Wave Functions

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Brian J Smith - One of the best experts on this subject based on the ideXlab platform.

  • photon Wave Functions Wave packet quantization of light and coherence theory
    New Journal of Physics, 2007
    Co-Authors: Brian J Smith, M G Raymer
    Abstract:

    The monochromatic Dirac and polychromatic Titulaer?Glauber quantized field theories (QFTs) of electromagnetism are derived from a photon-energy Wave function in much the same way that one derives QFT for electrons, i.e., by quantization of a single-particle Wave function. The photon Wave function and its equation of motion are established from the Einstein energy?momentum?mass relation, assuming a local energy density. This yields a theory of photon Wave mechanics (PWM). The proper Lorentz-invariant single-photon scalar product is found to be non-local in coordinate space, and is shown to correspond to orthogonalization of the Titulaer?Glauber Wave-packet modes. The Wave Functions of PWM and mode Functions of QFT are shown to be equivalent, evolving via identical equations of motion, and completely describe photonic states. We generalize PWM to two or more photons, and show how to switch between the PWM and QFT viewpoints. The second-order coherence tensors of classical coherence theory and the two-photon Wave Functions are shown to propagate equivalently. We give examples of beam-like states, which can be used as photon Wave Functions in PWM, or modes in QFT. We propose a practical mode converter based on spectral filtering to convert between Wave packets and their corresponding biorthogonal dual Wave packets.

  • photon Wave Functions Wave packet quantization of light and coherence theory
    arXiv: Quantum Physics, 2007
    Co-Authors: Brian J Smith, M G Raymer
    Abstract:

    The monochromatic Dirac and polychromatic Titulaer-Glauber quantized field theories (QFTs) of electromagnetism are derived from a photon-energy Wave function in much the same way that one derives QFT for electrons, that is, by quantization of a single-particle Wave function. The photon Wave function and its equation of motion are established from the Einstein energy-momentum-mass relation, assuming a local energy density. This yields a theory of photon Wave mechanics (PWM). The proper Lorentz-invariant single-photon scalar product is found to be non-local in coordinate space, and is shown to correspond to orthogonalization of the Titulaer-Glauber Wave-packet modes. The Wave Functions of PWM and mode Functions of QFT are shown to be equivalent, evolving via identical equations of motion, and completely describe photonic states. We generalize PWM to two or more photons, and show how to switch between the PWM and QFT viewpoints. The second-order coherence tensors of classical coherence theory and the two-photon Wave Functions are shown to propagate equivalently. We give examples of beam-like states, which can be used as photon Wave Functions in PWM, or modes in QFT. We propose a practical mode converter based on spectral filtering to convert between Wave packets and their corresponding biorthogonal dual Wave packets.

Lucas K Wagner - One of the best experts on this subject based on the ideXlab platform.

  • non orthogonal determinants in multi slater jastrow trial Wave Functions for fixed node diffusion monte carlo
    Journal of Chemical Physics, 2018
    Co-Authors: Shivesh Pathak, Lucas K Wagner
    Abstract:

    The accuracy and efficiency of ab initio Quantum Monte Carlo (QMC) algorithms benefit greatly from compact variational trial Wave Functions that accurately reproduce ground state properties of a system. We investigate the possibility of using multi-Slater-Jastrow trial Wave Functions with non-orthogonal determinants by optimizing identical single particle orbitals independently in separate determinants. As a test case, we compute variational and fixed-node diffusion Monte Carlo (FN-DMC) energies of a C2 molecule. For a given multi-determinant expansion, we find that this non-orthogonal orbital optimization results in a consistent improvement in the variational energy and the FN-DMC energy on the order of a few tenths of an eV. In some cases, fewer non-orthogonal determinants are required compared to orthogonal ones in order to achieve similar accuracy in FN-DMC. Our calculations indicate that trial Wave Functions with non-orthogonal determinants can improve computed energies in a QMC calculation when compared to their orthogonal counterparts.

  • non orthogonal determinants in multi slater jastrow trial Wave Functions for fixed node diffusion monte carlo
    arXiv: Materials Science, 2018
    Co-Authors: Shivesh Pathak, Lucas K Wagner
    Abstract:

    The accuracy and efficiency of ab-initio quantum Monte Carlo (QMC) algorithms benefits greatly from compact variational trial Wave Functions that accurately reproduce ground state properties of a system. We investigate the possibility of using multi-Slater-Jastrow trial Wave Functions with non-orthogonal determinants by optimizing identical single particle orbitals independently in separate determinants. As a test case, we compute variational and fixed-node diffusion Monte Carlo (FN-DMC) energies of a C$_2$ molecule. For a given multi-determinant expansion, we find that this non-orthogonal orbital optimization results in a consistent improvement in the variational energy and the FN-DMC energy on the order of a few tenths of an eV. Our calculations indicate that trial Wave Functions with non-orthogonal determinants can improve computed energies in a QMC calculation when compared to their orthogonal counterparts.

