Real time quantum dynamics in systems with many degrees of freedom ACS PRF Grant # 42187-AC6 PI: Eli Pollak, Chemical Physics Dept. Weizmann Institute.

Slides:

Advertisements

Similar presentations

Notes 6.6 Fundamental Theorem of Algebra

Advertisements

EXAMPLE 1 Find the number of solutions or zeros

1. 2 SUPERSYMMETRY Most popular solution to the hierarchy problem. Symmetry between fermions, and bosons With same mass and quantum number 3.

Network biology Wang Jie Shanghai Institutes of Biological Sciences.

Functions AII.7 e Objectives: Find the Vertical Asymptotes Find the Horizontal Asymptotes.

National Institute of Science & Technology TECHNICAL SEMINAR-2004 Dipanwita Dash [1] UNIT COMMITMENT Under the guidance of Mr. Debasisha Jena Presented.

Quantum Chemistry Revisited Powerpoint Templates.

Tunneling in Complex Systems: From Semiclassical Methods to Monte Carlo simulations Joachim Ankerhold Theoretical condensed matter physics University of.

Modeling, Simulation, and Control of a Real System Robert Throne Electrical and Computer Engineering Rose-Hulman Institute of Technology.

1 The Potts model Mike Sinclair. 2 Overview Potts model –Extension of Ising model –Uses interacting spins on a lattice –N-dimensional (spin states > 2)

A Bloch Band Base Level Set Method in the Semi-classical Limit of the Schrödinger Equation Hailiang Liu 1 and Zhongming Wang 2 Abstract It is now known.

EXAMPLE 2 Find the zeros of a polynomial function

EXAMPLE 2 Find all zeros of f (x) = x 5 – 4x 4 + 4x x 2 – 13x – 14. SOLUTION STEP 1 Find the rational zeros of f. Because f is a polynomial function.

The Quadratic Formula..

EXAMPLE 2 Find all real zeros of f (x) = x 3 – 8x 2 +11x SOLUTION List the possible rational zeros. The leading coefficient is 1 and the constant.

Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Complex Numbers Standard form of a complex number is: a + bi. Every complex polynomial function.

Objectives Fundamental Theorem of Algebra 6-6

6. Second Quantization and Quantum Field Theory

Algebra I Chapter 10 Review

Notes Over 6.7 Finding the Number of Solutions or Zeros

Complex Zeros; Fundamental Theorem of Algebra

5.6 Quadratic Equations and Complex Numbers

Solving Quadratic Equations

Chemical Reaction on the Born-Oppenheimer surface and beyond ISSP Osamu Sugino FADFT WORKSHOP 26 th July.

3.8 Warm Up Write the function in vertex form (by completing the square) and identify the vertex. a. y = x² + 14x + 11 b. y = 2x² + 4x – 5 c. y = x² -

5.8 Quadratic Formula. For quadratic equations written in standard form, the roots can be found using the following formula: This is called the Quadratic.

2.7 Apply the Fundamental Theorem of Algebra Polynomials Quiz: Tomorrow (over factoring and Long/Synthetic Division) Polynomials Test: Friday.

Lesson 8-4: Solutions of Quadratics Objectives Students will: Determine the nature of solutions of a quadratic equation Find and use sums and products.

Solving Quadratic Equations using the Quadratic Formula

1.Is it More, Less, or Exactly Half? 2. Is it More, Less, or Exactly Half?

Solving Polynomial Functions involving Complex Numbers.

Given a quadratic equation use the discriminant to determine the nature of the roots.

By the end of this section, you will be able to: 1. Determine the number and type of roots for a polynomial equation; 2. Find the zeros of a polynomial.

5.6 The Fundamental Theorem of Algebra. If P(x) is a polynomial of degree n where n > 1, then P(x) = 0 has exactly n roots, including multiple and complex.

PROPERTIES OF REAL NUMBERS. COMMUTATIVE PROPERTY OF ADDITION What it means We can add numbers in any order Numeric Example Algebraic Example

Atomic Orbitals And Quantum Numbers. Quantum Numbers A series of 4 numbers (and/or letters) that specify the properties of an electron in its orbit The.

The Fundamental Theorem of Algebra Intro - Chapter 4.6.

Stochastic Description of Quantum Dissipative Dynamics Jiushu Shao Beijing Normal University 11 August 2010 Physics and Chemistry in Quantum Dissipative.

The Ideal Diatomic and Polyatomic Gases. Canonical partition function for ideal diatomic gas Consider a system of N non-interacting identical molecules:

Every polynomial P(x) of degree n>0 has at least one zero in the complex number system. N Zeros Theorem Every polynomial P(x) of degree n>0 can be expressed.

Conjugate Pairs Theorem Every complex polynomial function of degree n  1 has exactly n complex zeros, some of which may repeat. 1) A polynomial function.

Quantum Mechanical Model. Quantum Numbers (n, l, m l, m s ) n = ____________ Quantum Number It has whole number values (1, 2, 3, …) An n increases, the.

EXAMPLE Ordering Real Numbers Order the numbers 0.47, 0.474, 0.47, and 0.23 from least to greatest. SOLUTION STEP 1 Write each decimal out to six.

Lesson 6.5: The Quadratic Formula and the Discriminant, pg. 313 Goals: To solve quadratic equations by using the Quadratic Formula. To use the discriminant.

SOLVE QUADRATIC EQUATIONS BY USING THE QUADRATIC FORMULA. USE THE DISCRIMINANT TO DETERMINE THE NUMBER AND TYPE OF ROOTS OF A QUADRATIC EQUATION. 5.6 The.

2.2 Solving Quadratic Equations Algebraically Quadratic Equation: Equation written in the form ax 2 + bx + c = 0 ( where a ≠ 0). Zero Product Property:

Dot Product and Angle Between Two Vectors

Solving Equations by Factoring

Promotion of Tunneling via Dissipative Molecular Bridges

Roots and Zeros 5.7.

Notes Over 3.4 The Rational Zero Test

Algebra II Explorations Review ( )

2.1 Complex Numbers.

Find all solutions of the polynomial equation by factoring and using the quadratic formula. x = 0 {image}

Factor Theorems.

أنماط الإدارة المدرسية وتفويض السلطة الدكتور أشرف الصايغ

Apply the Fundamental Theorem of Algebra

Bound Systems and Spectra

Invention List & Survey Brainstorm Page 4

Day 2 Write in Vertex form Completing the Square Imaginary Numbers Complex Roots.

Standard Form Quadratic Equation

Fundamental Theorem of Algebra

Nanoscale structure in colloid-polymer solutions

Warm Up #4 1. Write 15x2 + 6x = 14x2 – 12 in standard form. ANSWER

5-7A Classifying Zero’s Algebra II.

A feasible solution for problem 2.

Jaynes-Cummings Hamiltonian

Presentation transcript:

Real time quantum dynamics in systems with many degrees of freedom ACS PRF Grant # 42187-AC6 PI: Eli Pollak, Chemical Physics Dept. Weizmann Institute of Science New semiclassical initial value methods were invented for solution of electronic transitions in complex media. First examples with up to 100 degrees of freedom are for the spin boson problem: thermal bath f2 f2 D e f1 f1 thermal bath Time dependent population in an asymmetric spin boson problem. semiclassical zero-th order and 1-st Order solution gives exact answer. Solution feasible due to new f formulation developed under this grant. Numerically exact results taken from H. Wang, JCP 113, 9948 (2000).