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The analytical continuation of classical equations of motion to complex times suggests that a tunnelling particle spends in the barrier an imaginary duration $i|\mathcal T|$. Does this mean that it takes a finite time to tunnel, or should…
Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to…
The problem of relativity of motion in quantum vacuum is addressed by considering a cavity moving in vacuum in a monodimensional space. The cavity is an open system which emits photons when it oscillates in vacuum. Qualitatively new effects…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
First laws of black hole mechanics, or thermodynamics, come in a variety of different forms. In this paper, from a purely post-Newtonian (PN) analysis, we obtain a first law for binary systems of point masses moving along an exactly…
The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation, a no-relativistic particle with a time explicitly depending force, a no-relativistic particle with a constant force and time…
On the basis of the relativistic symmetry of Minkowski space, we derive a Lorentz invariant equation for a spread electron. This equation slightly differs from the Dirac equation and includes additional terms originating from the spread of…
The quantum conditions of the relativistic integrable systems whose classical motion is multiply periodic are given by considering the single-valuedness of the linear superposition of the approximate solutions $R_{i}\exp {\{iS_{i}/\hbar…
We consider a run-and-tumble particle on a finite interval $[a,b]$ with two absorbing end points. The particle has an internal velocity state that switches between three values $v,0,-v$ at exponential times, thus incorporating positive…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
The relativistic angular momentum is introduced as an extension of the non-relativistic analysis of allowed states in the phase space for a quantum particle. The paper shows the conceptual basis of the approach. An interesting feature of…
This paper investigates the problem of a relativistic Dirac half integer spin free particle tunneling through a rectangular quantum-mechanical barrier. If the energy difference between the barrier and the particle is positive, and the…
The canonical method of constrained system is discussed. The equations of motion for a free relativistic spinning particle are obtained without using gauge fixing conditions. The quantization of this model is discussed.
Quantum tunneling is a quantum phenomenon in which a microscopic object crosses through a potential barrier even if its energy cannot overcome the barrier. A general belief is that tunneling occurs only when the barrier width is comparable…
An equation of motion of the mass point with internal degrees of freedom in scalar potential $U$ depending on relative coordinates and time, velocity and accelerations is obtained both for non-relativistic and relativistic case. In…
Quantum mechanics states that a particle emitted at point (x_1,t_1) and detected at point (x_2,t_2) does not travel along a definite path between the two points. This conclusion arises essentially from the analysis of the two-slit…
According to the Maupertuis principle, the movement of a classical particle in an external potential $V(x)$ can be understood as the movement in a curved space with the metric $g_{\mu\nu}(x)=2M[V(x)-E]\delta_{\mu\nu}$. We show that the…
A charged particle which is allowed to accelerate must have relativistic behavior because it is coupled to electromagnetic radiation which propagates at the speed of light. We treat the simple steady-state situation of a charged particle…
The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. Arguably, the main theoretical problem in obtaining estimates for measurable times is the fact that…
The probable trajectory of the ground state wave function of the universe arises through a quantum tunneling by gravitational instantons. We calculate the quantum tunneling rate for a $n>2$ dimensional closed Friedmann-Robertson-Walker…