04-01
The dissociative electron transfer reaction CH3Cl+e-→CH3•+Cl- in aqueous solution is studied by using a QM/MM method. In this work the quantum subsystem (a methylchloride molecule plus an electron) is described using density functional theory while the solvent (300 water molecules) is described using the TIP3P classical potential. By means of molecular dynamics simulations and the thermodynamic integration technique we obtained the potential of mean force (PMF) for the carbon-chlorine bond dissociation of the neutral and radical anion species. Combining these two free energy curves we found a quadratic dependence of the activation free energy on the reaction free energy in agreement with Marcus' relationship, originally developed for electron transfer processes not involving bond breaking. We also investigated dynamical aspects by means of 60 dissociative trajectories started with the addition of an extra electron to different configurations of a methylchloride molecule in solution. The PMF shows the existence of a very flat region, in which the system is trapped during some finite time if the quantum subsystem quickly losses its excess kinetic energy transferring it to the solvent molecules. One of the most important factors determining the effectiveness of this energy transfer seems to be the existence of close contacts (hydrogen bonds) between the solute and the solvent.
Xu, Yulong; Zhang, Jingxue; Wang, Dunyou
2015-06-28
The CH{sub 3}Cl + CN{sup −} reaction in water was studied using a multilevel quantum mechanics/molecular mechanics (MM) method with the multilevels, electrostatic potential, density functional theory (DFT) and coupled-cluster single double triple (CCSD(T)), for the solute region. The detailed, back-side attack S{sub N}2 reaction mechanism was mapped along the reaction pathway. The potentials of mean force were calculated under both the DFT and CCSD(T) levels for the reaction region. The CCSD(T)/MM level of theory presents a free energy activation barrier height at 20.3 kcal/mol, which agrees very well with the experiment value at 21.6 kcal/mol. The results show that the aqueous solution has a dominant role in shaping the potential of mean force. The solvation effect and the polarization effect together increase the activation barrier height by ∼11.4 kcal/mol: the solvation effect plays a major role by providing about 75% of the contribution, while polarization effect only contributes 25% to the activation barrier height. Our calculated potential of mean force under the CCSD(T)/MM also has a good agreement with the one estimated using data from previous gas-phase studies.
NASA Astrophysics Data System (ADS)
Akin-Ojo, Omololu; Song, Yang; Wang, Feng
2008-08-01
A new method called adaptive force matching (AFM) has been developed that is capable of producing high quality force fields for condensed phase simulations. This procedure involves the parametrization of force fields to reproduce ab initio forces obtained from condensed phase quantum-mechanics/molecular-mechanics (QM/MM) calculations. During the procedure, the MM part of the QM/MM is iteratively improved so as to approach ab initio quality. In this work, the AFM method has been tested to parametrize force fields for liquid water so that the resulting force fields reproduce forces calculated using the ab initio MP2 and the Kohn-Sham density functional theory with the Becke-Lee-Yang-Parr (BLYP) and Becke three-parameter LYP (B3LYP) exchange correlation functionals. The AFM force fields generated in this work are very simple to evaluate and are supported by most molecular dynamics (MD) codes. At the same time, the quality of the forces predicted by the AFM force fields rivals that of very expensive ab initio calculations and are found to successfully reproduce many experimental properties. The site-site radial distribution functions (RDFs) obtained from MD simulations using the force field generated from the BLYP functional through AFM compare favorably with the previously published RDFs from Car-Parrinello MD simulations with the same functional. Technical aspects of AFM such as the optimal QM cluster size, optimal basis set, and optimal QM method to be used with the AFM procedure are discussed in this paper.
Raich, Lluís; Borodkin, Vladimir; Fang, Wenxia; Castro-López, Jorge; van Aalten, Daan M F; Hurtado-Guerrero, Ramón; Rovira, Carme
2016-03-16
The conversion of glycoside hydrolases (GHs) into transglycosylases (TGs), i.e., from enzymes that hydrolyze carbohydrates to enzymes that synthesize them, represents a promising solution for the large-scale synthesis of complex carbohydrates for biotechnological purposes. However, the lack of knowledge about the molecular details of transglycosylation hampers the rational design of TGs. Here we present the first crystallographic structure of a natural glycosyl-enzyme intermediate (GEI) of Saccharomyces cerevisiae Gas2 in complex with an acceptor substrate and demonstrate, by means of quantum mechanics/molecular mechanics metadynamics simulations, that it is tuned for transglycosylation (ΔG(⧧) = 12 kcal/mol). The 2-OH···nucleophile interaction is found to be essential for catalysis: its removal raises the free energy barrier significantly (11 and 16 kcal/mol for glycosylation and transglycosylation, respectively) and alters the conformational itinerary of the substrate (from (4)C1 → [(4)E](⧧) → (1,4)B/(4)E to (4)C1 → [(4)H3](⧧) → (4)C1). Our results suggest that changes in the interactions involving the 2-position could have an impact on the transglycosylation activity of several GHs. PMID:26859322
NASA Astrophysics Data System (ADS)
Cisneros, G. Andrés; Liu, Haiyan; Lu, Zhenyu; Yang, Weitao
2005-03-01
A two-step procedure for the determination of reaction paths in enzyme systems is presented. This procedure combines two chain-of-states methods: a quantum mechanical/molecular mechanical (QM/MM) implementation of the nudged elastic band (NEB) method and a second order parallel path optimizer method both recently developed in our laboratory. In the first step, a reaction path determination is performed with the NEB method, along with a restrained minimization procedure for the MM environment to obtain a first approximation to the reaction path. In the second step, the calculated path is refined with the parallel path optimizer method. By combining these two methods the reaction paths are determined accurately, and in addition, the number of path optimization iterations are significantly reduced. This procedure is tested by calculating both steps of the isomerization of 2-oxo-4-hexenedioate by 4-oxalocrotonate tautomerase, which have been previously determined by our group. The calculated paths agree with the previously reported results and we obtain a reduction of 45%-55% in the number of path optimization cycles.
NASA Astrophysics Data System (ADS)
Porro, Cristina S.; Sutcliffe, Michael J.; de Visser, Sam P.
2009-06-01
The cytochromes P450 are ubiquitous enzymes that are involved in key metabolizing processes in the body through the monoxygenation of substrates; however, their active oxidant is elusive. There have been reports that implicate that two oxidants, namely, the iron(IV)-oxo porphyrin cation radical (compound I) and the iron(III)-hydroperoxo complex (compound 0), both act as oxidants of sulfoxidation reactions, which contrasts theoretical studies on alkene epoxidation by compounds I and 0 that implicated compound 0 as a sluggish oxidant. To resolve this controversy and to establish the potency of compound I and compound 0 in sulfoxidation reactions, we have studied dimethyl sulfide sulfoxidation by both oxidants using the quantum mechanics/molecular mechanics (QM/MM) technique on cytochrome P450 enzymes and have set up a model of two P450 isozymes: P450cam and P450BM3. The calculations support earlier gas-phase density functional theory modeling and show that compound 0 is a sluggish oxidant that is unable to compete with compound I. Furthermore, compound I is shown to react with dimethyl sulfide via single-state reactivity on a dominant quartet spin state surface.
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
NASA Astrophysics Data System (ADS)
Passler, Peter P.; Rode, Bernd M.
2015-12-01
QMCF-MD simulations have been carried out for Pr(III), Nd(III), Pm(III) and Sm(III) ions in aqueous environment, employing ab initio quantum mechanical treatment for ion, first and second hydration shell. Interchanging prismatic structures are found for all ions, the main coordination number being 9, in good agreement with EXAFS experimental data. The ligand dynamics are characterized by first-shell mean residence times in the range of 50 to ∼200 ps and by force constants for the Ln(III)-O(water) bond between 75 and 100 Nm-1.
Capece, Luciana; Lewis-Ballester, Ariel; Batabyal, Dipanwita; Di Russo, Natali; Estrin, Dario A.
2015-01-01
Tryptophan dioxygenase (TDO) and indole-amine 2,3-dioxygenase (IDO) are two heme-containing enzymes which catalyze the conversion of L-tryptophan to N-formylkynurenine (NFK). In mammals, TDO is mostly expressed in liver and is involved in controlling homeostatic serum tryptophan concentrations, whereas IDO is ubiquitous and is involved in modulating immune responses. Previous studies suggested that the first step of the dioxygenase reaction involves the deprotonation of the indoleamine group of the substrate by an evolutionarily conserved distal histidine residue in TDO and the heme-bound dioxygen in IDO. Here, we used classical molecular dynamics and hybrid quantum mechanical/molecular mechanical methods to evaluate the base-catalyzed mechanism. Our data suggest that the deprotonation of the indoleamine group of the substrate by either histidine in TDO or heme-bound dioxygen in IDO is not energetically favorable. Instead, the dioxygenase reaction can be initiated by a direct attack of heme-bound dioxygen on the C2=C3 bond of the indole ring, leading to a protein-stabilized 2,3-alkylperoxide transition state and a ferryl epoxide intermediate, which subsequently recombine to generate NFK. The novel sequential two-step oxygen addition mechanism is fully supported by our recent resonance Raman data that allowed identification of the ferryl intermediate (Lewis-Ballester et al. in Proc Natl Acad Sci USA 106:17371–17376, 2009). The results reveal the subtle differences between the TDO and IDO reactions and highlight the importance of protein matrix in modulating stereoelectronic factors for oxygen activation and the stabilization of both transition and intermediate states. PMID:20361220
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 β-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
Yao, Yuan; Liu, Junjun; Zhan, Chang-Guo
2012-11-01
Human butyrylcholinesterase (BChE) is recognized as the most promising bioscavenger for organophosphorus (OP) warfare nerve agents. The G117H mutant of human BChE has been identified as a potential catalytic bioscavenger with a remarkably improved activity against OP nerve agents such as sarin, but it still does not satisfy the clinical use. For further design of the higher-activity mutants against OP nerve agents, it is essential to understand how the G117H mutation improves the activity. The reaction mechanisms and the free energy profiles for spontaneous reactivation of wild-type BChE and its G117H mutant phosphorylated by sarin have been explored, in this study, by performing first-principles quantum mechanical/molecular mechanical free energy calculations, and the remarkable role of the G117H mutation on the activity has been elucidated. For both the wild-type and G117H mutant enzymes, H438 acts as a general base to initiate the spontaneous reactivation that consists of two reaction steps: the nucleophilic attack at the phosphorus by a water molecule and decomposition of the pentacoordinated phosphorus intermediate. The calculated overall free energy barriers, i.e., 30.2 and 23.9 kcal/mol for the wild type and G117H mutant, respectively, are in good agreement with available experimental kinetic data. On the basis of the calculated results, the mutated residue (H117 in the G117H mutant) cannot initiate the spontaneous reactivation as a general base. Instead, it skews the oxyanion hole and makes the phosphorus more open to the nucleophilic water molecule, resulting in a remarkable change in the rate-determining step and significantly improved catalytic activity of human BChE. PMID:23092211
Wei, Donghui; Fang, Lei; Tang, Mingsheng; Zhan, Chang-Guo
2013-01-01
Proteasome is the major component of the crucial nonlysosomal protein degradation pathway in the cells, but the detailed reaction pathway is unclear. In this study, first-principles quantum mechanical/molecular mechanical free energy calculations have been performed to explore, for the first time, possible reaction pathways for proteasomal proteolysis/hydrolysis of a representative peptide, succinyl-leucyl-leucyl-valyl-tyrosyl-7-amino-4-methylcoumarin (Suc-LLVY-AMC). The computational results reveal that the most favorable reaction pathway consists of six steps. The first is a water-assisted proton transfer within proteasome, activating Thr1-Oγ. The second is a nucleophilic attack on the carbonyl carbon of a Tyr residue of substrate by the negatively charged Thr1-Oγ, followed by the dissociation of the amine AMC (third step). The fourth step is a nucleophilic attack on the carbonyl carbon of the Tyr residue of substrate by a water molecule, accompanied by a proton transfer from the water molecule to Thr1-Nz. Then, Suc-LLVY is dissociated (fifth step), and Thr1 is regenerated via a direct proton transfer from Thr1-Nz to Thr1-Oγ. According to the calculated energetic results, the overall reaction energy barrier of the proteasomal hydrolysis is associated with the transition state (TS3b) for the third step involving a water-assisted proton transfer. The determined most favorable reaction pathway and the rate-determining step have provided a reasonable interpretation of the reported experimental observations concerning the substituent and isotopic effects on the kinetics. The calculated overall free energy barrier of 18.2 kcal/mol is close to the experimentally-derived activation free energy of ~18.3–19.4 kcal/mol, suggesting that the computational results are reasonable. PMID:24111489
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
Koch, Denise M; Peslherbe, Gilles H
2008-01-17