C J Umrigar - One of the best experts on this subject based on the ideXlab platform.

  • approximating strongly correlated Wave Functions with correlator product states
    Physical Review B, 2009
    Co-Authors: Hitesh J Changlani, Jesse M Kinder, C J Umrigar, Garnet Kinlic Chan
    Abstract:

    We describe correlator product states, a class of numerically efficient many-body Wave Functions to describe strongly correlated Wave Functions in any dimension. Correlator product states introduce direct correlations between physical degrees of freedom in a simple way, yet provide the flexibility to describe a wide variety of systems. We show that many interesting Wave Functions can be mapped exactly onto correlator product states, including Laughlin’s quantum Hall Wave function, Kitaev’s toric code states, and Huse and Elser’s frustrated spin states. We also outline the relationship between correlator product states and other common families of variational Wave Functions such as matrix product states, tensor product states, and resonating valence-bond states. Variational calculations for the Heisenberg and spinless Hubbard models demonstrate the promise of correlator product states for describing both two-dimensional and fermion correlations. Even in one-dimensional systems, correlator product states are competitive with matrix product states for a fixed number of variational parameters.

  • optimization of quantum monte carlo Wave Functions by energy minimization
    Journal of Chemical Physics, 2007
    Co-Authors: Julien Toulouse, C J Umrigar
    Abstract:

    We study three Wave function optimization methods based on energy minimization in a variational Monte Carlo framework: the Newton, linear, and perturbative methods. In the Newton method, the parameter variations are calculated from the energy gradient and Hessian, using a reduced variance statistical estimator for the latter. In the linear method, the parameter variations are found by diagonalizing a nonsymmetric estimator of the Hamiltonian matrix in the space spanned by the Wave function and its derivatives with respect to the parameters, making use of a strong zero-variance principle. In the less computationally expensive perturbative method, the parameter variations are calculated by approximately solving the generalized eigenvalue equation of the linear method by a nonorthogonal perturbation theory. These general methods are illustrated here by the optimization of Wave Functions consisting of a Jastrow factor multiplied by an expansion in configuration state Functions (CSFs) for the C2 molecule, including both valence and core electrons in the calculation. The Newton and linear methods are very efficient for the optimization of the Jastrow, CSF, and orbital parameters. The perturbative method is a good alternative for the optimization of just the CSF and orbital parameters. Although the optimization is performed at the variational Monte Carlo level, we observe for the C2 molecule studied here, and for other systems we have studied, that as more parameters in the trial Wave Functions are optimized, the diffusion Monte Carlo total energy improves monotonically, implying that the nodal hypersurface also improves monotonically.

  • multiconfiguration Wave Functions for quantum monte carlo calculations of first row diatomic molecules
    Journal of Chemical Physics, 1996
    Co-Authors: Claudia Filippi, C J Umrigar
    Abstract:

    We use the variance minimization method to determine accurate Wave Functions for first‐row homonuclear diatomic molecules. The form of the Wave function is a product of a sum of determinants and a generalized Jastrow factor. One of the important features of the calculation is that we are including low‐lying determinants corresponding to single and double excitations from the Hartree–Fock configuration within the space of orbitals whose atomic principal quantum numbers do not exceed those occurring in the Hartree–Fock configuration. The idea is that near‐degeneracy correlation is most effectively described by a linear combination of low‐lying determinants whereas dynamic correlation is well described by the generalized Jastrow factor. All the parameters occurring in both the determinantal and the Jastrow parts of the Wave function are optimized. The optimized Wave Functions recover 79%–94% of the correlation energy in variational Monte Carlo and 93%–99% of the correlation energy in diffusion Monte Carlo.

M G Raymer - One of the best experts on this subject based on the ideXlab platform.

