I would like to learn how is VLAN management in 802.1X port based authentication. Are there something specific in 802.1X about VLANs? Because VLAN is also part of Layer 2.
Yes, you can configure your RADIUS server to specify the VLAN for the user.
Specifying an Authorized VLAN in the RADIUS Server Database The Internet Engineering Task Force (IETF) draft standard specifies a method for communicating vendor-specific information between the device and the RADIUS server by using the vendor-specific attribute (attribute 26). Vendor-specific attributes (VSAs) allow vendors to support their own extended attributes not suitable for general use. The Cisco RADIUS implementation supports one vendor-specific option by using the format recommended in the specification.
You must assign the following vendor-specific tunnel attributes in the RADIUS server database. The RADIUS server must return these attributes to the device:  Tunnel-Type = VLAN  Tunnel-Medium-Type = 802  Tunnel-Private-Group-ID = VLAN name or VLAN ID Attribute  must contain the value “VLAN” (type 13). Attribute  must contain the value “802” (type 6). Attribute  specifies the VLAN name or VLAN ID assigned to the IEEE 802.1X-authenticated user.