Sodium iodide has long been a paradigm for ionic and covalent curve crossing and ultrafast nonadiabatic dynamics, and our interest lies in the influence of solvation on this process. The NaI(H2O)n photodissociation dynamics are simulated with the molecular dynamics with quantum transitions method. A quantum mechanics/molecular mechanics (QM/MM) description is adopted for the NaI(H2O)n electronic states, in which a semiempirical valence bond approach is used to describe the NaI electronic structure, and a polarizable optimized potential for cluster simulations model is used to describe solute-solvent and solvent-solvent interactions. In contrast to previous work with a nonpolarizable MM model [Koch et al., J. Phys. Chem. A, 2006, 110, 1438], this approach predicts that the NaI ionic ground- to covalent first-excited-state Franck-Condon energy gaps reach a plateau by cluster size 16, in relatively good agreement with experiment and electronic structure calculations; this allows us to safely extend our previous simulations to larger cluster sizes, i.e., n > 4. The simulations suggest that the disappearance of the two-photon ionization probe signals observed in femtosecond pump-probe experiments of NaI(H2O)n, n >/= 4, is due to the shift of the NaI curve-crossing region toward larger NaI internuclear separations because of solvent stabilization of the NaI ionic state. Further, the latter causes the adiabatic ground and excited states to acquire pure ionic and covalent character, respectively, by cluster 8, resulting in NaI ionic ground-state recombination or dissociation. To make a connection with electron transfer in solution, free energy curves have been generated as a function of a solvent coordinate similar to that of solution theory. Inspection of the free energy curves together with the results of excited-state simulations reveal that the electron-transfer process in clusters is not governed by the collective motion of the solvent molecules, as in solution, but
Shen, Lin; Yang, Weitao
2016-04-12
We developed a new multiresolution method that spans three levels of resolution with quantum mechanical, atomistic molecular mechanical, and coarse-grained models. The resolution-adapted all-atom and coarse-grained water model, in which an all-atom structural description of the entire system is maintained during the simulations, is combined with the ab initio quantum mechanics and molecular mechanics method. We apply this model to calculate the redox potentials of the aqueous ruthenium and iron complexes by using the fractional number of electrons approach and thermodynamic integration simulations. The redox potentials are recovered in excellent accordance with the experimental data. The speed-up of the hybrid all-atom and coarse-grained water model renders it computationally more attractive. The accuracy depends on the hybrid all-atom and coarse-grained water model used in the combined quantum mechanical and molecular mechanical method. We have used another multiresolution model, in which an atomic-level layer of water molecules around redox center is solvated in supramolecular coarse-grained waters for the redox potential calculations. Compared with the experimental data, this alternative multilayer model leads to less accurate results when used with the coarse-grained polarizable MARTINI water or big multipole water model for the coarse-grained layer. PMID:26930454
Liu, Xingchen; Salahub, Dennis R
2015-04-01
Heterogeneous reactions catalyzed by transition-metal-containing nanoparticles represent a crucial type of reaction in chemical industry. Because of the existing gap in understanding heterogeneous catalysis between a cluster of a few atoms and a bulk model of periodic slabs, reactions catalyzed by transition-metal-containing nanoparticles are still not well understood. Herein, we provide a multiscale modeling approach to study the benzene hydrogenation reactions on molybdenum carbide nanoparticles (MCNPs) in the process of in situ heavy oil upgrading. By coupling the quantum mechanical (QM) density functional tight-binding (DFTB) method with a molecular mechanical (MM) force field, a QM/MM model was built to describe the reactants, the nanoparticles and the surroundings. Umbrella sampling (US) was used to calculate the free energy profiles of the benzene hydrogenation reactions in a model aromatic solvent in the in situ heavy oil upgrading conditions. By comparing with the traditional method in computational heterogeneous catalysis, the results reveal new features of the metallic MCNPs. Rather than being rigid, they are very flexible under working condition due to the entropic contributions of the MCNPs and the solvent, which greatly affect the free energy profiles of these nanoscale heterogeneous reactions. PMID:25774905
Yamada, Kenta; Koyano, Yoshiyuki; Okamoto, Takuya; Asada, Toshio; Koga, Nobuaki; Nagaoka, Masataka
2011-11-15
We present an alternative approach to determine "density-dependent property"-derived charges for molecules in the condensed phase. In the case of a solution, it is essential to take into consideration the electron polarization of molecules in the active site of this system. The solute and solvent molecules in this site have to be described by a quantum mechanical technique and the others are allowed to be treated by a molecular mechanical method (QM/MM scheme). For calculations based on this scheme, using the forces and interaction energy as density-dependent property our charges from interaction energy and forces (CHIEF) approach can provide the atom-centered charges on the solute atoms. These charges reproduce well the electrostatic potentials around the solvent molecules and present properly the picture of the electron density of the QM subsystem in the solution system. Thus, the CHIEF charges can be considered as the atomic charges under the conditions of the QM/MM simulation, and then enable one to analyze electrostatic interactions between atoms in the QM and MM regions. This approach would give a view of the QM nuclei and electrons different from the conventional methods. PMID:21815177
Nakamura, Shin; Ota, Kai; Shibuya, Yuichi; Noguchi, Takumi
2016-01-26
Photosynthetic water oxidation takes place at the Mn4CaO5 cluster in photosystem II. Around the Mn4CaO5 cluster, a hydrogen bond network is formed by several water molecules, including four water ligands. To clarify the role of this water network in the mechanism of water oxidation, we investigated the effects of the removal of Ca(2+) and substitution with metal ions on the vibrations of water molecules coupled to the Mn4CaO5 cluster by means of Fourier transform infrared (FTIR) difference spectroscopy and quantum mechanics/molecular mechanics (QM/MM) calculations. The OH stretching vibrations of nine water molecules forming a network between D1-D61 and YZ were calculated using the QM/MM method. On the the calculated normal modes, a broad positive feature at 3200-2500 cm(-1) in an S2-minus-S1 FTIR spectrum was attributed to the vibrations of strongly hydrogen-bonded OH bonds of water involving the vibrations of water ligands to a Mn ion and the in-phase coupled vibration of a water network connected to YZ, while bands in the 3700-3500 cm(-1) region were assigned to the coupled vibrations of weakly hydrogen-bonded OH bonds of water. All the water bands were lost upon Ca(2+) depletion and Ba(2+) substitution, which inhibit the S2 → S3 transition, indicating that a solid water network was broken by these treatments. By contrast, Sr(2+) substitution slightly altered the water bands around 3600 cm(-1), reflecting minor modification in water interactions, consistent with the retention of water oxidation activity with a decreased efficiency. These results suggest that the water network around the Mn4CaO5 cluster plays an essential role in the water oxidation mechanism particularly in a concerted process of proton transfer and water insertion during the S2 → S3 transition. PMID:26716470
2015-01-01
Mercuric reductase, MerA, is a key enzyme in bacterial mercury resistance. This homodimeric enzyme captures and reduces toxic Hg2+ to Hg0, which is relatively unreactive and can exit the cell passively. Prior to reduction, the Hg2+ is transferred from a pair of cysteines (C558′ and C559′ using Tn501 numbering) at the C-terminus of one monomer to another pair of cysteines (C136 and C141) in the catalytic site of the other monomer. Here, we present the X-ray structure of the C-terminal Hg2+ complex of the C136A/C141A double mutant of the Tn501 MerA catalytic core and explore the molecular mechanism of this Hg transfer with quantum mechanical/molecular mechanical (QM/MM) calculations. The transfer is found to be nearly thermoneutral and to pass through a stable tricoordinated intermediate that is marginally less stable than the two end states. For the overall process, Hg2+ is always paired with at least two thiolates and thus is present at both the C-terminal and catalytic binding sites as a neutral complex. Prior to Hg2+ transfer, C141 is negatively charged. As Hg2+ is transferred into the catalytic site, a proton is transferred from C136 to C559′ while C558′ becomes negatively charged, resulting in the net transfer of a negative charge over a distance of ∼7.5 Å. Thus, the transport of this soft divalent cation is made energetically feasible by pairing a competition between multiple Cys thiols and/or thiolates for Hg2+ with a competition between the Hg2+ and protons for the thiolates. PMID:25343681
Nishizawa, Hiroaki; Nishimura, Yoshifumi; Kobayashi, Masato; Irle, Stephan; Nakai, Hiromi
2016-08-01
The linear-scaling divide-and-conquer (DC) quantum chemical methodology is applied to the density-functional tight-binding (DFTB) theory to develop a massively parallel program that achieves on-the-fly molecular reaction dynamics simulations of huge systems from scratch. The functions to perform large scale geometry optimization and molecular dynamics with DC-DFTB potential energy surface are implemented to the program called DC-DFTB-K. A novel interpolation-based algorithm is developed for parallelizing the determination of the Fermi level in the DC method. The performance of the DC-DFTB-K program is assessed using a laboratory computer and the K computer. Numerical tests show the high efficiency of the DC-DFTB-K program, a single-point energy gradient calculation of a one-million-atom system is completed within 60 s using 7290 nodes of the K computer. © 2016 Wiley Periodicals, Inc. PMID:27317328
Ramanan, Rajeev; Dubey, Kshatresh Dutta; Wang, Binju; Mandal, Debasish; Shaik, Sason
2016-06-01
This work uses combined quantum mechanical/molecular mechanical and molecular dynamics simulations to investigate the mechanism and selectivity of H2O2-dependent hydroxylation of fatty acids by the P450SPα class of enzymes. H2O2 is found to serve as the surrogate oxidant for generating the principal oxidant, Compound I (Cpd I), in a mechanism that involves homolytic O-O bond cleavage followed by H-abstraction from the Fe-OH moiety. Our results rule out a substrate-assisted heterolytic cleavage of H2O2 en route to Cpd I. We show, however, that substrate binding stabilizes the resultant Fe-H2O2 complex, which is crucial for the formation of Cpd I in the homolytic pathway. A network of hydrogen bonds locks the HO· radical, formed by the O-O homolysis, thus directing it to exclusively abstract the hydrogen atom from Fe-OH, thereby forming Cpd I, while preventing the autoxoidative reaction, with the porphyrin ligand, and the substrate oxidation. The so formed Cpd I subsequently hydroxylates fatty acids at their α-position with S-enantioselectivity. These selectivity patterns are controlled by the active site: substrate's binding by Arg241 determines the α-regioselectivity, while the Pro242 residue locks the prochiral α-CH2, thereby leading to hydroxylation of the pro-S C-H bond. Our study of the mutant Pro242Ala sheds light on potential modifications of the enzyme's active site in order to modify reaction selectivity. Comparisons of P450SPα to P450BM3 and to P450BSβ reveal that function has evolved in these related metalloenzymes by strategically placing very few residues in the active site. PMID:27059179
NASA Astrophysics Data System (ADS)
Schieve, William C.; Horwitz, Lawrence P.
2009-04-01
1. Foundations of quantum statistical mechanics; 2. Elementary examples; 3. Quantum statistical master equation; 4. Quantum kinetic equations; 5. Quantum irreversibility; 6. Entropy and dissipation: the microscopic theory; 7. Global equilibrium: thermostatics and the microcanonical ensemble; 8. Bose-Einstein ideal gas condensation; 9. Scaling, renormalization and the Ising model; 10. Relativistic covariant statistical mechanics of many particles; 11. Quantum optics and damping; 12. Entanglements; 13. Quantum measurement and irreversibility; 14. Quantum Langevin equation: quantum Brownian motion; 15. Linear response: fluctuation and dissipation theorems; 16. Time dependent quantum Green's functions; 17. Decay scattering; 18. Quantum statistical mechanics, extended; 19. Quantum transport with tunneling and reservoir ballistic transport; 20. Black hole thermodynamics; Appendix; Index.
NASA Astrophysics Data System (ADS)
Murdin, P.
2000-11-01
A development of quantum theory that was initiated in the 1920s by Werner Heisenberg (1901-76) and Erwin Schrödinger (1887-1961). The theory drew on a proposal made in 1925 Prince Louis de Broglie (1892-1987), that particles have wavelike properties (the wave-particle duality) and that an electron, for example, could in some respects be regarded as a wave with a wavelength that depended on its mo...
NASA Astrophysics Data System (ADS)
Gardner, David E.
This thesis describes qualitative research conducted to understand the problems students have when learning quantum mechanics. It differs from previous studies on educational issues associated with quantum mechanics in that I have examined the difficulties from the students' perspective. Three questions guided this research: What are the experiences of students learning quantum mechanics? What conceptual difficulties do students have with quantum mechanics? and, How do students approach learning quantum mechanics? From these questions, two themes emerged. First, students do not consider the quantum mechanical concepts of wave-particle duality or the uncertainty principle to be important sources of difficulties for them. Second, many of the difficulties students encounter are not related to conceptual understanding of specific topics, but stem from a mindset that is incongruent with the nature and structure of quantum mechanics. The implications for teaching are that the nature and structure of quantum mechanics should be emphasized and be an explicit part of instruction.
