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hamiltonian
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in Simulating Transmembrane Proteins with the Coarse-Grained SIRAH Force Field: Tips and Tricks for Setting Up and Running in AMBER
> A Practical Guide to Recent Advances in Multiscale Modeling and Simulation of Biomolecules
Published: January 2023
FIG. 3.1 Top: two-body Hamiltonian used by most MD simulation packages and SIRAH to calculate the potential energy. Bottom: superposition of atomistic and CG representations for SIRAH residues relevant to this chapter. Only one residue among some groups of molecules sharing similar mapping is show... More about this image found in Top: two-body Hamiltonian used by most MD simulation packages and SIRAH to ...
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Published: December 2022
FIG. 3.33 (a) Three-dimensional energy spectrum of the Hamiltonian H [Eq. ( 3.172 )]. (b) Fermi energy contours for the Hamiltonian H . (c) Energy spectrum for a free electron. (d) Energy spectrum for an electron in the presence of a magnetic field (Zeeman splitting). (e) Energy... More about this image found in (a) Three-dimensional energy spectrum of the Hamiltonian H [Eq. (...
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Published: November 2022
FIG. 4.1 Structure of Hamiltonian for laser–atom interaction for fixed magnetic quantum number ml, ordered with increasing l = 0, 1, …, 5. Each of the different l blocks may have different size denoted by Ns(l) ≡ Nl. Generally, the matrix is either symmetric (length gauge) or Hermitian (velocity gauge) because D l l ′ = D l ′ l † . More about this image found in Structure of Hamiltonian for laser–atom interaction for fixed magnetic quan...
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Published: November 2022
FIG. 7.4 Diagonal matrix elements for the various terms of the Hamiltonian (black dots) along its diagonal. Red dots represent S i i ′ , green dots represent ⟨ 1 / r i i ⟩ , and blue dots represent ⟨ 1 / r 2 i i ⟩ , all for i = 1(1)100. The numerical parameters are as in Fig. 7.3 . More about this image found in Diagonal matrix elements for the various terms of the Hamiltonian (black do...
Book Chapter
Series: AIPP Books, Methods
Published: March 2023
EISBN: 978-0-7354-2574-3
ISBN: 978-0-7354-2572-9
.... , “ Modeling and prediction of the transmission dynamics of COVID-19 based on the SINDy-LM method ,” Nonlinear Dyn. 105 ( 3 ), 2775 – 2794 ( 2021 ). 10.1007/s11071-021-06707-6 Koopman , B. O. , “ Hamiltonian systems and transformation in Hilbert space ,” Proc. Natl. Acad. Sci. U.S.A. 17 ( 5...
Book Chapter
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425590_001
EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
... ; Nagy, 1998 ; and Martin, 2020 ). In this approach, the many-body interaction problem is reduced to an effective single-electron problem where every individual non-interacting electron experiences the same charge density map of the crystal. In KS-DFT, we first describe a Hamiltonian that consists...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_004
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... these energies are converted into each other. Hamilton has taken this perspective a step further to include systems in which the total energy is not constant. Hamilton incorporated the positions and momenta of all the particles in a system of particles into one function, the Hamiltonian function—or short...
Book Chapter
Series: AIPP Books, Principles
Published: March 2023
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EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
... of ferroelectric phase transitions in perovskite oxides: Energy functional and effective Hamiltonian ,” Phys. Rev. B 95 , 054111 ( 2017 ). 10.1103/PhysRevB.95.054111 Perdew , J. P. , Burke , K. , and Ernzerhof , M. , “ Generalized gradient approximation made simple ,” Phys. Rev. Lett. 77...
Book Chapter
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425590_002
EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
... of materials. Among these, modeling of materials at the atomistic length scale pertains to methods in which the electrons are treated as the starting entities. Interactions among the electrons, written as a Hamiltonian or the total energy operator, are used to describe the system. Methods that rely on solving...
Book Chapter
Series: AIPP Books, Methods
Published: March 2023
10.1063/9780735425743_010
EISBN: 978-0-7354-2574-3
ISBN: 978-0-7354-2572-9
... – 2794 ( 2021 ). 10.1007/s11071-021-06707-6 Koopman , B. O. , “ Hamiltonian systems and transformation in Hilbert space ,” Proc. Natl. Acad. Sci. U.S.A. 17 ( 5 ), 315 – 318 ( 1931 ). 10.1073/pnas.17.5.315 McAuley , K. , Macdonald , D. , and McLellan , P. , “ Effects...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425712_019
EISBN: 978-0-7354-2571-2
ISBN: 978-0-7354-2568-2
... functions, probability, wave-particle duality, uncertainty principle, infinite square well, one-dimensional tunneling, energy levels Intro college, University, Graduate level MCT R38 Quantum Mechanics Survey (QMS) Wave functions, measurement, expectation values, Hamiltonian, time dependence...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_008
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... and its dependence on time, also in relation to the commutator with the Hamiltonian, and the meanings of eigenvectors and eigenvalues. It happens that the ontological meanings of the entities change depending on the phenomenon under consideration. In the diagnostic questionnaires, attention is drawn...
Book
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425590
EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
Book
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
Book
Series: AIPP Books, Methods
Published: March 2023
10.1063/9780735425743
EISBN: 978-0-7354-2574-3
ISBN: 978-0-7354-2572-9
Book
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425712
EISBN: 978-0-7354-2571-2
ISBN: 978-0-7354-2568-2
Book Chapter
Series: AIPP Books, Perspectives
Published: December 2022
10.1063/9780735422537_frontmatter
EISBN: 978-0-7354-2253-7
ISBN: 978-0-7354-2251-3
.... It studies the Quantum Hall Effect (integer and fractional) and superconductivity from phenomenological and microscopic perspectives. Magnetism and magnetic phenomena in solids via approximate solutions of the Hamiltonian model are also addressed. The book also discusses the topological aspects of materials...
Book Chapter
Series: AIPP Books, Perspectives
Published: December 2022
10.1063/9780735422537_index
EISBN: 978-0-7354-2253-7
ISBN: 978-0-7354-2251-3
.... It studies the Quantum Hall Effect (integer and fractional) and superconductivity from phenomenological and microscopic perspectives. Magnetism and magnetic phenomena in solids via approximate solutions of the Hamiltonian model are also addressed. The book also discusses the topological aspects of materials...
Book Chapter
Series: AIPP Books, Perspectives
Published: December 2022
10.1063/9780735422537_003
EISBN: 978-0-7354-2253-7
ISBN: 978-0-7354-2251-3
.... The objective is to determine whether such a continuous deformation can lead to a change from one geometric shape to another. The connection to the problem of deformation of geometrical shapes in condensed matter physics may be established if the Hamiltonian for a particular system can be continuously...
Book Chapter
Series: AIPP Books, Methods
Published: January 2023
10.1063/9780735425279_003
EISBN: 978-0-7354-2527-9
ISBN: 978-0-7354-2524-8
... illustrates how to perform MD simulations of membrane proteins using the SIRAH force field for CG and multiscale simulations using the AMBER package ( https://ambermd.org ). SIRAH (Southamerican Initiative for a Rapid and Accurate Hamiltonian, https://www.sirahff.com ) constitutes one of the most complete CG...
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