  • photon Wave Functions Wave packet quantization of light and coherence theory
    New Journal of Physics, 2007
    Co-Authors: Brian J Smith, M G Raymer
    Abstract:

    The monochromatic Dirac and polychromatic Titulaer?Glauber quantized field theories (QFTs) of electromagnetism are derived from a photon-energy Wave function in much the same way that one derives QFT for electrons, i.e., by quantization of a single-particle Wave function. The photon Wave function and its equation of motion are established from the Einstein energy?momentum?mass relation, assuming a local energy density. This yields a theory of photon Wave mechanics (PWM). The proper Lorentz-invariant single-photon scalar product is found to be non-local in coordinate space, and is shown to correspond to orthogonalization of the Titulaer?Glauber Wave-packet modes. The Wave Functions of PWM and mode Functions of QFT are shown to be equivalent, evolving via identical equations of motion, and completely describe photonic states. We generalize PWM to two or more photons, and show how to switch between the PWM and QFT viewpoints. The second-order coherence tensors of classical coherence theory and the two-photon Wave Functions are shown to propagate equivalently. We give examples of beam-like states, which can be used as photon Wave Functions in PWM, or modes in QFT. We propose a practical mode converter based on spectral filtering to convert between Wave packets and their corresponding biorthogonal dual Wave packets.

  • photon Wave Functions Wave packet quantization of light and coherence theory
    arXiv: Quantum Physics, 2007
    Co-Authors: Brian J Smith, M G Raymer
    Abstract:

    The monochromatic Dirac and polychromatic Titulaer-Glauber quantized field theories (QFTs) of electromagnetism are derived from a photon-energy Wave function in much the same way that one derives QFT for electrons, that is, by quantization of a single-particle Wave function. The photon Wave function and its equation of motion are established from the Einstein energy-momentum-mass relation, assuming a local energy density. This yields a theory of photon Wave mechanics (PWM). The proper Lorentz-invariant single-photon scalar product is found to be non-local in coordinate space, and is shown to correspond to orthogonalization of the Titulaer-Glauber Wave-packet modes. The Wave Functions of PWM and mode Functions of QFT are shown to be equivalent, evolving via identical equations of motion, and completely describe photonic states. We generalize PWM to two or more photons, and show how to switch between the PWM and QFT viewpoints. The second-order coherence tensors of classical coherence theory and the two-photon Wave Functions are shown to propagate equivalently. We give examples of beam-like states, which can be used as photon Wave Functions in PWM, or modes in QFT. We propose a practical mode converter based on spectral filtering to convert between Wave packets and their corresponding biorthogonal dual Wave packets.

Shivesh Pathak - One of the best experts on this subject based on the ideXlab platform.

  • non orthogonal determinants in multi slater jastrow trial Wave Functions for fixed node diffusion monte carlo
    Journal of Chemical Physics, 2018
    Co-Authors: Shivesh Pathak, Lucas K Wagner
    Abstract:

    The accuracy and efficiency of ab initio Quantum Monte Carlo (QMC) algorithms benefit greatly from compact variational trial Wave Functions that accurately reproduce ground state properties of a system. We investigate the possibility of using multi-Slater-Jastrow trial Wave Functions with non-orthogonal determinants by optimizing identical single particle orbitals independently in separate determinants. As a test case, we compute variational and fixed-node diffusion Monte Carlo (FN-DMC) energies of a C2 molecule. For a given multi-determinant expansion, we find that this non-orthogonal orbital optimization results in a consistent improvement in the variational energy and the FN-DMC energy on the order of a few tenths of an eV. In some cases, fewer non-orthogonal determinants are required compared to orthogonal ones in order to achieve similar accuracy in FN-DMC. Our calculations indicate that trial Wave Functions with non-orthogonal determinants can improve computed energies in a QMC calculation when compared to their orthogonal counterparts.

  • non orthogonal determinants in multi slater jastrow trial Wave Functions for fixed node diffusion monte carlo
    arXiv: Materials Science, 2018
    Co-Authors: Shivesh Pathak, Lucas K Wagner
    Abstract:

    The accuracy and efficiency of ab-initio quantum Monte Carlo (QMC) algorithms benefits greatly from compact variational trial Wave Functions that accurately reproduce ground state properties of a system. We investigate the possibility of using multi-Slater-Jastrow trial Wave Functions with non-orthogonal determinants by optimizing identical single particle orbitals independently in separate determinants. As a test case, we compute variational and fixed-node diffusion Monte Carlo (FN-DMC) energies of a C$_2$ molecule. For a given multi-determinant expansion, we find that this non-orthogonal orbital optimization results in a consistent improvement in the variational energy and the FN-DMC energy on the order of a few tenths of an eV. Our calculations indicate that trial Wave Functions with non-orthogonal determinants can improve computed energies in a QMC calculation when compared to their orthogonal counterparts.