Quantum Mechanics Based Multiscale Modeling of Materials
NASA Astrophysics Data System (ADS)
Lu, Gang
2013-03-01
We present two quantum mechanics based multiscale approaches that can simulate extended defects in metals accurately and efficiently. The first approach (QCDFT) can treat multimillion atoms effectively via density functional theory (DFT). The method is an extension of the original quasicontinuum approach with DFT as its sole energetic formulation. The second method (QM/MM) has to do with quantum mechanics/molecular mechanics coupling based on the constrained density functional theory, which provides an exact framework for a self-consistent quantum mechanical embedding. Several important materials problems will be addressed using the multiscale modeling approaches, including hydrogen-assisted cracking in Al, magnetism-controlled dislocation properties in Fe and Si pipe diffusion along Al dislocation core. We acknowledge the support from the Office of Navel Research and the Army Research Office.
NASA Astrophysics Data System (ADS)
Kapustin, Anton
2013-06-01
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.
Relativity and Quantum Mechanics
Braendas, Erkki J.
2007-12-26
The old dilemma of quantum mechanics versus the theory of relativity is reconsidered via a first principles relativistically invariant theory. By analytic extension of quantum mechanics into the complex plane one may (i) include dynamical features such as time- and length-scales and (ii) examine the possibility and flexibility of so-called general Jordan block formations. The present viewpoint asks for a new perspective on the age-old problem of quantum mechanics versus the theory of relativity. To bring these ideas together, we will establish the relation with the Klein-Gordon-Dirac relativistic theory and confirm some dynamical features of both the special and the general relativity theory.
NASA Astrophysics Data System (ADS)
Błaszak, Maciej; Domański, Ziemowit
2012-02-01
This paper develops an alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative ⋆-product and the deformation of the Poisson bracket to an appropriate Lie bracket are the key elements in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of any smooth Hamiltonian function and for a very wide class of deformations. The considered class of deformations and the corresponding ⋆-products contains as a special case all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of ⋆-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the ⋆-multiplication. The most important result of the paper shows that developed formalism is more fundamental than the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. The equivalence of two formulations of quantum mechanics is proved by observing that the Wigner-Moyal transform has all properties of the tensor product. This observation allows writing many previous results found in the literature in a transparent way, from which the equivalence of the two formulations of quantum mechanics follows naturally. In addition, examples of a free particle and a simple harmonic
Quantum Mechanics From the Cradle?
ERIC Educational Resources Information Center
Martin, John L.
1974-01-01
States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)
Fundamentals of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Tang, C. L.
2005-06-01
Quantum mechanics has evolved from a subject of study in pure physics to one with a wide range of applications in many diverse fields. The basic concepts of quantum mechanics are explained in this book in a concise and easy-to-read manner emphasising applications in solid state electronics and modern optics. Following a logical sequence, the book is focused on the key ideas and is conceptually and mathematically self-contained. The fundamental principles of quantum mechanics are illustrated by showing their application to systems such as the hydrogen atom, multi-electron ions and atoms, the formation of simple organic molecules and crystalline solids of practical importance. It leads on from these basic concepts to discuss some of the most important applications in modern semiconductor electronics and optics. Containing many homework problems and worked examples, the book is suitable for senior-level undergraduate and graduate level students in electrical engineering, materials science and applied physics. Clear exposition of quantum mechanics written in a concise and accessible style Precise physical interpretation of the mathematical foundations of quantum mechanics Illustrates the important concepts and results by reference to real-world examples in electronics and optoelectronics Contains homeworks and worked examples, with solutions available for instructors
NASA Astrophysics Data System (ADS)
Nishimura, Hirokazu
1996-06-01
Machida and Namiki developed a many-Hilbert-spaces formalism for dealing with the interaction between a quantum object and a measuring apparatus. Their mathematically rugged formalism was polished first by Araki from an operator-algebraic standpoint and then by Ozawa for Boolean quantum mechanics, which approaches a quantum system with a compatible family of continuous superselection rules from a notable and perspicacious viewpoint. On the other hand, Foulis and Randall set up a formal theory for the empirical foundation of all sciences, at the hub of which lies the notion of a manual of operations. They deem an operation as the set of possible outcomes and put down a manual of operations at a family of partially overlapping operations. Their notion of a manual of operations was incorporated into a category-theoretic standpoint into that of a manual of Boolean locales by Nishimura, who looked upon an operation as the complete Boolean algebra of observable events. Considering a family of Hilbert spaces not over a single Boolean locale but over a manual of Boolean locales as a whole, Ozawa's Boolean quantum mechanics is elevated into empirical quantum mechanics, which is, roughly speaking, the study of quantum systems with incompatible families of continuous superselection rules. To this end, we are obliged to develop empirical Hilbert space theory. In particular, empirical versions of the square root lemma for bounded positive operators, the spectral theorem for (possibly unbounded) self-adjoint operators, and Stone's theorem for one-parameter unitary groups are established.
NASA Astrophysics Data System (ADS)
Blencowe, Miles
The emergence of the macroscopic classical world from the microscopic quantum world is commonly understood to be a consequence of the fact that any given quantum system is open, unavoidably interacting with unobserved environmental degrees of freedom that will cause initial quantum superposition states of the system to decohere, resulting in classical mixtures of either-or alternatives. A fundamental question concerns how large a macroscopic object can be placed in a manifest quantum state, such as a center of mass quantum superposition state, under conditions where the effects of the interacting environmental degrees of freedom are reduced (i.e. in ultrahigh vacuum and at ultralow temperatures). Recent experiments have in fact demonstrated manifest quantum behavior in nano-to-micron-scale mechanical systems. Gravity has been invoked in various ways as playing a possible fundamental role in enforcing classicality of matter systems beyond a certain scale. Adopting the viewpoint that the standard perturbative quantization of general relativity provides an effective description of quantum gravity that is valid at ordinary energies, we show that it is possible to describe quantitatively how gravity as an environment can induce the decoherence of matter superposition states. The justification for such an approach follows from the fact that we are considering laboratory scale systems, where the matter is localized to regions of small curvature. As with other low energy effects, such as the quantum gravity correction to the Newtonian potential between two ordinary masses, it should be possible to quantitatively evaluate gravitationally induced decoherence rates by employing standard perturbative quantum gravity as an effective field theory; whatever the final form the eventual correct quantum theory of gravity takes, it must converge in its predictions with the effective field theory description at low energies. Research supported by the National Science Foundation (NSF
Grassmann matrix quantum mechanics
NASA Astrophysics Data System (ADS)
Anninos, Dionysios; Denef, Frederik; Monten, Ruben
2016-04-01
We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. We discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.
Noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
Gamboa, J.; Loewe, M.; Rojas, J. C.
2001-09-01
A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.
NASA Astrophysics Data System (ADS)
Ellerman, David
2014-03-01
In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.
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
Supersymmetry in quantum mechanics
Lahiri, A. ); Roy, P.K. ); Bagghi, B. )
1990-04-20
A pedagogical review on supersymmetry in quantum mechanics is presented which provides a comprehensive coverage of the subject. First, the key ingredients of the quantization of the systems with anticommuting variables are discussed. The supersymmetric Hamiltonian in quantum mechanics is then constructed by emphasizing the role of partner potentials and the superpotentials. The authors also make explicit the mathematical formulation of the Hamiltonian by considering in detail the N = 1 and N = 2 supersymmetric (quantum) mechanics. Supersymmetry is then discussed in the context of one-dimensional problems and the importance of the factorization method is highlighted. They treat in detail the technique of constructing a hierarchy of Hamiltonians employing the so-called 'shape-invariance' of potentials. To make transparent the relationship between supersymmetry and solvable potentials, they also solve several examples. They then go over the formulation of supersymmetry in radial problems, paying a special attention to the Coulomb and isotropic oscillator potentials. They show that the ladder operator technique may be suitable modified in higher dimensions for generating isospectral Hamiltonians. Next, the criteria for the breaking of supersymmetry is considered and their range of applicability is examined by suitably modifying he definition of Witten's index. Finally, the authors perform some numerical calculations for a class of potentials to show how a modified WKB approximation works in supersymmetric cases.
Feynman's simple quantum mechanics
NASA Astrophysics Data System (ADS)
Taylor, Edwin F.
1997-03-01
This sample class presents an alternative to the conventional introduction to quantum mechanics and describes its current use in a credit course. This alternative introduction rests on theory presented in professional and popular writings by Richard Feynman. Feynman showed that Nature gives a simple command to the electron: "Explore all paths." All of nonrelativistic quantum mechanics, among other fundamental results, comes from this command. With a desktop computer the student points and clicks to tell a modeled electron which paths to follow. The computer then shows the results, which embody the elemental strangeness and paradoxical behaviors of the world of the very small. Feynman's approach requires few equations and provides a largely non-mathematical introduction to the wave function of conventional quantum mechanics. Draft software and materials already used for two semesters in an e-mail computer conference credit university course show that Feynman's approach works well with a variety of students. The sample class explores computer and written material and describes the next steps in its development.
Emergent mechanics, quantum and un-quantum
NASA Astrophysics Data System (ADS)
Ralston, John P.
2013-10-01
There is great interest in quantum mechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantum mechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantum mechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications
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.
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.
Diagrammatic quantum mechanics
NASA Astrophysics Data System (ADS)
Kauffman, Louis H.; Lomonaco, Samuel J.
2015-05-01
This paper explores how diagrams of quantum processes can be used for modeling and for quantum epistemology. The paper is a continuation of the discussion where we began this formulation. Here we give examples of quantum networks that represent unitary transformations by dint of coherence conditions that constitute a new form of non-locality. Local quantum devices interconnected in space can form a global quantum system when appropriate coherence conditions are maintained.
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
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.
Principles of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Landé, Alfred
2013-10-01
ödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.
Dissipative Forces and Quantum Mechanics
ERIC Educational Resources Information Center
Eck, John S.; Thompson, W. J.
1977-01-01
Shows how to include the dissipative forces of classical mechanics in quantum mechanics by the use of non-Hermetian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. (MLH)
Communication: Quantum mechanics without wavefunctions
Schiff, Jeremy; Poirier, Bill
2012-01-21
We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.
Entangled states in quantum mechanics
NASA Astrophysics Data System (ADS)
Ruža, Jānis
2010-01-01
In some circles of quantum physicists, a view is maintained that the nonseparability of quantum systems-i.e., the entanglement-is a characteristic feature of quantum mechanics. According to this view, the entanglement plays a crucial role in the solution of quantum measurement problem, the origin of the “classicality” from the quantum physics, the explanation of the EPR paradox by a nonlocal character of the quantum world. Besides, the entanglement is regarded as a cornerstone of such modern disciplines as quantum computation, quantum cryptography, quantum information, etc. At the same time, entangled states are well known and widely used in various physics areas. In particular, this notion is widely used in nuclear, atomic, molecular, solid state physics, in scattering and decay theories as well as in other disciplines, where one has to deal with many-body quantum systems. One of the methods, how to construct the basis states of a composite many-body quantum system, is the so-called genealogical decomposition method. Genealogical decomposition allows one to construct recurrently by particle number the basis states of a composite quantum system from the basis states of its forming subsystems. These coupled states have a structure typical for entangled states. If a composite system is stable, the internal structure of its forming basis states does not manifest itself in measurements. However, if a composite system is unstable and decays onto its forming subsystems, then the measurables are the quantum numbers, associated with these subsystems. In such a case, the entangled state has a dynamical origin, determined by the Hamiltonian of the corresponding decay process. Possible correlations between the quantum numbers of resulting subsystems are determined by the symmetries-conservation laws of corresponding dynamical variables, and not by the quantum entanglement feature.
Phase space quantum mechanics - Direct
Nasiri, S.; Sobouti, Y.; Taati, F.
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.
Quantum mechanics from classical statistics
Wetterich, C.
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.
Quantum Mechanics in Insulators
NASA Astrophysics Data System (ADS)
Aeppli, G.
2009-08-01
Atomic physics is undergoing a large revival because of the possibility of trapping and cooling ions and atoms both for individual quantum control as well as collective quantum states, such as Bose-Einstein condensates. The present lectures start from the `atomic' physics of isolated atoms in semiconductors and insulators and proceed to coupling them together to yield magnets undergoing quantum phase transitions as well as displaying novel quantum states with no classical analogs. The lectures are based on: G.-Y. Xu et al., Science 317, 1049-1052 (2007); G. Aeppli, P. Warburton, C. Renner, BT Technology Journal, 24, 163-169 (2006); H. M. Ronnow et al., Science 308, 392-395 (2005) and N. Q. Vinh et al., PNAS 105, 10649-10653 (2008).
