The particle internal clock conjectured by de Broglie in 1924 was investigated in a channeling experiment using a beam of ∼80 MeV electrons aligned along the 110 direction of a 1 μm thick silicon crystal. Some of the electrons undergo a rosette motion, in which they interact with a single atomic row. When the electron energy is finely varied, the rate of electron transmission at 0°shows a 8% dip within 0.5% of the resonance energy, 80.874 MeV, for which the frequency of atomic collisions matches the electron's internal clock frequency. A model is presented to show the compatibility of our data with the de Broglie hypothesis.In a previous publication [1], we showed data which can be interpreted as a manifestation of the particle internal clock postulated by L. de Broglie in 1924. In the present paper we shall report again this result in the light of a phenomenological calculation that we used as a guide to design the experiment and understand its significance.At the beginning of quantum mechanics, L. de Broglie [2, 3] associated a particle of mass m 0 in its rest frame with an internal frequency ν 0 = m 0 c 2 /h and a wave

The dependence of charges accumulated on a quantum dot under an external voltage bias is studied. The charge is sensitive to the changes of number of filled levels and the number of conducting levels ͑channels͒. We clarify that there are two possible outcomes of applying a bias. ͑a͒ The number of conducting channels increases, but the number of filled levels decreases. ͑b͒ The number of filled levels increases or does not change while the number of conducting channels ͑levels͒ increases with the bias. In case ͑b͒, charges are generally expected to increase monotonically with the applied bias. We show, however, that this expectation may not materialize when the electron transmission coefficients depend on bias. Numerical evidences and a theoretical explanation of this negative differential capacitance, i.e., charges accumulated on a quantum dot decrease with applied bias, are presented. The capacitance of a quantum dot ͑QD͒ has been the subject of many studies.1,2 This is largely due to the fact that classical results derived from a macroscopic system are not applicable to a system of nanometer scale at which electron levels are discrete and the density of state is finite. So far, most studies have been on modifications of classical capacitance due to the finite density of states and electron tunneling, such as fluctuation of differential capacitance with respect to the gate voltage.3 However the nonlinear chargevoltage characteristics 4,5 has been less studied. A QD can be viewed as a potential well which is capable of accommodating electrons. Figure 1 is a schematic diagram of a QD connected to two external leads. The two leads can have different electrochemical potentials, and their difference is called the external bias on the dot. At nonzero bias, a tunneling current may pass through the QD while the electric charges on the QD can also vary with bias. There are three possible ways of applying a bias. Without losing generality, let us assume the electrochemical potential of the left lead L is no less than that of right lead R , i.e., L у R . The first way is to raise L while one keeps R unchanged as shown in Fig. 1͑b͒. The dashed line is electrochemical potentials of two leads at zero bias. The second way is to lower R , but L does not change. This is shown in Fig. 1͑c͒. The third way is to raise L and to lower R simultaneously as shown in Fig. 1͑d͒. Experimentally, all three ways described in Fig. 1 can be realized easily by controlling the gate voltage of the QD. Here we shall be interested in how the charge Q(V) on the QD change with the bias V. Intuitively, the behavior Q(V) depends on how a bias V is applied.An electron on the dot must occupy on one energy level. At zero temperature, there are three types of energy levels. One is the empty levels on which there are no electrons. They are the levels above L . The second type is the filled levels below R . The third type is conducting levels ͑chan-nels͒ which are between R and L , and are partially filled by electrons. In the case of Fig. 1͑b͒, as the exte...