Quantum Monte Carlo

	Quantum Monte Carlo Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution (or an accurate approximation) of the quantum many-body problem. The diverse flavors of quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi-dimensional integrals that arise in the different formulations of the many-body problem. Quantum Monte Carlo methods allow for a direct treatment and description of complex many-body effects encoded in the wave function, going beyond mean-field theory. In particular, there exist numerically exact and polynomially-scaling algorithms to exactly study static properties of boson systems without geometrical frustration. For fermions, there exist very good approximations to their static properties and numerically exact exponentially scaling quantum Monte Carlo algorithms, but none that are b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Quantum System Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Biological System A biological system is a complex Biological network inference, network which connects several biologically relevant entities. Biological organization spans several scales and are determined based different structures depending on what the system is. Examples of biological systems at the macro scale are populations of organisms. On the organ (anatomy), organ and Tissue (biology), tissue scale in mammals and other animals, examples include the circulatory system, the respiratory system, and the nervous system. On the Micrometre, micro to the Nanometre, nanoscopic scale, examples of biological systems are cell (biology), cells, organelles, macromolecular complexes and Regulatory T cell, regulatory pathways. A biological system is not to be confused with a Living systems, living system, such as a living organism. Organ and tissue systems These specific systems are widely studied in human anatomy and are also present in many other animals. * Respiratory system: the organs used for b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Diffusion Monte Carlo Diffusion Monte Carlo (DMC) or diffusion quantum Monte Carlo is a quantum Monte Carlo method that uses a Green's function to calculate low-lying energies of a quantum many-body Hamiltonian. Introduction and motivation of the algorithm Diffusion Monte Carlo has the potential to be numerically exact, meaning that it can find the exact ground state energy for any quantum system within a given error, but approximations must often be made and their impact must be assessed in particular cases. When actually attempting the calculation, one finds that for bosons, the algorithm scales as a polynomial with the system size, but for fermions, DMC scales exponentially with the system size. This makes exact large-scale DMC simulations for fermions impossible; however, DMC employing a clever approximation known as the fixed-node approximation can still yield very accurate results. To motivate the algorithm, let's look at the Schrödinger equation for a particle in some potential in one dimensi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Variational Monte Carlo In computational physics, variational Monte Carlo (VMC) is a quantum Monte Carlo method that applies the Variational method (quantum mechanics), variational method to approximate the ground state of a quantum system. The basic building block is a generic wave function , \Psi(a) \rangle depending on some parameters a . The optimal values of the parameters a is then found upon minimizing the total energy of the system. In particular, given the Hamiltonian (quantum mechanics), Hamiltonian \mathcal , and denoting with X a Many-body problem, many-body configuration, the expectation value of the energy can be written as: E(a) = \frac = \frac . Following the Monte Carlo method for evaluating integrals, we can interpret \frac as a probability distribution function, sample it, and evaluate the energy expectation value E(a) as the average of the so-called local energy E_(X) = \frac . Once E(a) is known for a given set of variational parameters a , then optimization is pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]