Quantum Mechanics in Insulators
Aeppli, G.
2009-08-20
Atomic physics is undergoing a large revival because of the possibility of trapping and cooling ions and atoms both for individual quantum control as well as collective quantum states, such as Bose-Einstein condensates. The present lectures start from the 'atomic' physics of isolated atoms in semiconductors and insulators and proceed to coupling them together to yield magnets undergoing quantum phase transitions as well as displaying novel quantum states with no classical analogs. The lectures are based on: G.-Y. Xu et al., Science 317, 1049-1052 (2007); G. Aeppli, P. Warburton, C. Renner, BT Technology Journal, 24, 163-169 (2006); H. M. Ronnow et al., Science 308, 392-395 (2005) and N. Q. Vinh et al., PNAS 105, 10649-10653 (2008).
Quantum mechanics from invariance principles
NASA Astrophysics Data System (ADS)
Moldoveanu, Florin
2015-07-01
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.
Emergent quantum mechanics without wavefunctions
NASA Astrophysics Data System (ADS)
Mesa Pascasio, J.; Fussy, S.; Schwabl, H.; Grössing, G.
2016-03-01
We present our model of an Emergent Quantum Mechanics which can be characterized by “realism without pre-determination”. This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like “surreal” trajectories, which are obtained classically, i.e. without the use of any quantum mechanical tool such as wavefunctions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantum mechanics in a high-low intesity double slit scenario gives rise to the “quantum sweeper effect” with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques.
Quantum Mechanics and Narratability
NASA Astrophysics Data System (ADS)
Myrvold, Wayne C.
2016-05-01
As has been noted by several authors, in a relativistic context, there is an interesting difference between classical and quantum state evolution. For a classical system, a state history of a quantum system given along one foliation uniquely determines, without any consideration of the system's dynamics, a state history along any other foliation. This is not true for quantum state evolution; there are cases in which a state history along one foliation is compatible with multiple distinct state histories along some other, a phenomenon that David Albert has dubbed "non-narratability." In this article, we address the question of whether non-narratability is restricted to the sorts of special states that so far have been used to illustrate it. The results of the investigation suggest that there has been a misplaced emphasis on underdetermination of state histories; though this is generic for the special cases that have up until now been considered, involving bipartite systems in pure entangled states, it fails generically in cases in which more component systems are taken into account, and for bipartite systems that have some entanglement with their environment. For such cases, if we impose relativistic causality constraints on the evolution, then, except for very special states, a state history along one foliation uniquely determines a state history along any other. But this in itself is a marked difference between classical and quantum state evolution, because, in a classical setting, no considerations of dynamics at all are needed to go from a state history along one foliation to a state history along another.
Quantum Mechanics and Narratability
NASA Astrophysics Data System (ADS)
Myrvold, Wayne C.
2016-07-01
As has been noted by several authors, in a relativistic context, there is an interesting difference between classical and quantum state evolution. For a classical system, a state history of a quantum system given along one foliation uniquely determines, without any consideration of the system's dynamics, a state history along any other foliation. This is not true for quantum state evolution; there are cases in which a state history along one foliation is compatible with multiple distinct state histories along some other, a phenomenon that David Albert has dubbed "non-narratability." In this article, we address the question of whether non-narratability is restricted to the sorts of special states that so far have been used to illustrate it. The results of the investigation suggest that there has been a misplaced emphasis on underdetermination of state histories; though this is generic for the special cases that have up until now been considered, involving bipartite systems in pure entangled states, it fails generically in cases in which more component systems are taken into account, and for bipartite systems that have some entanglement with their environment. For such cases, if we impose relativistic causality constraints on the evolution, then, except for very special states, a state history along one foliation uniquely determines a state history along any other. But this in itself is a marked difference between classical and quantum state evolution, because, in a classical setting, no considerations of dynamics at all are needed to go from a state history along one foliation to a state history along another.
Kowalevski top in quantum mechanics
Matsuyama, A.
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.
PT quantum mechanics - Recent results
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2012-09-01
Most quantum physicists believe that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under matrix transposition and complex conjugation) to be sure that the energy eigenvalues are real and that time evolution is unitary. However, the non-Dirac-hermitian Hamiltonian H = p2+ix3 has a real positive discrete spectrum and generates unitary time evolution and defines a fully consistent and physical quantum theory. Evidently, Dirac Hermiticity is too restrictive. While H = p2+ix3 is not Dirac Hermitian, it is PT symmetric (invariant under combined space reflection P and time reversal T). Another PT-symmetric Hamiltonian whose energy levels are real, positive and discrete is H = p2-x4, which contains an upside-down potential. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics and quantum field theory are extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past two years some of these properties have been verified in laboratory experiments. Here, we first discuss PT-symmetric Hamiltonians at a simple intuitive level and explain why the energy levels of such Hamiltonians may be real, positive, and discrete. Second, we describe a recent experiment in which the PT phase transition was observed. Third, we briefly mention that PT-symmetric theories can be useful at a fundamental level. While the double-scaling limit of an O(N)-symmetric gφ4 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.
Energy conservation in quantum mechanics
NASA Astrophysics Data System (ADS)
Prentis, Jeffrey J.; Fedak, William A.
2004-05-01
In the classical mechanics of conservative systems, the position and momentum evolve deterministically such that the sum of the kinetic energy and potential energy remains constant in time. This canonical trademark of energy conservation is absent in the standard presentations of quantum mechanics based on the Schrödinger picture. We present a purely canonical proof of energy conservation that focuses exclusively on the time-dependent position x(t) and momentum p(t) operators. This treatment of energy conservation serves as an introduction to the Heisenberg picture and illuminates the classical-quantum connection. We derive a quantum-mechanical work-energy theorem and show explicitly how the time dependence of x and p and the noncommutivity of x and p conspire to bring about a perfect temporal balance between the evolving kinetic and potential parts of the total energy operator.
Quantum Mechanical Earth: Where Orbitals Become Orbits
ERIC Educational Resources Information Center
Keeports, David
2012-01-01
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
BOOK REVIEW: Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Antoine, J.-P.
2004-01-01
The aim of relativistic quantum mechanics is to describe the finer details of the structure of atoms and molecules, where relativistic effects become nonnegligible. It is a sort of intermediate realm, between the familiar nonrelativistic quantum mechanics and fully relativistic quantum field theory, and thus it lacks the simplicity and elegance of both. Yet it is a necessary tool, mostly for quantum chemists. Pilkuhn's book offers to this audience an up-to-date survey of these methods, which is quite welcome since most previous textbooks are at least ten years old. The point of view of the author is to start immediately in the relativistic domain, following the lead of Maxwell's equations rather than classical mechanics, and thus to treat the nonrelativistic version as an approximation. Thus Chapter 1 takes off from Maxwell's equations (in the noncovariant Coulomb gauge) and gradually derives the basic aspects of Quantum Mechanics in a rather pedestrian way (states and observables, Hilbert space, operators, quantum measurement, scattering,. Chapter 2 starts with the Lorentz transformations, then continues with the Pauli spin equation and the Dirac equation and some of their applications (notably the hydrogen atom). Chapter 3 is entitled `Quantum fields and particles', but falls short of treating quantum field theory properly: only creation/annihilation operators are considered, for a particle in a box. The emphasis is on two-electron states (the Pauli principle, the Foldy--Wouthuysen elimination of small components of Dirac spinors, Breit projection operators. Chapter 4 is devoted to scattering theory and the description of relativistic bound states. Chapter 5, finally, covers hyperfine interactions and radiative corrections. As we said above, relativistic quantum mechanics is by nature limited in scope and rather inelegant and Pilkuhn's book is no exception. The notation is often heavy (mostly noncovariant) and the mathematical level rather low. The central topic
Faster than Hermitian quantum mechanics.
Bender, Carl M; Brody, Dorje C; Jones, Hugh F; Meister, Bernhard K
2007-01-26
Given an initial quantum state |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(F)>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi(I)> to |psi(F)> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing. PMID:17358747
Hermeneutics, Underdetermination and Quantum Mechanics.
ERIC Educational Resources Information Center
Cushing, James T.
1995-01-01
States that the existence of an essential underdetermination in the interpretation of the formalism of quantum mechanics, in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics, legitimizes the analysis of hermeneutics in science education. (LZ)
Renormalization group in quantum mechanics
Polony, J.
1996-12-01
The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright {copyright} 1996 Academic Press, Inc.
Effective equations for the quantum pendulum from momentous quantum mechanics
Hernandez, Hector H.; Chacon-Acosta, Guillermo
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.
Quantum mechanics of black holes.
Witten, Edward
2012-08-01
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely. PMID:22859480
Three-space from quantum mechanics
Chew, G.F.; Stapp, H.P.
1988-08-01
We formulate a discrete quantum-mechanical precursor to spacetime geometry. The objective is to provide the foundation for a quantum mechanics that is rooted exclusively in quantum-mechanical concepts, with all classical features, including the three-dimensional spatial continuum, emerging dynamically.
Geometrical Phases in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
Quantum Mechanics Beyond Hilbert Space
NASA Astrophysics Data System (ADS)
Antoine, J.-P.
Going Beyond Hilbert Space Why? The Different Formalisms What Does One Obtain? The Mathematical Formalism Rigged Hilbert Spaces Scales and Lattices of Hilbert Spaces Partial Inner Product Spaces Operators on PIP-Spaces Application in Quantum Mechanics: The Fock-Bargmann Representation - Revisited A RHS of Entire Functions A LHS of Entire Functions Around ℑ Application in Scattering Theory RHS: Resonances, Gamow Vectors, Arrow of Time LHS: Integral Equations vs. Complex Scaling Conclusion
Hermeneutics, underdetermination and quantum mechanics
NASA Astrophysics Data System (ADS)
Cushing, James T.
1995-04-01
There exists an essential underdetermination in the interpretation of the formalism of quantum mechanics and this extends even to the question of whether or not physical phenomena at the most fundamental level are irreducibly and ineliminably indeterministic or absolutely deterministic. This is true in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics. This lends support to Martin Eger's analysis of a role for hermeneutics in science education.
Quantum mechanics and heat conduction
Bajpai, S.D. ); Mishra, S. )
1991-08-01
One of the fundamental problems in quantum mechanics is to find a solution of Schroedinger equation for different forms of potentials. The object of this paper is to obtain a series solution of a particular one-dimensional, time-dependent Schroedinger equation involving Hermite polynomials. The authors also show a relationship of their particular one-dimensional, time-dependent Schroedinger equation with an equation of heat conduction.
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.
Faster than Hermitian Quantum Mechanics
Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.; Meister, Bernhard K.
2007-01-26
Given an initial quantum state vertical bar {psi}{sub I}> and a final quantum state vertical bar {psi}{sub F}>, there exist Hamiltonians H under which vertical bar {psi}{sub I}> evolves into vertical bar {psi}{sub F}>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time {tau}? For Hermitian Hamiltonians {tau} has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, {tau} can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from vertical bar {psi}{sub I}> to vertical bar {psi}{sub F}> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.
Facets of contextual realism in quantum mechanics
Pan, Alok Kumar; Home, Dipankar
2011-09-23
In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.
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.
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
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
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.
Quantum localization of classical mechanics
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.
2016-07-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
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).
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
Mechanism for quantum speedup in open quantum systems
NASA Astrophysics Data System (ADS)
Liu, Hai-Bin; Yang, W. L.; An, Jun-Hong; Xu, Zhen-Yu
2016-02-01
The quantum speed limit (QSL) time for open system characterizes the most efficient response of the system to the environmental influences. Previous results showed that the non-Markovianity governs the quantum speedup. Via studying the dynamics of a dissipative two-level system, we reveal that the non-Markovian effect is only the dynamical way of the quantum speedup, while the formation of the system-environment bound states is the essential reason for the quantum speedup. Our attribution of the quantum speedup to the energy-spectrum character can supply another vital path for experiments when the quantum speedup shows up without any dynamical calculations. The potential experimental observation of our quantum speedup mechanism in the circuit QED system is discussed. Our results may be of both theoretical and experimental interest in exploring the ultimate QSL in realistic environments, and may open new perspectives for devising active quantum speedup devices.
Quantum squeezing of a mechanical resonator
NASA Astrophysics Data System (ADS)
Lei, Chan U.; Weinstein, Aaron; Suh, Junho; Wollman, Emma; Schwab, Keith
Generating nonclassical states of a macroscopic object has been a subject of considerable interest. It offers a route toward fundamental test of quantum mechanics in an unexplored regime. However, a macroscopic quantum state is very susceptible to decoherence due to the environment. One way to generate robust quantum states is quantum reservoir engineering. In this work, we utilize the reservoir engineering scheme developed by Kronwald et al. to generate a steady quantum squeezed state of a micron-scale mechanical oscillator in an electromechanical system. Together with the backaction evading measurement technique, we demonstrate a quantum nondemolition measurement of the mechanical quadratures to characterize the quantum squeezed state. By measuring the quadrature variances of the mechanical motion, more than 3dB squeezing below the zero-point level has been achieved.
