Motion of a biharmonic system under action of small periodic force and small damped force is studied. The biharmonic oscillator is a physical system acting under a biharmonic force like a sin θ b sin 2θ. The article contains biharmonic oscillator analysis, phase space research, and analytic solutions for separatrixes. The biharmonic oscillator performs chaotic motion near separatrixes under sma...

The evaluation of the specific heat of an open damped quantum system is a subtle issue. One possible route is based on the thermodynamic partition function which is the ratio of the partition functions of system plus bath and of the bath alone. For the free damped particle it has been shown, however, that the ensuing specific heat may become negative for appropriately chosen environments. Being...

In this paper, vibrations and bifurcation of a damped system consists of a mass grounded by linear and nonlinear springs and a nonlinear damper is studied. Nonlinear equation of motion is derived using Newton’s equations. Approximate analytical solutions are obtained using multiple time scales (MTS) method. For free vibration, the approximate analytical results are compared with the numerical i...

The stability properties of a class of dissipative quantum mechanical systems are investigated. The nonlinear stability and asymptotic stability of stationary states (with zero and nonzero dissipation respectively) is investigated by Liapunov’s direct method. The results are demonstrated by numerical calculations on the example of the damped harmonic oscillator.

In this paper, a new approach for constructing Lagrangians driven and undriven linearly damped systems is proposed, by introducing redefined time coordinate an associated transformation to ensure that the resulting Lagrangian satisfies Helmholtz conditions. The applied canonically quantize harmonic oscillator although it predicts energy spectrum decays at same rate previous models, unlike those...

The definition of the specific heat for a damped quantum system is a subtle issue. A possible approach is based on an effective partition function defined as the ratio of the partition functions of system plus bath and of the bath alone. For the free damped particle it has been shown, however, that the ensuing specific heat may become negative for appropriately chosen environments. We argue tha...

6 Von Neumann Entropy 16 6.1 A Warmup Exercise: Damped Harmonic Oscillator . . . . . . 16 6.2 Double Well Coupled to a Dissipative Heat Bath . . . . . . . 17 6.3 Disordered Systems . . . . . . . . . . . . . . . . . . . . . . . . 19 6.3.1 Anderson Localization . . . . . . . . . . . . . . . . . . 20 6.3.2 Integer Quantum Hall Plateau Transitions . . . . . . . 21 6.3.3 Infinite Randomness Fixed Po...

Quantum dynamics of a general dissipative system investigated by its coupling to a Klein-Gordon type field as the environment by introducing a minimal coupling method. As an example, the quantum dynamics of a damped three dimensional harmonic oscillator investigated and some transition probabilities indicating the way energy flows between the subsystems obtained. The quantum dynamics of a dissi...

We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose solutions exactly coincide with solutions of the corresponding differential equation evaluated at a discrete sequence of points (a lattice). Such exact discret...