Heisenberg and the Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Camilleri, Kristian
2009-02-01
Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Heisenberg and the Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Camilleri, Kristian
2011-09-01
Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Moin, Syed Tarique; Hofer, Thomas S.; Weiss, Alexander K. H.; Rode, Bernd M.
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.
Speakable and Unspeakable in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Bell, J. S.; Aspect, Introduction by Alain
2004-06-01
List of papers on quantum philosophy by J. S. Bell; Preface; Acknowledgements; Introduction by Alain Aspect; 1. On the problem of hidden variables in quantum mechanics; 2. On the Einstein-Rosen-Podolsky paradox; 3. The moral aspects of quantum mechanics; 4. Introduction to the hidden-variable question; 5. Subject and object; 6. On wave packet reduction in the Coleman-Hepp model; 7. The theory of local beables; 8. Locality in quantum mechanics: reply to critics; 9. How to teach special relativity; 10. Einstein-Podolsky-Rosen experiments; 11. The measurement theory of Everett and de Broglie's pilot wave; 12. Free variables and local causality; 13. Atomic-cascade photons and quantum-mechanical nonlocality; 14. de Broglie-Bohm delayed choice double-slit experiments and density matrix; 15. Quantum mechanics for cosmologists; 16. Bertlmann's socks and the nature of reality; 17. On the impossible pilot wave; 18. Speakable and unspeakable in quantum mechanics; 19. Beables for quantum field theory; 20. Six possible worlds of quantum mechanics; 21. EPR correlations and EPR distributions; 22. Are there quantum jumps?; 23. Against 'measurement'; 24. La Nouvelle cuisine.
NASA Astrophysics Data System (ADS)
Oss, Stefano; Rosi, Tommaso
2015-04-01
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 reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.
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
Quantum mechanics without potential function
Alhaidari, A. D.; Ismail, M. E. H.
2015-07-15
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.
The Measurement Problem in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Ogawa, Shuzo
2001-02-01
Since the establishment of quantum mechanics in the 20s of this century, the controversial discussions 1 have ever continued about its basis, that is the measurement problem of quantum mechanics. Strangely those discussions are prevailed mainly in the circle of theoretical group, while the experimental physicists who are directly concerned with the measurement, indifferently to the discussion have performed their study works, showing firmly the validity of quantum theory. This curious affair seems to be stemmed from the situation that the discussions overlooked by basing on what quantum theoretic ground the experimental equipments are installed, its sure operations are examined and the obtained results are explained, etc. In this talk 2 we shall aim to make clear the relation between the experiment and the structure of quantum mechanics, and to present some epistemological considerations on the quantum mechanics.
Thermodynamic integration from classical to quantum mechanics
Habershon, Scott; Manolopoulos, David E.
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.
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
Quantum Mechanics with a Little Less Mystery
ERIC Educational Resources Information Center
Cropper, William H.
1969-01-01
Suggests the "route of the inquiring mind in presenting the esoteric quantum mechanical postulates and concepts in an understandable form. Explains that the quantum mechanical postulates are but useful mathematical forms to express thebroader principles of superposition and correspondence. Briefly describes some of the features which makes the…
Relativity of representations in quantum mechanics
NASA Astrophysics Data System (ADS)
de la Torre, A. C.
2002-03-01
Only the position representation is used in introductory quantum mechanics and the momentum representation is not usually presented until advanced undergraduate courses. To emphasize the relativity of the representations of the abstract formulation of quantum mechanics, two examples of representations related to the operators αX+(1-α)P and 1/2(XP+PX) are presented.
Quantum mechanics of open systems
NASA Astrophysics Data System (ADS)
Melikidze, Akakii
In quantum mechanics, there is a set of problems where the system of interest interacts with another system, usually called "environment". This interaction leads to the exchange of energy and information and makes the dynamics of the system of interest essentially non-unitary. Such problems often appeared in condensed matter physics and attracted much attention after recent advances in nanotechnology. As broadly posed as they are, these problems require a variety of different approaches. This thesis is an attempt to examine several of these approaches in applications to different condensed matter problems. The first problem concerns the so-called "Master equation" approach which is very popular in quantum optics. I show that analytic properties of environmental correlators lead to strong restrictions on the applicability of the approach to the strong-coupling regime of interest in condensed matter physics. In the second problem, I use path integrals to treat the localization of particles on attractive short-range potentials when the environment produces an effective viscous friction force. I find that friction changes drastically the localization properties and leads to much stronger localization in comparison to the non-dissipative case. This has implications for the motion of heavy particles in fermionic liquids and, as will be argued below, is also relevant to the problem of high-temperature superconductivity. Finally, the third problem deals with the interplay of geometric phases and energy dissipation which occurs in the motion of vortices in superconductors. It is shown that this interplay leads to interesting predictions for vortex tunneling in high-temperature superconductors which have been partially confirmed by experiments.
Polymer quantum mechanics and its continuum limit
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.
2007-08-15
A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.
Improving students' understanding of quantum mechanics
NASA Astrophysics Data System (ADS)
Zhu, Guangtian
2011-12-01
Learning physics is challenging at all levels. Students' difficulties in the introductory level physics courses have been widely studied and many instructional strategies have been developed to help students learn introductory physics. However, research shows that there is a large diversity in students' preparation and skills in the upper-level physics courses and it is necessary to provide scaffolding support to help students learn advanced physics. This thesis explores issues related to students' common difficulties in learning upper-level undergraduate quantum mechanics and how these difficulties can be reduced by research-based learning tutorials and peer instruction tools. We investigated students' difficulties in learning quantum mechanics by administering written tests and surveys to many classes and conducting individual interviews with a subset of students. Based on these investigations, we developed Quantum Interactive Learning Tutorials (QuILTs) and peer instruction tools to help students build a hierarchical knowledge structure of quantum mechanics through a guided approach. Preliminary assessments indicate that students' understanding of quantum mechanics is improved after using the research-based learning tools in the junior-senior level quantum mechanics courses. We also designed a standardized conceptual survey that can help instructors better probe students' understanding of quantum mechanics concepts in one spatial dimension. The validity and reliability of this quantum mechanics survey is discussed.
Realist model approach to quantum mechanics
NASA Astrophysics Data System (ADS)
Hájíček, P.
2013-06-01
The paper proves that quantum mechanics is compatible with the constructive realism of modern philosophy of science. The proof is based on the observation that properties of quantum systems that are uniquely determined by their preparations can be assumed objective without the difficulties that are encountered by the same assumption about values of observables. The resulting realist interpretation of quantum mechanics is made rigorous by studying the space of quantum states—the convex set of state operators. Prepared states are classified according to their statistical structure into indecomposable and decomposable instead of pure and mixed. Simple objective properties are defined and showed to form a Boolean lattice.
Quantum Mechanical Models Of The Fermi Shuttle
Sternberg, James
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.
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
Operational Axioms for Quantum Mechanics
D'Ariano, Giacomo Mauro
2007-02-21
The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of physical experiment and from five simple Postulates concerning experimental accessibility and simplicity. For the infinite dimensional case, on the other hand, a C*-algebra representation of physical transformations is derived, starting from just four of the five Postulates via a Gelfand-Naimark-Segal (GNS) construction. The present paper simplifies and sharpens the previous derivation in Ref. [1]. The main ingredient of the axiomatization is the postulated existence of faithful states that allows one to calibrate the experimental apparatus. Such notion is at the basis of the operational definitions of the scalar product and of the transposed of a physical transformation. What is new in the present paper with respect to Ref. [1], is the operational deduction of an involution corresponding to the complex-conjugation for effects, whose extension to transformations allows to define the adjoint of a transformation when the extension is composition-preserving. The existence of such composition-preserving extension among possible extensions is analyzed.
Voityuk, Alexander A
2008-03-21
The electron hole transfer (HT) properties of DNA are substantially affected by thermal fluctuations of the pi stack structure. Depending on the mutual position of neighboring nucleobases, electronic coupling V may change by several orders of magnitude. In the present paper, we report the results of systematic QM/molecular dynamic (MD) calculations of the electronic couplings and on-site energies for the hole transfer. Based on 15 ns MD trajectories for several DNA oligomers, we calculate the average coupling squares V(2) and the energies of basepair triplets XG(+)Y and XA(+)Y, where X, Y=G, A, T, and C. For each of the 32 systems, 15,000 conformations separated by 1 ps are considered. The three-state generalized Mulliken-Hush method is used to derive electronic couplings for HT between neighboring basepairs. The adiabatic energies and dipole moment matrix elements are computed within the INDO/S method. We compare the rms values of V with the couplings estimated for the idealized B-DNA structure and show that in several important cases the couplings calculated for the idealized B-DNA structure are considerably underestimated. The rms values for intrastrand couplings G-G, A-A, G-A, and A-G are found to be similar, approximately 0.07 eV, while the interstrand couplings are quite different. The energies of hole states G(+) and A(+) in the stack depend on the nature of the neighboring pairs. The XG(+)Y are by 0.5 eV more stable than XA(+)Y. The thermal fluctuations of the DNA structure facilitate the HT process from guanine to adenine. The tabulated couplings and on-site energies can be used as reference parameters in theoretical and computational studies of HT processes in DNA. PMID:18361616
The transactional interpretation of quantum mechanics
NASA Astrophysics Data System (ADS)
Cramer, John G.
1986-07-01
The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet is relativistically invariant and fully causal. A detailed comparison of the transactional and Copenhagen interpretations is made in the context of well-known quantum-mechanical Gedankenexperimente and "paradoxes." The transactional interpretation permits quantum-mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the Copenhagen interpretation. The transactional interpretation is shown to provide insight into the complex character of the quantum-mechanical state vector and the mechanism associated with its "collapse." It also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law (P=ψψ*), basic elements of the Copenhagen interpretation.
Consecutive Measurements in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Glick, Jennifer R.; Adami, Christoph
The physics of quantum measurement still continues to puzzle with no resolution in sight between competing interpretations, in particular because no interpretation has so far produced predictions that would be falsifiable via experiment. Here we present an analysis of consecutive projective measurements performed on a quantum state using quantum information theory, where the entanglement between the quantum system and a measuring device is explicitly taken into account, and where the consecutive measurements increase the joint Hilbert space while the wavefunction of the joint system never collapses. Using this relative-state formalism we rederive well-known results for the pairwise correlation between any two measurement devices, but show that considering the joint as well as conditional entropy of three devices reveals a difference between the collapse and no-collapse pictures of quantum measurement that is experimentally testable. This research was funded by a Michigan State University Enrichment Fellowship.
On the tomographic picture of quantum mechanics
NASA Astrophysics Data System (ADS)
Ibort, A.; Man'ko, V. I.; Marmo, G.; Simoni, A.; Ventriglia, F.
2010-06-01
We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by means of Naimark positive definite functions on the Weyl-Heisenberg group. This connection is used to formulate properties which guarantee that tomographic probabilities describe quantum states in the probability representation of quantum mechanics.
Strange Bedfellows: Quantum Mechanics and Data Mining
Weinstein, Marvin; /SLAC
2009-12-16
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
Strange Bedfellows: Quantum Mechanics and Data Mining
NASA Astrophysics Data System (ADS)
Weinstein, Marvin
2010-02-01
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
Consistency of PT-symmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Brody, Dorje C.
2016-03-01
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully consistent with standard quantum mechanics. This follows from the surprising fact that the much-discussed metric operator on Hilbert space is not physically observable. In particular, for closed quantum systems in finite dimensions there is no statistical test that one can perform on the outcomes of measurements to determine whether the Hamiltonian is Hermitian in the conventional sense, or PT-symmetric—the two theories are indistinguishable. Nontrivial physical effects arising as a consequence of PT symmetry are expected to be observed, nevertheless, for open quantum systems with balanced gain and loss.
Optimization of a relativistic quantum mechanical engine
NASA Astrophysics Data System (ADS)
Peña, Francisco J.; Ferré, Michel; Orellana, P. A.; Rojas, René G.; Vargas, P.
2016-08-01
We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.
Quantum mechanics and the generalized uncertainty principle
Bang, Jang Young; Berger, Micheal S.
2006-12-15
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.
Mechanical equivalent of quantum heat engines.
Arnaud, Jacques; Chusseau, Laurent; Philippe, Fabrice
2008-06-01
Quantum heat engines employ as working agents multilevel systems instead of classical gases. We show that under some conditions quantum heat engines are equivalent to a series of reservoirs at different altitudes containing balls of various weights. A cycle consists of picking up at random a ball from one reservoir and carrying it to the next, thereby performing or absorbing some work. In particular, quantum heat engines, employing two-level atoms as working agents, are modeled by reservoirs containing balls of weight 0 or 1. The mechanical model helps us prove that the maximum efficiency of quantum heat engines is the Carnot efficiency. Heat pumps and negative temperatures are considered. PMID:18643212
A Reconstruction of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Kochen, Simon
2015-05-01
We show that exactly the same intuitively plausible definitions of state, observable, symmetry, dynamics, and compound systems of the classical Boolean structure of intrinsic properties of systems lead, when applied to the structure of extrinsic, relational quantum properties, to the standard quantum formalism, including the Schrödinger equation and the von Neumann-Lüders Projection Rule. This approach is then applied to resolving the paradoxes and difficulties of the orthodox interpretation.
Intrusion Detection with Quantum Mechanics: A Photonic Quantum Fence
Humble, Travis S; Bennink, Ryan S; Grice, Warren P; Owens, Israel J
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.
Interpretation and Predictability of Quantum Mechanics and Quantum Cosmology
NASA Astrophysics Data System (ADS)
Wada, Sumio
A non-probabilistic interpretation of quantum mechanics asserts that we get a prediction only when a wave function has a peak. Taking this interpretation seriously, we discuss how to find a peak in the wave function of the universe, by using some minisuperspace models with homogeneous degrees of freedom and also a model with cosmological perturbations. Then we show how to recover our classical picture of the universe from the quantum theory, and comment on the physical meaning of the backreaction equation.
Fundamental Quantum Mechanics--A Graphic Presentation
ERIC Educational Resources Information Center
Wise, M. N.; Kelley, T. G.
1977-01-01
Describes a presentation of basic quantum mechanics for nonscience majors that relies on a computer-generated graphic display to circumvent the usual mathematical difficulties. It allows a detailed treatment of free-particle motion in a wave picture. (MLH)
How Rutherford missed discovering quantum mechanical identity
NASA Astrophysics Data System (ADS)
Temmer, G. M.
1989-03-01
An interesting quirk in the energy dependence of alpha-particle scattering from helium caused Lord Rutherford to miss a major discovery—namely, the consequences of quantum mechanical identity—before their prediction by Mott a short time later.
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.
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)
Quantum mechanical stabilization of Minkowski signature wormholes
Visser, M.
1989-05-19
When one attempts to construct classical wormholes in Minkowski signature Lorentzian spacetimes violations of both the weak energy hypothesis and averaged weak energy hypothesis are encountered. Since the weak energy hypothesis is experimentally known to be violated quantum mechanically, this suggests that a quantum mechanical analysis of Minkowski signature wormholes is in order. In this note I perform a minisuperspace analysis of a simple class of Minkowski signature wormholes. By solving the Wheeler-de Witt equation for pure Einstein gravity on this minisuperspace the quantum mechanical wave function of the wormhole is obtained in closed form. The wormhole is shown to be quantum mechanically stabilized with an average radius of order the Planck length. 8 refs.
Uncertainty in quantum mechanics: faith or fantasy?
Penrose, Roger
2011-12-13
The word 'uncertainty', in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very 'truth' into question. This article addresses the issue of quantum 'uncertainty' from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications. PMID:22042902
On the geometrization of quantum mechanics
NASA Astrophysics Data System (ADS)
Tavernelli, Ivano
2016-08-01
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave-particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie-Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space-time, as it is the case for gravitation in the general relativity.
Experimental status of quaternionic quantum mechanics
NASA Astrophysics Data System (ADS)
Brumby, S. P.; Joshi, G. C.
1996-05-01
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.
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.
Relativistic Quantum Mechanics and Field Theory
NASA Astrophysics Data System (ADS)
Gross, Franz
1999-04-01
An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field. Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay. Subsequent chapters prepare readers for advanced work, covering such major topics as gauge theories, path integral techniques, spontaneous symmetry breaking, and an introduction to QCD, chiral symmetry, and the Standard Model. A special chapter is devoted to relativistic bound state wave equations-an important topic that is often overlooked in other books. Clear and concise throughout, Relativistic Quantum Mechanics and Field Theory boasts examples from atomic and nuclear physics as well as particle physics, and includes appendices with background material. It is an essential reference for anyone working in quantum mechanics today.
Conformal quantum mechanics and holographic quench
NASA Astrophysics Data System (ADS)
Järvelä, Jarkko; Keränen, Ville; Keski-Vakkuri, Esko
2016-02-01
Recently, there has been much interest in holographic computations of two-point nonequilibrium Green functions from anti-de Sitter- (AdS-)Vaidya backgrounds. In the strongly coupled quantum field theory on the boundary, the dual interpretation of the background is an equilibration process called a holographic quench. The two-dimensional AdS-Vaidya spacetime is a special case, dual to conformal quantum mechanics. We study how the quench is incorporated into a Hamiltonian H +θ (t )Δ H and into correlation functions. With the help of recent work on correlation functions in conformal quantum mechanics, we first rederive the known two-point functions, and then compute nonequilibrium three- and four-point functions. We also compute the three-point function Witten diagram in the two-dimensional AdS-Vaidya background, and find agreement with the conformal quantum mechanics result.
Quantum Probability Theory and the Foundations of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Fröhlich, Jürg; Schubnel, Baptiste
By and large, people are better at coining expressions than at filling them with interesting, concrete contents. Thus, it may not be very surprising that there are many professional probabilists who may have heard the expression but do not appear to be aware of the need to develop "quantum probability theory" into a thriving, rich, useful field featured at meetings and conferences on probability theory. Although our aim, in this essay, is not to contribute new results on quantum probability theory, we hope to be able to let the reader feel the enormous potential and richness of this field. What we intend to do, in the following, is to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras).
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…
Optimal guidance law in quantum mechanics
Yang, Ciann-Dong Cheng, Lieh-Lieh
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 Ψ(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for Ψ(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 Ψ{sup ∗}Ψ. -- 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.
Computations in quantum mechanics made easy
NASA Astrophysics Data System (ADS)
Korsch, H. J.; Rapedius, K.
2016-09-01
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.
Hot Fluids and Nonlinear Quantum Mechanics
NASA Astrophysics Data System (ADS)
Mahajan, Swadesh M.; Asenjo, Felipe A.
2015-05-01
A hot relativistic fluid is viewed as a collection of quantum objects that represent interacting elementary particles. We present a conceptual framework for deriving nonlinear equations of motion obeyed by these hypothesized objects. A uniform phenomenological prescription, to affect the quantum transition from a corresponding classical system, is invoked to derive the nonlinear Schrödinger, Klein-Gordon, and Pauli-Schrödinger and Feynman-GellMaan equations. It is expected that the emergent hypothetical nonlinear quantum mechanics would advance, in a fundamental way, both the conceptual understanding and computational abilities, particularly, in the field of extremely high energy-density physics.
Quantum Mechanics, Spacetime Locality, and Gravity
NASA Astrophysics Data System (ADS)
Nomura, Yasunori
2013-08-01
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only one of the many, bringing an apparent arbitrariness in defining probabilities, called the measure problem. In this paper, we discuss how these two problems are related with each other, developing a picture for quantum measurement and cosmological histories in the quantum mechanical universe. In order to describe the cosmological dynamics correctly within the full quantum mechanical context, we need to identify the structure of the Hilbert space for a system with gravity. We argue that in order to keep spacetime locality, the Hilbert space for dynamical spacetime must be defined only in restricted spacetime regions: in and on the (stretched) apparent horizon as viewed from a fixed reference frame. This requirement arises from eliminating all the redundancies and overcountings in a general relativistic, global spacetime description of nature. It is responsible for horizon complementarity as well as the "observer dependence" of horizons/spacetime—these phenomena arise to represent changes of the reference frame in the relevant Hilbert space. This can be viewed as an extension of the Poincaré transformation in the quantum gravitational context. Given an initial condition, the evolution of the multiverse state obeys the laws of quantum mechanics—it evolves deterministically and unitarily. The beginning of the multiverse, however, is still an open issue.
Interpretation and predictability of quantum mechanics and quantum cosmology
Wada, S.
1988-06-01
A non-probabilistic interpretation of quantum mechanics asserts that the authors get a prediction only when a wave function has a peak. Taking this interpretation seriously, the authors discuss how to find a peak in the wave function of the universe, by using some minisuperspace models. With homogeneous degrees of freedom and also a model with cosmological perturbations. Then the authors show how to recover their classical picture of the universe from the quantum theory, and comment on the physical meaning of the backreaction equation.
Superstrings and the Foundations of Quantum Mechanics
NASA Astrophysics Data System (ADS)
't Hooft, Gerard
2014-05-01
It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell's powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.
Multichannel framework for singular quantum mechanics
Camblong, Horacio E.; Epele, Luis N.; Fanchiotti, Huner; García Canal, Carlos A.; Ordóñez, Carlos R.
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.
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.
Statistical mechanics based on fractional classical and quantum mechanics
Korichi, Z.; Meftah, M. T.
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.
An Axiomatic Basis for Quantum Mechanics
NASA Astrophysics Data System (ADS)
Cassinelli, Gianni; Lahti, Pekka
2016-06-01
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Solér which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of Solér's theorem to the theory of symmetry in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions.
Two basic Uncertainty Relations in Quantum Mechanics
Angelow, Andrey
2011-04-07
In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schroedinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.
Two basic Uncertainty Relations in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Angelow, Andrey
2011-04-01
In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schrödinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.
Remarks on Dersarkissian's cosmic quantum mechanics
NASA Astrophysics Data System (ADS)
Massa, C.
1985-12-01
Dersarkissian (1984) has proposed a cosmic quantum mechanics (CQM) characterized by the constant hg approximately equal to 10 to the 75th ergs approximately equal to 10 to the 102nd h, where h is Planck's constant of ordinary quantum mechanics; galaxies are the elementary particles of CQM. Uncertainty arguments in CQM give a number of constraints on the masses of galaxies and thus a concrete way to test CQM. A condition that has to be satisfied for a massive body to be subject to CQM is proposed.
A proof of von Neumann's postulate in Quantum Mechanics
Conte, Elio
2010-05-04
A Clifford algebraic analysis is explained. It gives proof of von Neumann's postulate on quantum measurement. It is of basic significance to explain the problem of quantum wave function reduction in quantum mechanics.
Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
NASA Astrophysics Data System (ADS)
Grössing, Gerhard
2015-10-01
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...
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.
Suardíaz, Reynier; Jambrina, Pablo G; Masgrau, Laura; González-Lafont, Àngels; Rosta, Edina; Lluch, José M
2016-04-12
Lipoxygenases (LOXs) are a family of enzymes involved in the biosynthesis of several lipid mediators. In the case of human 15-LOX, the 15-LOX-1 and 15-LOX-2 isoforms show slightly different reaction regiospecificity and substrate specificity, indicating that substrate binding and recognition may be different, a fact that could be related to their different biological role. Here, we have used long molecular dynamics simulations, QM(DFT)/MM potential energy and free energy calculations (using the newly developed DHAM method), to investigate the binding mode of the arachidonic acid (AA) substrate into 15-LOX-2 and the rate-limiting hydrogen-abstraction reaction 15-LOX-2 catalyzes. Our results strongly indicate that hydrogen abstraction from C13 in 15-LOX-2 is only consistent with the "tail-first" orientation of AA, with its carboxylate group interacting with Arg429, and that only the pro-S H13 hydrogen will be abstracted (being the pro-R H13 and H10 too far from the acceptor oxygen atom). At the B3LYP/6-31G(d) level the potential and free energy barriers for the pro-S H13 abstraction of AA by 15-LOX-2 are 18.0 and 18.6 kcal/mol, respectively. To analyze the kinetics of the hydrogen abstraction process, we determined a Markov model corresponding to the unbiased simulations along the state-discretized reaction coordinate. The calculated rates based on the second largest eigenvalue of the Markov matrices agree well with experimental measurements, and also provide the means to directly determine the pre-exponential factor for the reaction by comparing with the free energy barrier height. Our calculated pre-exponential factor is close to the value of kBT/h. On the other hand, our results suggest that the spin inversion of the complete system (including the O2 molecule) that is required to happen at some point along the full process to lead to the final hydroperoxide product, is likely to take place during the hydrogen transfer, which is a proton coupled electron transfer. Overall, a different binding mode from the one accepted for 15-LOX-1 is proposed, which provides a molecular basis for 15-LOX-2 exclusive 15-HPETE production in front of the double (although highly 15-) 12/15 regiospecificity of 15-LOX-1. Understanding how these different isoenzymes achieve their regiospecificity is expected to help in specific inhibitor design. PMID:26918937
Consistent interpretations of quantum mechanics
NASA Astrophysics Data System (ADS)
Omnès, Roland
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 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)
Subjective and objective probabilities in quantum mechanics
Srednicki, Mark
2005-05-15
We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, and Schack, but our approach and emphasis are different. We also discuss the problem of choosing a noninformative prior for a density matrix.
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...
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.
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 in classical and in quantum mechanics
NASA Astrophysics Data System (ADS)
Elçi, A.
2010-07-01
This paper presents an analysis of the time concept in classical mechanics from the perspective of the invariants of a motion. The analysis shows that there is a conceptual gap concerning time in the Dirac-Heisenberg-von Neumann formalism and that Bohr's complementarity principle does not fill the gap. In the Dirac-Heisenberg-von Neumann formalism, a particle's properties are represented by Heisenberg matrices. This axiom is the source of the time problem in quantum mechanics.
Quantum mechanical studies of carbon structures
Bartelt, Norman Charles; Ward, Donald; Zhou, Xiaowang; Foster, Michael E.; Schultz, Peter A.; Wang, Bryan M.; McCarty, Kevin F.
2015-10-01
Carbon nanostructures, such as nanotubes and graphene, are of considerable interest due to their unique mechanical and electrical properties. The materials exhibit extremely high strength and conductivity when defects created during synthesis are minimized. Atomistic modeling is one technique for high resolution studies of defect formation and mitigation. To enable simulations of the mechanical behavior and growth mechanisms of C nanostructures, a high-fidelity analytical bond-order potential for the C is needed. To generate inputs for developing such a potential, we performed quantum mechanical calculations of various C structures.
A Primer on Resonances in Quantum Mechanics
Rosas-Ortiz, Oscar; Fernandez-Garcia, Nicolas; Cruz y Cruz, Sara
2008-11-13
After a pedagogical introduction to the concept of resonance in classical and quantum mechanics, some interesting applications are discussed. The subject includes resonances occurring as one of the effects of radiative reaction, the resonances involved in the refraction of electromagnetic waves by a medium with a complex refractive index, and quantum decaying systems described in terms of resonant states of the energy (Gamow-Siegert functions). Some useful mathematical approaches like the Fourier transform, the complex scaling method and the Darboux transformation are also reviewed.
Quantum mechanics of 4-derivative theories
NASA Astrophysics Data System (ADS)
Salvio, Alberto; Strumia, Alessandro
2016-04-01
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.
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.
The emergent Copenhagen interpretation of quantum mechanics
NASA Astrophysics Data System (ADS)
Hollowood, Timothy J.
2014-05-01
We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR-Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.
Emergence of quantum mechanics from a sub-quantum statistical mechanics
NASA Astrophysics Data System (ADS)
Grössing, Gerhard
2014-07-01
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wavefunctions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" non-locality.
``the Human BRAIN & Fractal quantum mechanics''
NASA Astrophysics Data System (ADS)
Rosary-Oyong, Se, Glory
In mtDNA ever retrieved from Iman Tuassoly, et.al:Multifractal analysis of chaos game representation images of mtDNA''.Enhances the price & valuetales of HE. Prof. Dr-Ing. B.J. HABIBIE's N-219, in J. Bacteriology, Nov 1973 sought:'' 219 exist as separate plasmidDNA species in E.coli & Salmonella panama'' related to ``the brain 2 distinct molecular forms of the (Na,K)-ATPase..'' & ``neuron maintains different concentration of ions(charged atoms'' thorough Rabi & Heisenber Hamiltonian. Further, after ``fractal space time are geometric analogue of relativistic quantum mechanics''[Ord], sought L.Marek Crnjac: ``Chaotic fractals at the root of relativistic quantum physics''& from famous Nottale: ``Scale relativity & fractal space-time:''Application to Quantum Physics , Cosmology & Chaotic systems'',1995. Acknowledgements to HE. Mr. H. TUK SETYOHADI, Jl. Sriwijaya Raya 3, South-Jakarta, INDONESIA.
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 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.
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.
Logical reformulation of quantum mechanics. I. Foundations
Omnes, R.
1988-11-01
The basic rules of quantum mechanics are reformulated. They deal primarily with individual systems and do not assume that every ket may represent a physical state. The customary kinematic and dynamic rules then allow to construct consistent Boolean logics describing the history of a system, following essentially Griffiths' proposal. Logical implication is defined within these logics, the multiplicity of which reflects the complementary principle. Only one interpretive rule of quantum mechanics is necessary in such a framework. It states that these logics provide bona fide foundations for the description of a quantum system and for reasoning about it. One attempts to build up classical physics, including classical logic, on these quantum foundations. The resulting theory of measurement needs not to state a priori that the eigenvalues of an observable have to be the results of individual measurements nor to assume wave packet reduction. Both these properties can be obtained as consequences of the basic rules. One also needs not to postulate that every observable is measurable, even in principle. A proposition calculus is obtained, allowing in principle the replacement of the discussion of problems concerned with the practical interpretation of experiments by due calculations.
Hidden variables and nonlocality in quantum mechanics
NASA Astrophysics Data System (ADS)
Hemmick, Douglas Lloyd
1997-05-01
Most physicists hold a skeptical attitude toward a 'hidden variables' interpretation of quantum theory, despite David Bohm's successful construction of such a theory and John S. Bell's strong arguments in favor of the idea. The first reason for doubt concerns certain mathematical theorems (von Neumann's, Gleason's, Kochen and Specker's, and Bell's) which can be applied to the hidden variables issue. These theorems are often credited with proving that hidden variables are indeed 'impossible', in the sense that they cannot replicate the predictions of quantum mechanics. Many who do not draw such a strong conclusion nevertheless accept that hidden variables have been shown to exhibit prohibitively complicated features. The second concern is that the most sophisticated example of a hidden variables theory-that of David Bohm-exhibits non-locality, i.e., consequences of events at one place can propagate to other places instantaneously. However, neither the mathematical theorems in question nor the attribute of nonlocality detract from the importance of a hidden variables interpretation of quantum theory. Nonlocality is present in quantum mechanics itself, and is a required characteristic of any theory that agrees with the quantum mechanical predictions. We first discuss the earliest analysis of hidden variables-that of von Neumann's theorem-and review John S. Bell's refutation of von Neumann's 'impossibility proof'. We recall and elaborate on Bell's arguments regarding the theorems of Gleason, and Kochen and Specker. According to Bell, these latter theorems do not imply that hidden variables interpretations are untenable, but instead that such theories must exhibit contextuality, i.e., they must allow for the dependence of measurement results on the characteristics of both measured system and measuring apparatus. We demonstrate a new way to understand the implications of both Gleason's theorem and Kochen and Specker's theorem by noting that they prove a result we call
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
Beyond relativity and quantum mechanics: space physics
NASA Astrophysics Data System (ADS)
Lindner, Henry H.
2011-09-01
Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.
Quantum mechanics without the projection postulate
NASA Astrophysics Data System (ADS)
Bub, Jeffrey
1992-05-01
I show that the quantum state ω can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with ω and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of “determinate” quantities (selected by ω and the boundary conditions) can have values. The probabilities defined by ω (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate.
The interpretation of quantum mechanics through1935
NASA Astrophysics Data System (ADS)
Cushing, J. T.
2000-11-01
I first define what I mean by the term interpretation, then trace some of the major developments in attempts to fashion an interpretation of quantum mechanics from its early mathematical formulation (ca. 1925) up through the Einstein-Podolsky-Rosen paper, Bohr's response to it, and Schrödinger's insights on entanglement, in 1935. In the process, I question some of the conventional wisdom about how a unified interpretation emerged.
Diffeomorphism groups and nonlinear quantum mechanics
NASA Astrophysics Data System (ADS)
Goldin, Gerald A.
2012-02-01
This talk is dedicated to my friend and collaborator, Prof. Dr. Heinz-Dietrich Doebner, on the occasion of his 80th birthday. I shall review some highlights of the approach we have taken in deriving and interpreting an interesting class of nonlinear time-evolution equations for quantum-mechanical wave functions, with few equations; more detail may be found in the references. Then I shall comment on the corresponding hydrodynamical description.
Covariant quantum mechanics applied to noncommutative geometry
NASA Astrophysics Data System (ADS)
Astuti, Valerio
2015-08-01
We here report a result obtained in collaboration with Giovanni Amelino-Camelia, first shown in the paper [1]. Applying the manifestly covariant formalism of quantum mechanics to the much studied Snyder spacetime [2] we show how it is trivial in every physical observables, this meaning that every measure in this spacetime gives the same results that would be obtained in the flat Minkowski spacetime.
Collocation method for fractional quantum mechanics
Amore, Paolo; Hofmann, Christoph P.; Saenz, Ricardo A.; Fernandez, Francisco M.
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.
A Local Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Lopez, Carlos
2016-04-01
A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the "virtual" paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born's rule; therefore, Bell's type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference (wave like behaviour) instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system.
Hunting for Snarks in Quantum Mechanics
Hestenes, David
2009-12-08
A long-standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger's wave function {psi} for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school(led by Bohr, Heisenberg and Pauli) holds that {psi} provides a complete description of a single electron state; hence the probability interpretation of {psi}{psi}* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school(led by Einstein, de Broglie, Bohm and Jaynes) holds that {psi} represents a statistical ensemble of possible electron states; hence it is an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung(first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in {psi}. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark{exclamation_point}.
A quantum-mechanical relaxation model
NASA Astrophysics Data System (ADS)
Skomski, R.; Kashyap, A.; Sellmyer, D. J.
2012-04-01
The atomic origin of micromagnetic damping is investigated by developing and solving a quantum-mechanical relaxation model. A projection-operator technique is used to derive an analytical expression for the relaxation time as a function of the heat-bath and interaction parameters. The present findings are consistent with earlier research beyond the Landau-Lifshitz-Gilbert (LLG) equation and show that the underlying relaxation mechanism is very general. Zermelo's recurrence paradox means that there is no true irreversibility in non-interacting nanoparticles, but the corresponding recurrence times are very long and can be ignored in many cases.
The cognitive life of mechanical molecular models.
Charbonneau, Mathieu
2013-12-01
The use of physical models of molecular structures as research tools has been central to the development of biochemistry and molecular biology. Intriguingly, it has received little attention from scholars of science. In this paper, I argue that these physical models are not mere three-dimensional representations but that they are in fact very special research tools: they are cognitive augmentations. Despite the fact that they are external props, these models serve as cognitive tools that augment and extend the modeler's cognitive capacities and performance in molecular modeling tasks. This cognitive enhancement is obtained because of the way the modeler interacts with these models, the models' materiality contributing to the solving of the molecule's structure. Furthermore, I argue that these material models and their component parts were designed, built and used specifically to serve as cognitive facilitators and cognitive augmentations. PMID:23910718
Quantum mechanics with coordinate dependent noncommutativity
Kupriyanov, V. G.
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.
Bohmian Mechanics In A Macroscopic Quantum System
NASA Astrophysics Data System (ADS)
Haven, Emmanuel
2006-01-01
In the so called `causal' interpretation of quantum mechanics, an electron is considered as a particle and such particle is influenced not only by a classical but also by a so called quantum potential. This idea was developed by Professor Bohm in an important paper. In this paper we use some of the basics of this interpretation in a financial option pricing environment. The causal interpretation allows for trajectories. Path breaking work by Professors Bohm and Hiley and Khrennikov and Choustova have made that the causal interpretation is a step closer to potential applications in social science. In this paper we consider the wave function as a wave of information. We consider the gradient of the phase of this wave function and show how the option price could be influenced by this gradient.
Indirect Acquisition of Information in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Ballesteros, M.; Fraas, M.; Fröhlich, J.; Schubnel, B.
2016-02-01
Long sequences of successive direct (projective) measurements or observations of just a few "uninteresting" physical quantities pertaining to a quantum system, such as clicks of some detectors, may reveal indirect, but precise and unambiguous information on the values of some very "interesting" observables of the system. In this paper, the mathematics underlying this claim is developed; i.e., we attempt to contribute to a mathematical theory of indirect and, in particular, non-demolition observations and measurements in quantum mechanics. Our attempt leads us to make some novel uses of classical notions and results of probability theory, such as the "algebra of functions measurable at infinity", the Central Limit Theorem, results concerning relative entropy and its role in the theory of large deviations, etc.
Unstable trajectories and the quantum mechanical uncertainty
NASA Astrophysics Data System (ADS)
Moser, Hans R.
2008-08-01
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.
Reciprocal relativity of noninertial frames: quantum mechanics
NASA Astrophysics Data System (ADS)
Low, Stephen G.
2007-04-01
Noninertial transformations on time-position-momentum-energy space {t, q, p, e} with invariant Born-Green metric ds^{2}=-d t^{2}+\\frac{1}{c^{2}}\\,d q^{2}+\\frac{1}{b^{2}} \\big(d p^{2}-\\frac{1}{c^{2}}\\,d e^{2}\\big) and the symplectic metric -de ∧ dt + dp ∧ dq are studied. This {\\cal U}1,3) group of transformations contains the Lorentz group as the inertial special case and, in the limit of small forces and velocities, reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds2 = -dt2. The {\\cal U}( 1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. In the limit of b → ∞, spacetime is invariant. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary representations of its central extension. The same method of projective representations for the inhomogeneous {\\cal U}( 1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous {\\cal U}( 1,3) group is the cover of the quaplectic group {\\cal Q}( 1,3) ={\\cal U}( 1,3) \\otimes _{s}{\\cal H}(4) . {\\cal H}( 4) is the Weyl-Heisenberg group. The {\\cal H}( 4) group, and the associated Heisenberg commutation relations central to quantum mechanics, results directly from requiring projective representations. A set of second-order wave equations result from the representations of the Casimir operators.
Quantum time and spatial localization in relativistic quantum mechanics
NASA Astrophysics Data System (ADS)
von Zuben, Francis Stephen Geisler
1999-11-01
Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles, and the dependence of their localization on the motion of the observer, are analyzed in the context of the theory of constraints. Time and energy operators are introduced for the free relativistic particle, and a parametrization invariant formulation is obtained through Dirac constraint theory. The resulting description is of a system constrained in momentum and energy, but not in position or time, for which observables are constants of the motion. The Klein-Gordon equation is recovered on a physical Hilbert space, constructed via integration over the proper time from an augmented Hilbert space, wherein time and energy are dynamical variables. It is shown that the position observable acts on states in the augmented space; those states having strictly positive energy are non-local in time. Localization arises on a particular space-like hyperplane from quantum interference in time, position measurements receiving contributions from the past and future. Apparent causality problems are resolved by noting that, as the particle is potentially in the past, it can propagate to distant regions without exceeding the speed of light. Non-locality of the same system to a moving observer is due to Lorentz rotation of spatial axes out of the interference minimum.
Murphy, Robert B.; Philipp, Dean M.; Friesner, Richard A.
2000-07-13
A QM/MM method, using our previously developed frozen orbital QM/MM interface methodology, is presented as a general, accurate, and computationally efficient model for studying chemical problems in a protein environment. The method, its parameterization, and a preliminary application to modeling cytochrome P-450 chemistry are presented.
The metaphysics of quantum mechanics: Modal interpretations
NASA Astrophysics Data System (ADS)
Gluck, Stuart Murray
2004-11-01
This dissertation begins with the argument that a preferred way of doing metaphysics is through philosophy of physics. An understanding of quantum physics is vital to answering questions such as: What counts as an individual object in physical ontology? Is the universe fundamentally indeterministic? Are indiscernibles identical? This study explores how the various modal interpretations of quantum mechanics answer these sorts of questions; modal accounts are one of the two classes of interpretations along with so-called collapse accounts. This study suggests a new alternative within the class of modal views that yields a more plausible ontology, one in which the Principle of the Identity of Indisceribles is necessarily true. Next, it shows that modal interpretations can consistently deny that the universe must be fundamentally indeterministic so long as they accept certain other metaphysical commitments: either a perfect initial distribution of states in the universe or some form of primitive dispositional properties. Finally, the study sketches out a future research project for modal interpretations based on developing quantified quantum logic.
Supersymmetric quantum mechanics and its applications
Sukumar, C.V.
2004-12-23
The Hamiltonian in Supersymmetric Quantum Mechanics is defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of the component parts that constitute the supersymmetric system are explored. The implications of supersymmetry for the solutions of the Schroedinger equation, the Dirac equation, the inverse scattering theory and the multi-soliton solutions of the KdV equation are examined. Applications to scattering problems in Nuclear Physics with specific reference to singular potentials which arise from considerations of supersymmetry will be discussed.
Landau problem in noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
Sayipjamal, Dulat; Li, Kang
2008-02-01
The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schrödinger equations on noncommutative (NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity. Then we discuss the noncommutative phase space case, namely, space-space and momentum-momentum non-commutative case, and we get the explicit expression of the Hamiltonian as well as the corresponding eigenfunctions and eigenvalues. Supported by National Natural Science Foundation of China (10465004, 10665001, 10575026) and Abdus Salam ICTP, Trieste, Italy
Differentiability of correlations in realistic quantum mechanics
Cabrera, Alejandro; Faria, Edson de; Pujals, Enrique; Tresser, Charles
2015-09-15
We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumed to be twice differentiable at the origin, then we arrive at a version of Bell’s theorem. On the one hand, we are showing that any realistic theory of quantum mechanics which incorporates the kinematic aspects of relativity must lead to this type of rough correlation function that is once but not twice differentiable. On the other hand, this study brings us a single degree of differentiability away from a relativistic von Neumann no hidden variables theorem.
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.
Differentiability of correlations in realistic quantum mechanics
NASA Astrophysics Data System (ADS)
Cabrera, Alejandro; de Faria, Edson; Pujals, Enrique; Tresser, Charles
2015-09-01
We prove a version of Bell's theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumed to be twice differentiable at the origin, then we arrive at a version of Bell's theorem. On the one hand, we are showing that any realistic theory of quantum mechanics which incorporates the kinematic aspects of relativity must lead to this type of rough correlation function that is once but not twice differentiable. On the other hand, this study brings us a single degree of differentiability away from a relativistic von Neumann no hidden variables theorem.
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
NASA Astrophysics Data System (ADS)
Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk
2015-03-01
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.
Supersymmetric quantum mechanics and the Korteweg--de Vries hierarchy
Grant, A.K.; Rosner, J.L. )
1994-05-01
The connection between supersymmetric quantum mechanics and the Korteweg--de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the [tau] function by means of supersymmetric quantum mechanics is discussed.
Student Understanding of Time Dependence in Quantum Mechanics
ERIC Educational Resources Information Center
Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.
2015-01-01
The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…
NASA Astrophysics Data System (ADS)
Mugur-Schächter, Mioara
1993-01-01
In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (“states” of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a “general syntax of relativized conceptualization” where any description is explicitly and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualization. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides toward answers. Globally the results obtained provide a basis for future attempts at a general mathematical representation of the processes of conceptualization. “Il pourrait, en effet, être dangereux pour l'avenir de la Physique qu'elle se contente trop facilement de purs formalismes, d'images floues et d'explications toutes verbales s'exprimant par des mots à signification imprécise”—Louis de Broglie, Certitudes et Incertitudes de la Science (Albin Michel, Paris, 1965).
NASA Astrophysics Data System (ADS)
Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; Takeuchi, Tatsu
2013-12-01
We propose mutant versions of quantum mechanics constructed on vector spaces over the finite Galois fields GF(3) and GF(9). The mutation we consider here is distinct from what we proposed in previous papers on Galois field quantum mechanics. In this new mutation, the canonical expression for expectation values is retained instead of that for probabilities. In fact, probabilities are indeterminate. Furthermore, it is shown that the mutant quantum mechanics over the finite field GF(9) exhibits super-quantum correlations (i.e. the Bell-Clauser-Horne-Shimony-Holt bound is 4). We comment on the fundamental physical importance of these results in the context of quantum gravity.
Three Attempts at Two Axioms for Quantum Mechanics
NASA Astrophysics Data System (ADS)
Rohrlich, Daniel
The axioms of nonrelativistic quantum mechanics lack clear physical meaning. In particular, they say nothing about nonlocality. Yet quantum mechanics is not only nonlocal, it is twice nonlocal: there are nonlocal quantum correlations, and there is the Aharonov-Bohm effect, which implies that an electric or magnetic field here may act on an electron there. Can we invert the logical hierarchy? That is, can we adopt nonlocality as an axiom for quantum mechanics and derive quantum mechanics from this axiom and an additional axiom of causality? Three versions of these two axioms lead to three different theories, characterized by "maximal nonlocal correlations", "jamming" and "modular energy". Where is quantum mechanics in these theories?
Symmetry as a foundational concept in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Ziaeepour, Houri
2015-07-01
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.
Paul A.M. Dirac's The Principles of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Brown, Laurie M.
2006-12-01
Paul A.M. Dirac’s book, The Principles of Quantum Mechanics, summarized the foundations of a new science, much of which was his own creation. It expressed the spirit of the new quantum mechanics, creating a descriptive language that we still use. I discuss the successive editions of Dirac’s book and their critical reception, noting changes, especially in the formulation of the general theory and in its treatment of relativistic quantum theory and quantum electrodynamics. In the case of the later editions, I discuss Dirac’s negative attitude toward renormalized quantum electrodynamics.
Dynamical phase transitions in quantum mechanics
NASA Astrophysics Data System (ADS)
Rotter, Ingrid
2012-02-01
The nucleus is described as an open many-body quantum system with a non-Hermitian Hamilton operator the eigenvalues of which are complex, in general. The eigenvalues may cross in the complex plane (exceptional points), the phases of the eigenfunctions are not rigid in approaching the crossing points and the widths bifurcate. By varying only one parameter, the eigenvalue trajectories usually avoid crossing and width bifurcation occurs at the critical value of avoided crossing. An analog spectroscopic redistribution takes place for discrete states below the particle decay threshold. By this means, a dynamical phase transition occurs in the many-level system starting at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model) and those of highly excited nuclear states (described by random ensembles) differ fundamentally from one another. The statement of Niels Bohr on the collective features of compound nucleus states at high level density is therefore not in contradiction to the shell-model description of nuclear (and atomic) states at low level density. Dynamical phase transitions are observed experimentally in different quantum mechanical systems by varying one or two parameters.
Causal localizations in relativistic quantum mechanics
Castrigiano, Domenico P. L. Leiseifer, Andreas D.
2015-07-15
Causal localizations describe the position of quantum systems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a mere consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac’s localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantum mechanics attributing an important role to the negative energy states.
Supersymmetric Quantum Mechanics For Atomic Electronic Systems
NASA Astrophysics Data System (ADS)
Markovich, Thomas; Biamonte, Mason; Kouri, Don
2012-02-01
We employ our new approach to non-relativistic supersymmetric quantum mechanics (SUSY-QM), (J. Phys. Chem. A 114, 8202(2010)) for any number of dimensions and distinguishable particles, to treat the hydrogen atom in full three-dimensional detail. In contrast to the standard one-dimensional radial equation SUSY-QM treatment of the hydrogen atom, where the superpotential is a scalar, in a full three-dimensional treatment, it is a vector which is independent of the angular momentum quantum number. The original scalar Schr"odinger Hamiltonian operator is factored into vector ``charge'' operators: Q and Q^. Using these operators, the first sector Hamiltonian is written as H1= Q^.Q + E0^1. The second sector Hamiltonian is a tensor given by H2= Q Q^ + E0^11 and is isospectral with H1. The second sector ground state, ψ0^(2), can be used to obtain the excited state wave functions of the first sector by application of the adjoint charge operator. We then adapt the aufbau principle to show this approach can be applied to treat the helium atom.
Harmonizing General Relativity with Quantum Mechanics
NASA Astrophysics Data System (ADS)
Alfonso-Faus, Antonio
2007-04-01
Gravitation is the common underlying texture between General Relativity and Quantum Mechanics. We take gravitation as the link that can make possible the marriage between these two sciences. We use here the duality of Nature for gravitation: A continuous warped space, wave-like, and a discrete quantum gas, particle-like, both coexistent and producing an equilibrium state in the Universe. The result is a static, non expanding, spherical, unlimited and finite Universe, with no cosmological constant and no dark energy. Macht's Principle is reproduced here by the convergence of the two cosmological equations of Einstein. From this a Mass Boom concept is born given by M = t, M the mass of the Universe and t its age. Also a decreasing speed of light is the consequence of the Mass Boom, c = 1/t, which explains the Supernovae Type Ia observations without the need of expansion (nor, of course, accelerated expansion). Our Mass Boom model completely wipes out the problems and paradoxes built in the Big Bang model, like the horizon, monopole, entropy, flatness, fine tuning, etc. It also eliminates the need for inflation.
Extending quantum mechanics entails extending special relativity
NASA Astrophysics Data System (ADS)
Aravinda, S.; Srikanth, R.
2016-05-01
The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an ontological extension for quantum mechanics (QMs) through the oblivious embedding of a sound simulation protocol in a Newtonian spacetime. Minkowski or other intermediate spacetimes are ruled out as the locus of the embedding by virtue of hidden influence inequalities. The complementarity transferred from a simulation to the extension unifies a number of results about quantum non-locality, and implies that special relativity has a different significance for the ontological model and for the operational theory it reproduces. Only the latter, being experimentally accessible, is required to be Lorentz covariant. There may be certain Lorentz non-covariant elements at the ontological level, but they will be inaccessible at the operational level in a valid extension. 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 at the ontological level has Minkowski causal structure.